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Add ed25519 (GH #764, PR #767)

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Add ed25519
This commit is contained in:
Jeffrey Walton 2018-12-24 17:17:32 -05:00 committed by GitHub
parent 2ba3c1fc73
commit d62674b561
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
29 changed files with 5092 additions and 365 deletions
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35
Filelist.txt
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@ -102,6 +102,9 @@ dlltest.vcxproj.filters
dmac.h
drbg.h
donna.h
donna_32.h
donna_64.h
donna_sse.h
donna_32.cpp
donna_64.cpp
donna_sse.cpp
@ -412,6 +415,10 @@ TestData/dlie2048.dat
TestData/dsa1024.dat
TestData/dsa1024b.dat
TestData/dsa512.dat
TestData/ed25519.dat
TestData/ed25519_ver.dat
TestData/ed25519v0.dat
TestData/ed25519v1.dat
TestData/elgc1024.dat
TestData/esig1023.dat
TestData/esig1536.dat
@ -447,10 +454,10 @@ TestData/rc6val.dat
TestData/rijndael.dat
TestData/rsa1024.dat
TestData/rsa2048.dat
TestData/rsa2048a.dat
TestData/rsa400pb.dat
TestData/rsa400pv.dat
TestData/rsa512a.dat
TestData/rsa2048a.dat
TestData/rw1024.dat
TestData/rw2048.dat
TestData/saferval.dat
@ -462,41 +469,43 @@ TestData/squareva.dat
TestData/twofishv.dat
TestData/usage.dat
TestData/x25519.dat
TestData/x25519v0.dat
TestData/x25519v1.dat
TestData/xtrdh171.dat
TestData/xtrdh342.dat
TestVectors/Readme.txt
TestVectors/aes.txt
TestVectors/all.txt
TestVectors/aria.txt
TestVectors/blake2.txt
TestVectors/blake2b.txt
TestVectors/blake2s.txt
TestVectors/aria.txt
TestVectors/camellia.txt
TestVectors/cham.txt
TestVectors/ccm.txt
TestVectors/chacha.txt
TestVectors/chacha_tls.txt
TestVectors/cham.txt
TestVectors/cmac.txt
TestVectors/dlies.txt
TestVectors/dsa.txt
TestVectors/dsa_rfc6979.txt
TestVectors/dsa_1363.txt
TestVectors/dsa_rfc6979.txt
TestVectors/eax.txt
TestVectors/esign.txt
TestVectors/gcm.txt
TestVectors/hc128.txt
TestVectors/hc256.txt
TestVectors/hkdf.txt
TestVectors/hight.txt
TestVectors/hkdf.txt
TestVectors/hmac.txt
TestVectors/kalyna.txt
TestVectors/keccak.txt
TestVectors/lea.txt
TestVectors/mars.txt
TestVectors/nr.txt
TestVectors/ocb.txt
TestVectors/panama.txt
TestVectors/rabbit.txt
TestVectors/Readme.txt
TestVectors/rsa_oaep.txt
TestVectors/rsa_pkcs1_1_5.txt
TestVectors/rsa_pss.txt
@ -505,20 +514,20 @@ TestVectors/salsa.txt
TestVectors/seal.txt
TestVectors/seed.txt
TestVectors/sha.txt
TestVectors/sha2.txt
TestVectors/sha3.txt
TestVectors/sha1_fips_180.txt
TestVectors/sha1_160_fips_180.txt
TestVectors/sha2_fips_180.txt
TestVectors/sha1_fips_180.txt
TestVectors/sha2.txt
TestVectors/sha2_224_fips_180.txt
TestVectors/sha2_256_fips_180.txt
TestVectors/sha2_384_fips_180.txt
TestVectors/sha2_512_fips_180.txt
TestVectors/sha3_fips_202.txt
TestVectors/sha2_fips_180.txt
TestVectors/sha3.txt
TestVectors/sha3_224_fips_202.txt
TestVectors/sha3_256_fips_202.txt
TestVectors/sha3_384_fips_202.txt
TestVectors/sha3_512_fips_202.txt
TestVectors/sha3_fips_202.txt
TestVectors/shacal2.txt
TestVectors/simeck.txt
TestVectors/simon.txt
@ -541,9 +550,9 @@ TestPrograms/test_arm_asimd.cxx
TestPrograms/test_arm_crc.cxx
TestPrograms/test_arm_neon.cxx
TestPrograms/test_arm_pmull.cxx
TestPrograms/test_arm_sha.cxx
TestPrograms/test_arm_sha3.cxx
TestPrograms/test_arm_sha512.cxx
TestPrograms/test_arm_sha.cxx
TestPrograms/test_arm_sm3.cxx
TestPrograms/test_arm_sm4.cxx
TestPrograms/test_cxx.cxx
@ -558,9 +567,9 @@ TestPrograms/test_ppc_sha.cxx
TestPrograms/test_ppc_vmull.cxx
TestPrograms/test_pthreads.cxx
TestPrograms/test_x86_aes.cxx
TestPrograms/test_x86_avx.cxx
TestPrograms/test_x86_avx2.cxx
TestPrograms/test_x86_avx512.cxx
TestPrograms/test_x86_avx.cxx
TestPrograms/test_x86_clmul.cxx
TestPrograms/test_x86_cpuid.cxx
TestPrograms/test_x86_sha.cxx

1
TestData/ed25519.dat Normal file
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@ -0,0 +1 @@
302E020100300506032B65700422042098C59D3F097FB23D44BA90791281B453258D691A55AF5CE4F1EE712FDF91AE6D

1
TestData/ed25519v0.dat Normal file
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@ -0,0 +1 @@
302E020100300506032B65700422042030BF776A497D7F1E0E26AC4FB03F5BE7E187DDFEFB914CD292A6FEDB7F70CE6B

1
TestData/ed25519v1.dat Normal file
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@ -0,0 +1 @@
3053020101300506032B6570042204206861FD53C7643DABDCDF4C3969CE44A156BAC261242A5AAEC140EDE510071C6CA12303210029CF90E6C1CF1ADC7105720303B2EE303412D2B682C6FEEF3D8736A286B2E27F

2
TestData/x25519.dat
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@ -1 +1 @@
3045032100D06927B313A78535F70AE1EC299D0FE86CDF0A655FC3EC7685BDA8E8D2F67174042097DD7D94CF3A33BB8374FD50C2663DD5F35F6CDFB8D7F01A8B22508DEA59195B
302E020100300506032B656E0422042030D407BB0CC97D0EC493BDB00A4A8EFA06A50D2388F5BA62947030E7D9873F49

1
TestData/x25519v0.dat Normal file
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@ -0,0 +1 @@
302E020100300506032B656E042204202818E54DE6B88EEF3E99E25042CB98E69373B222E4C1E8B3FB10AC9B26C1007B

1
TestData/x25519v1.dat Normal file
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@ -0,0 +1 @@
3053020101300506032B656E04220420A00FADD6D29BE764B851F64F7620E80B700DF65914BED31E486362281BB5D061A123032100E9AD4CC54DAA36F312D98B253854F0076E2BC26FCE5802B3AC79A5B59B3D2C4F

6
asn.h
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@ -201,6 +201,10 @@ public:
/// </pre>
void BERDecodeAndCheck(BufferedTransformation &bt) const;
bool Empty() const {
return m_values.empty();
}
const std::vector<word32>& GetValues() const {
return m_values;
}
@ -413,7 +417,7 @@ public:
virtual void DEREncodePublicKey(BufferedTransformation &bt) const =0;
};
/// \brief Encodes and decodesprivateKeyInfo
/// \brief Encodes and Decodes privateKeyInfo
class CRYPTOPP_DLL PKCS8PrivateKey : public ASN1CryptoMaterial<PrivateKey>
{
public:

19
bench3.cpp
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@ -29,10 +29,10 @@
#include "ec2n.h"
#include "asn.h"
#include "dh.h"
#include "xed25519.h"
#include "mqv.h"
#include "hmqv.h"
#include "fhmqv.h"
#include "xed25519.h"
#include "xtrcrypt.h"
#include "esign.h"
#include "pssr.h"
@ -380,6 +380,18 @@ void Benchmark3(double t, double hertz)
}
std::cout << "\n<TBODY style=\"background: yellow;\">";
{
ed25519::Signer sign(Test::GlobalRNG());
ed25519::Verifier verify(sign);
x25519 agree(Test::GlobalRNG());
BenchMarkSigning("ed25519", sign, t);
BenchMarkVerification("ed25519", sign, verify, t);
BenchMarkKeyGen("x25519", agree, t);
BenchMarkAgreement("x25519", agree, t);
}
std::cout << "\n<TBODY style=\"background: white;\">";
{
ECIES<ECP>::Decryptor cpriv(Test::GlobalRNG(), ASN1::secp256k1());
ECIES<ECP>::Encryptor cpub(cpriv);
@ -391,7 +403,6 @@ void Benchmark3(double t, double hertz)
ECGDSA<ECP, SHA1>::Verifier spub3(spriv3);
ECDH<ECP>::Domain ecdhc(ASN1::secp256k1());
ECMQV<ECP>::Domain ecmqvc(ASN1::secp256k1());
x25519 x25519ka(Test::GlobalRNG());
BenchMarkEncryption("ECIES over GF(p) 256", cpub, t);
BenchMarkDecryption("ECIES over GF(p) 256", cpriv, cpub, t);
@ -401,15 +412,13 @@ void Benchmark3(double t, double hertz)
BenchMarkVerification("ECDSA-RFC6979 over GF(p) 256", spriv2, spub2, t);
BenchMarkSigning("ECGDSA over GF(p) 256", spriv3, t);
BenchMarkVerification("ECGDSA over GF(p) 256", spriv3, spub3, t);
BenchMarkKeyGen("x25519", x25519ka, t);
BenchMarkAgreement("x25519", x25519ka, t);
BenchMarkKeyGen("ECDHC over GF(p) 256", ecdhc, t);
BenchMarkAgreement("ECDHC over GF(p) 256", ecdhc, t);
BenchMarkKeyGen("ECMQVC over GF(p) 256", ecmqvc, t);
BenchMarkAgreement("ECMQVC over GF(p) 256", ecmqvc, t);
}
std::cout << "\n<TBODY style=\"background: white;\">";
std::cout << "\n<TBODY style=\"background: yellow;\">";
{
ECIES<EC2N>::Decryptor cpriv(Test::GlobalRNG(), ASN1::sect233r1());
ECIES<EC2N>::Encryptor cpub(cpriv);

1
cryptest.vcxproj
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@ -318,6 +318,7 @@
<None Include="TestData\dsa1024.dat" />
<None Include="TestData\dsa1024b.dat" />
<None Include="TestData\dsa512.dat" />
<None Include="TestData\ed25519.dat" />
<None Include="TestData\elgc1024.dat" />
<None Include="TestData\esig1023.dat" />
<None Include="TestData\esig1536.dat" />

3
cryptest.vcxproj.filters
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@ -279,6 +279,9 @@
<None Include="TestData\dsa512.dat">
<Filter>TestData</Filter>
</None>
<None Include="TestData\ed25519.dat">
<Filter>TestData</Filter>
</None>
<None Include="TestData\elgc1024.dat">
<Filter>TestData</Filter>
</None>

3
cryptlib.vcxproj
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@ -418,6 +418,9 @@
<ClInclude Include="dmac.h" />
<ClInclude Include="drbg.h" />
<ClInclude Include="donna.h" />
<ClInclude Include="donna_32.h" />
<ClInclude Include="donna_64.h" />
<ClInclude Include="donna_sse.h" />
<ClInclude Include="dsa.h" />
<ClInclude Include="eax.h" />
<ClInclude Include="ec2n.h" />

9
cryptlib.vcxproj.filters
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@ -639,6 +639,15 @@
<ClInclude Include="donna.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="donna_32.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="donna_64.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="donna_sse.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="eax.h">
<Filter>Header Files</Filter>
</ClInclude>

92
donna.h
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@ -1,13 +1,28 @@
// donna.h - written and placed in public domain by Jeffrey Walton
// This is a integration of Andrew Moon's public domain code.
// Also see https://github.com/floodyberry/curve25519-donna.
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// Benchmarking on a modern Core i5-6400 shows SSE2 on Linux is not
// profitable. You can enable it with CRYPTOPP_CURVE25519_SSE2.
// The curve25519 and ed25519 source files multiplex different repos and
// architectures using namespaces. The repos are Andrew Moon's
// curve25519-donna and ed25519-donna. The architectures are 32-bit, 64-bit
// and SSE. For example, 32-bit x25519 uses symbols from Donna::X25519 and
// Donna::Arch32.
// If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
// https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658
/// \file donna.h
/// \details Functions for curve25519 and ed25519 operations
/// \details This header provides the entry points into Andrew Moon's
/// curve25519 and ed25519 curve functions. The Crypto++ classes x25519
/// and ed25519 use the functions. The functions are in the <tt>Donna</tt>
/// namespace and are curve25519_mult(), ed25519_publickey(),
/// ed25519_sign() and ed25519_sign_open().
/// \details At the moment the hash function for signing is fixed at
/// SHA512.
#ifndef CRYPTOPP_DONNA_H
#define CRYPTOPP_DONNA_H
@ -17,25 +32,68 @@
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
/// \brief Generate public key
//***************************** curve25519 *****************************//
/// \brief Generate a public key
/// \param publicKey byte array for the public key
/// \param secretKey byte array with the private key
/// \returns 0 on success, non-0 otherwise
/// \details This curve25519() overload generates a public key from an existing
/// secret key. Internally curve25519() performs a scalar multiplication
/// using the base point and writes the result to <tt>pubkey</tt>.
int curve25519(byte publicKey[32], const byte secretKey[32]);
/// \details curve25519_mult() generates a public key from an existing
/// secret key. Internally curve25519_mult() performs a scalar
/// multiplication using the base point and writes the result to
/// <tt>pubkey</tt>.
int curve25519_mult(byte publicKey[32], const byte secretKey[32]);
/// \brief Generate shared key
/// \brief Generate a shared key
/// \param sharedKey byte array for the shared secret
/// \param secretKey byte array with the private key
/// \param othersKey byte array with the peer's public key
/// \returns 0 on success, non-0 otherwise
/// \details This curve25519() overload generates a shared key from an existing
/// a secret key and the other party's public key. Internally curve25519()
/// performs a scalar multiplication using the two keys and writes the result
/// to <tt>sharedKey</tt>.
int curve25519(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32]);
/// \details curve25519_mult() generates a shared key from an existing
/// secret key and the other party's public key. Internally
/// curve25519_mult() performs a scalar multiplication using the two keys
/// and writes the result to <tt>sharedKey</tt>.
int curve25519_mult(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32]);
//******************************* ed25519 *******************************//
/// \brief Creates a public key from a secret key
/// \param publicKey byte array for the public key
/// \param secretKey byte array with the private key
/// \returns 0 on success, non-0 otherwise
/// \details ed25519_publickey() generates a public key from a secret key.
/// Internally ed25519_publickey() performs a scalar multiplication
/// using the secret key and then writes the result to <tt>publicKey</tt>.
int ed25519_publickey(byte publicKey[32], const byte secretKey[32]);
/// \brief Creates a signature on a message
/// \param message byte array with the message
/// \param messageLength size of the message, in bytes
/// \param publicKey byte array with the public key
/// \param secretKey byte array with the private key
/// \param signature byte array for the signature
/// \returns 0 on success, non-0 otherwise
/// \details ed25519_sign() generates a signature on a message using
/// the public and private keys. The various buffers can be exact
/// sizes, and do not require extra space like when using the
/// NaCl library functions.
/// \details At the moment the hash function for signing is fixed at
/// SHA512.
int ed25519_sign(const byte* message, size_t messageLength, const byte secretKey[32], const byte publicKey[32], byte signature[64]);
/// \brief Verifies a signature on a message
/// \param message byte array with the message
/// \param messageLength size of the message, in bytes
/// \param publicKey byte array with the public key
/// \param signature byte array with the signature
/// \returns 0 on success, non-0 otherwise
/// \details ed25519_sign_open() verifies a signature on a message using
/// the public. The various buffers can be exact sizes, and do not
/// require extra space like when using the NaCl library functions.
/// \details At the moment the hash function for signing is fixed at
/// SHA512.
int
ed25519_sign_open(const byte *message, size_t messageLength, const byte publicKey[32], const byte signature[64]);
//****************************** Internal ******************************//
@ -62,7 +120,7 @@ int curve25519(byte sharedKey[32], const byte secretKey[32], const byte othersKe
// * Moon, SSE2: 0.061
// * Moon, native: 0.045
//
// However, a modern 64-bit Core i5-3200 @2.3 GHz shows SSE2 is profitable
// However, a modern 64-bit Core i5-3200 @2.5 GHz shows SSE2 is profitable
// for MS compilers. Here are the numbers in milliseconds/operation:
//
// * x86, no SSE2, 0.294
@ -75,7 +133,7 @@ int curve25519(byte sharedKey[32], const byte secretKey[32], const byte othersKe
#endif
#if (CRYPTOPP_CURVE25519_SSE2)
extern int curve25519_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32]);
extern int curve25519_mult_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32]);
#endif
NAMESPACE_END // Donna

1469
donna_32.cpp
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File diff suppressed because it is too large Load Diff

409
donna_32.h Normal file
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@ -0,0 +1,409 @@
// donna_32.h - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// This source file multiplexes two different repos using namespaces. This
// was a little easier from a project management standpoint. We only need
// two files per architecture at the expense of namespaces and bloat.
#ifndef CRYPTOPP_DONNA_32_H
#define CRYPTOPP_DONNA_32_H
#include "config.h"
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(Arch32)
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::word64;
// ******************** x25519 Agreement ************************* //
#define ALIGN(n) CRYPTOPP_ALIGN_DATA(n)
#define mul32x32_64(a,b) (((word64)(a))*(b))
typedef word32 bignum25519[10];
const byte basePoint[32] = {9};
const word32 reduce_mask_25 = (1 << 25) - 1;
const word32 reduce_mask_26 = (1 << 26) - 1;
// ****************** ed25519 Signatures *********************** //
typedef byte hash_512bits[64];
const int bignum256modm_bits_per_limb = 30;
const int bignum256modm_limb_size = 9;
typedef word32 bignum256modm_element_t;
typedef bignum256modm_element_t bignum256modm[9];
struct ge25519 {
bignum25519 x, y, z, t;
};
struct ge25519_p1p1 {
bignum25519 x, y, z, t;
};
struct ge25519_niels {
bignum25519 ysubx, xaddy, t2d;
};
struct ge25519_pniels {
bignum25519 ysubx, xaddy, z, t2d;
};
#define S1_SWINDOWSIZE 5
#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
#define S2_SWINDOWSIZE 7
#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
// *************** ed25519-donna-32bit-tables.h *************** //
ALIGN(16) const ge25519 ge25519_basepoint = {
{0x0325d51a,0x018b5823,0x00f6592a,0x0104a92d,0x01a4b31d,0x01d6dc5c,0x027118fe,0x007fd814,0x013cd6e5,0x0085a4db},
{0x02666658,0x01999999,0x00cccccc,0x01333333,0x01999999,0x00666666,0x03333333,0x00cccccc,0x02666666,0x01999999},
{0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000},
{0x01b7dda3,0x01a2ace9,0x025eadbb,0x0003ba8a,0x0083c27e,0x00abe37d,0x01274732,0x00ccacdd,0x00fd78b7,0x019e1d7c}
};
ALIGN(16) const bignum25519 ge25519_ecd = {
0x035978a3,0x00d37284,0x03156ebd,0x006a0a0e,0x0001c029,0x0179e898,0x03a03cbb,0x01ce7198,0x02e2b6ff,0x01480db3
};
ALIGN(16) const bignum25519 ge25519_ec2d = {
0x02b2f159,0x01a6e509,0x022add7a,0x00d4141d,0x00038052,0x00f3d130,0x03407977,0x019ce331,0x01c56dff,0x00901b67
};
ALIGN(16) const bignum25519 ge25519_sqrtneg1 = {
0x020ea0b0,0x0186c9d2,0x008f189d,0x0035697f,0x00bd0c60,0x01fbd7a7,0x02804c9e,0x01e16569,0x0004fc1d,0x00ae0c92
};
ALIGN(16) const ge25519_niels ge25519_niels_sliding_multiples[32] = {
{{0x0340913e,0x000e4175,0x03d673a2,0x002e8a05,0x03f4e67c,0x008f8a09,0x00c21a34,0x004cf4b8,0x01298f81,0x0113f4be},{0x018c3b85,0x0124f1bd,0x01c325f7,0x0037dc60,0x033e4cb7,0x003d42c2,0x01a44c32,0x014ca4e1,0x03a33d4b,0x001f3e74},{0x037aaa68,0x00448161,0x0093d579,0x011e6556,0x009b67a0,0x0143598c,0x01bee5ee,0x00b50b43,0x0289f0c6,0x01bc45ed}},
{{0x00fcd265,0x0047fa29,0x034faacc,0x01ef2e0d,0x00ef4d4f,0x014bd6bd,0x00f98d10,0x014c5026,0x007555bd,0x00aae456},{0x00ee9730,0x016c2a13,0x017155e4,0x01874432,0x00096a10,0x01016732,0x01a8014f,0x011e9823,0x01b9a80f,0x01e85938},{0x01d0d889,0x01a4cfc3,0x034c4295,0x0110e1ae,0x0162508c,0x00f2db4c,0x0072a2c6,0x0098da2e,0x02f12b9b,0x0168a09a}},
{{0x0047d6ba,0x0060b0e9,0x0136eff2,0x008a5939,0x03540053,0x0064a087,0x02788e5c,0x00be7c67,0x033eb1b5,0x005529f9},{0x00a5bb33,0x00af1102,0x01a05442,0x001e3af7,0x02354123,0x00bfec44,0x01f5862d,0x00dd7ba3,0x03146e20,0x00a51733},{0x012a8285,0x00f6fc60,0x023f9797,0x003e85ee,0x009c3820,0x01bda72d,0x01b3858d,0x00d35683,0x0296b3bb,0x010eaaf9}},
{{0x023221b1,0x01cb26aa,0x0074f74d,0x0099ddd1,0x01b28085,0x00192c3a,0x013b27c9,0x00fc13bd,0x01d2e531,0x0075bb75},{0x004ea3bf,0x00973425,0x001a4d63,0x01d59cee,0x01d1c0d4,0x00542e49,0x01294114,0x004fce36,0x029283c9,0x01186fa9},{0x01b8b3a2,0x00db7200,0x00935e30,0x003829f5,0x02cc0d7d,0x0077adf3,0x0220dd2c,0x0014ea53,0x01c6a0f9,0x01ea7eec}},
{{0x039d8064,0x01885f80,0x00337e6d,0x01b7a902,0x02628206,0x015eb044,0x01e30473,0x0191f2d9,0x011fadc9,0x01270169},{0x02a8632f,0x0199e2a9,0x00d8b365,0x017a8de2,0x02994279,0x0086f5b5,0x0119e4e3,0x01eb39d6,0x0338add7,0x00d2e7b4},{0x0045af1b,0x013a2fe4,0x0245e0d6,0x014538ce,0x038bfe0f,0x01d4cf16,0x037e14c9,0x0160d55e,0x0021b008,0x01cf05c8}},
{{0x01864348,0x01d6c092,0x0070262b,0x014bb844,0x00fb5acd,0x008deb95,0x003aaab5,0x00eff474,0x00029d5c,0x0062ad66},{0x02802ade,0x01c02122,0x01c4e5f7,0x00781181,0x039767fb,0x01703406,0x0342388b,0x01f5e227,0x022546d8,0x0109d6ab},{0x016089e9,0x00cb317f,0x00949b05,0x01099417,0x000c7ad2,0x011a8622,0x0088ccda,0x01290886,0x022b53df,0x00f71954}},
{{0x027fbf93,0x01c04ecc,0x01ed6a0d,0x004cdbbb,0x02bbf3af,0x00ad5968,0x01591955,0x0094f3a2,0x02d17602,0x00099e20},{0x02007f6d,0x003088a8,0x03db77ee,0x00d5ade6,0x02fe12ce,0x0107ba07,0x0107097d,0x00482a6f,0x02ec346f,0x008d3f5f},{0x032ea378,0x0028465c,0x028e2a6c,0x018efc6e,0x0090df9a,0x01a7e533,0x039bfc48,0x010c745d,0x03daa097,0x0125ee9b}},
{{0x028ccf0b,0x00f36191,0x021ac081,0x012154c8,0x034e0a6e,0x01b25192,0x00180403,0x01d7eea1,0x00218d05,0x010ed735},{0x03cfeaa0,0x01b300c4,0x008da499,0x0068c4e1,0x0219230a,0x01f2d4d0,0x02defd60,0x00e565b7,0x017f12de,0x018788a4},{0x03d0b516,0x009d8be6,0x03ddcbb3,0x0071b9fe,0x03ace2bd,0x01d64270,0x032d3ec9,0x01084065,0x0210ae4d,0x01447584}},
{{0x0020de87,0x00e19211,0x01b68102,0x00b5ac97,0x022873c0,0x01942d25,0x01271394,0x0102073f,0x02fe2482,0x01c69ff9},{0x010e9d81,0x019dbbe5,0x0089f258,0x006e06b8,0x02951883,0x018f1248,0x019b3237,0x00bc7553,0x024ddb85,0x01b4c964},{0x01c8c854,0x0060ae29,0x01406d8e,0x01cff2f9,0x00cff451,0x01778d0c,0x03ac8c41,0x01552e59,0x036559ee,0x011d1b12}},
{{0x00741147,0x0151b219,0x01092690,0x00e877e6,0x01f4d6bb,0x0072a332,0x01cd3b03,0x00dadff2,0x0097db5e,0x0086598d},{0x01c69a2b,0x01decf1b,0x02c2fa6e,0x013b7c4f,0x037beac8,0x013a16b5,0x028e7bda,0x01f6e8ac,0x01e34fe9,0x01726947},{0x01f10e67,0x003c73de,0x022b7ea2,0x010f32c2,0x03ff776a,0x00142277,0x01d38b88,0x00776138,0x03c60822,0x01201140}},
{{0x0236d175,0x0008748e,0x03c6476d,0x013f4cdc,0x02eed02a,0x00838a47,0x032e7210,0x018bcbb3,0x00858de4,0x01dc7826},{0x00a37fc7,0x0127b40b,0x01957884,0x011d30ad,0x02816683,0x016e0e23,0x00b76be4,0x012db115,0x02516506,0x0154ce62},{0x00451edf,0x00bd749e,0x03997342,0x01cc2c4c,0x00eb6975,0x01a59508,0x03a516cf,0x00c228ef,0x0168ff5a,0x01697b47}},
{{0x00527359,0x01783156,0x03afd75c,0x00ce56dc,0x00e4b970,0x001cabe9,0x029e0f6d,0x0188850c,0x0135fefd,0x00066d80},{0x02150e83,0x01448abf,0x02bb0232,0x012bf259,0x033c8268,0x00711e20,0x03fc148f,0x005e0e70,0x017d8bf9,0x0112b2e2},{0x02134b83,0x001a0517,0x0182c3cc,0x00792182,0x0313d799,0x001a3ed7,0x0344547e,0x01f24a0d,0x03de6ad2,0x00543127}},
{{0x00dca868,0x00618f27,0x015a1709,0x00ddc38a,0x0320fd13,0x0036168d,0x0371ab06,0x01783fc7,0x0391e05f,0x01e29b5d},{0x01471138,0x00fca542,0x00ca31cf,0x01ca7bad,0x0175bfbc,0x01a708ad,0x03bce212,0x01244215,0x0075bb99,0x01acad68},{0x03a0b976,0x01dc12d1,0x011aab17,0x00aba0ba,0x029806cd,0x0142f590,0x018fd8ea,0x01a01545,0x03c4ad55,0x01c971ff}},
{{0x00d098c0,0x000afdc7,0x006cd230,0x01276af3,0x03f905b2,0x0102994c,0x002eb8a4,0x015cfbeb,0x025f855f,0x01335518},{0x01cf99b2,0x0099c574,0x01a69c88,0x00881510,0x01cd4b54,0x0112109f,0x008abdc5,0x0074647a,0x0277cb1f,0x01e53324},{0x02ac5053,0x01b109b0,0x024b095e,0x016997b3,0x02f26bb6,0x00311021,0x00197885,0x01d0a55a,0x03b6fcc8,0x01c020d5}},
{{0x02584a34,0x00e7eee0,0x03257a03,0x011e95a3,0x011ead91,0x00536202,0x00b1ce24,0x008516c6,0x03669d6d,0x004ea4a8},{0x00773f01,0x0019c9ce,0x019f6171,0x01d4afde,0x02e33323,0x01ad29b6,0x02ead1dc,0x01ed51a5,0x01851ad0,0x001bbdfa},{0x00577de5,0x00ddc730,0x038b9952,0x00f281ae,0x01d50390,0x0002e071,0x000780ec,0x010d448d,0x01f8a2af,0x00f0a5b7}},
{{0x031f2541,0x00d34bae,0x0323ff9d,0x003a056d,0x02e25443,0x00a1ad05,0x00d1bee8,0x002f7f8e,0x03007477,0x002a24b1},{0x0114a713,0x01457e76,0x032255d5,0x01cc647f,0x02a4bdef,0x0153d730,0x00118bcf,0x00f755ff,0x013490c7,0x01ea674e},{0x02bda3e8,0x00bb490d,0x00f291ea,0x000abf40,0x01dea321,0x002f9ce0,0x00b2b193,0x00fa54b5,0x0128302f,0x00a19d8b}},
{{0x022ef5bd,0x01638af3,0x038c6f8a,0x01a33a3d,0x039261b2,0x01bb89b8,0x010bcf9d,0x00cf42a9,0x023d6f17,0x01da1bca},{0x00e35b25,0x000d824f,0x0152e9cf,0x00ed935d,0x020b8460,0x01c7b83f,0x00c969e5,0x01a74198,0x0046a9d9,0x00cbc768},{0x01597c6a,0x0144a99b,0x00a57551,0x0018269c,0x023c464c,0x0009b022,0x00ee39e1,0x0114c7f2,0x038a9ad2,0x01584c17}},
{{0x03b0c0d5,0x00b30a39,0x038a6ce4,0x01ded83a,0x01c277a6,0x01010a61,0x0346d3eb,0x018d995e,0x02f2c57c,0x000c286b},{0x0092aed1,0x0125e37b,0x027ca201,0x001a6b6b,0x03290f55,0x0047ba48,0x018d916c,0x01a59062,0x013e35d4,0x0002abb1},{0x003ad2aa,0x007ddcc0,0x00c10f76,0x0001590b,0x002cfca6,0x000ed23e,0x00ee4329,0x00900f04,0x01c24065,0x0082fa70}},
{{0x02025e60,0x003912b8,0x0327041c,0x017e5ee5,0x02c0ecec,0x015a0d1c,0x02b1ce7c,0x0062220b,0x0145067e,0x01a5d931},{0x009673a6,0x00e1f609,0x00927c2a,0x016faa37,0x01650ef0,0x016f63b5,0x03cd40e1,0x003bc38f,0x0361f0ac,0x01d42acc},{0x02f81037,0x008ca0e8,0x017e23d1,0x011debfe,0x01bcbb68,0x002e2563,0x03e8add6,0x000816e5,0x03fb7075,0x0153e5ac}},
{{0x02b11ecd,0x016bf185,0x008f22ef,0x00e7d2bb,0x0225d92e,0x00ece785,0x00508873,0x017e16f5,0x01fbe85d,0x01e39a0e},{0x01669279,0x017c810a,0x024941f5,0x0023ebeb,0x00eb7688,0x005760f1,0x02ca4146,0x0073cde7,0x0052bb75,0x00f5ffa7},{0x03b8856b,0x00cb7dcd,0x02f14e06,0x001820d0,0x01d74175,0x00e59e22,0x03fba550,0x00484641,0x03350088,0x01c3c9a3}},
{{0x00dcf355,0x0104481c,0x0022e464,0x01f73fe7,0x00e03325,0x0152b698,0x02ef769a,0x00973663,0x00039b8c,0x0101395b},{0x01805f47,0x019160ec,0x03832cd0,0x008b06eb,0x03d4d717,0x004cb006,0x03a75b8f,0x013b3d30,0x01cfad88,0x01f034d1},{0x0078338a,0x01c7d2e3,0x02bc2b23,0x018b3f05,0x0280d9aa,0x005f3d44,0x0220a95a,0x00eeeb97,0x0362aaec,0x00835d51}},
{{0x01b9f543,0x013fac4d,0x02ad93ae,0x018ef464,0x0212cdf7,0x01138ba9,0x011583ab,0x019c3d26,0x028790b4,0x00e2e2b6},{0x033bb758,0x01f0dbf1,0x03734bd1,0x0129b1e5,0x02b3950e,0x003bc922,0x01a53ec8,0x018c5532,0x006f3cee,0x00ae3c79},{0x0351f95d,0x0012a737,0x03d596b8,0x017658fe,0x00ace54a,0x008b66da,0x0036c599,0x012a63a2,0x032ceba1,0x00126bac}},
{{0x03dcfe7e,0x019f4f18,0x01c81aee,0x0044bc2b,0x00827165,0x014f7c13,0x03b430f0,0x00bf96cc,0x020c8d62,0x01471997},{0x01fc7931,0x001f42dd,0x00ba754a,0x005bd339,0x003fbe49,0x016b3930,0x012a159c,0x009f83b0,0x03530f67,0x01e57b85},{0x02ecbd81,0x0096c294,0x01fce4a9,0x017701a5,0x0175047d,0x00ee4a31,0x012686e5,0x008efcd4,0x0349dc54,0x01b3466f}},
{{0x02179ca3,0x01d86414,0x03f0afd0,0x00305964,0x015c7428,0x0099711e,0x015d5442,0x00c71014,0x01b40b2e,0x01d483cf},{0x01afc386,0x01984859,0x036203ff,0x0045c6a8,0x0020a8aa,0x00990baa,0x03313f10,0x007ceede,0x027429e4,0x017806ce},{0x039357a1,0x0142f8f4,0x0294a7b6,0x00eaccf4,0x0259edb3,0x01311e6e,0x004d326f,0x0130c346,0x01ccef3c,0x01c424b2}},
{{0x0364918c,0x00148fc0,0x01638a7b,0x01a1fd5b,0x028ad013,0x0081e5a4,0x01a54f33,0x0174e101,0x003d0257,0x003a856c},{0x00051dcf,0x00f62b1d,0x0143d0ad,0x0042adbd,0x000fda90,0x01743ceb,0x0173e5e4,0x017bc749,0x03b7137a,0x0105ce96},{0x00f9218a,0x015b8c7c,0x00e102f8,0x0158d7e2,0x0169a5b8,0x00b2f176,0x018b347a,0x014cfef2,0x0214a4e3,0x017f1595}},
{{0x006d7ae5,0x0195c371,0x0391e26d,0x0062a7c6,0x003f42ab,0x010dad86,0x024f8198,0x01542b2a,0x0014c454,0x0189c471},{0x0390988e,0x00b8799d,0x02e44912,0x0078e2e6,0x00075654,0x01923eed,0x0040cd72,0x00a37c76,0x0009d466,0x00c8531d},{0x02651770,0x00609d01,0x0286c265,0x0134513c,0x00ee9281,0x005d223c,0x035c760c,0x00679b36,0x0073ecb8,0x016faa50}},
{{0x02c89be4,0x016fc244,0x02f38c83,0x018beb72,0x02b3ce2c,0x0097b065,0x034f017b,0x01dd957f,0x00148f61,0x00eab357},{0x0343d2f8,0x003398fc,0x011e368e,0x00782a1f,0x00019eea,0x00117b6f,0x0128d0d1,0x01a5e6bb,0x01944f1b,0x012b41e1},{0x03318301,0x018ecd30,0x0104d0b1,0x0038398b,0x03726701,0x019da88c,0x002d9769,0x00a7a681,0x031d9028,0x00ebfc32}},
{{0x0220405e,0x0171face,0x02d930f8,0x017f6d6a,0x023b8c47,0x0129d5f9,0x02972456,0x00a3a524,0x006f4cd2,0x004439fa},{0x00c53505,0x0190c2fd,0x00507244,0x009930f9,0x01a39270,0x01d327c6,0x0399bc47,0x01cfe13d,0x0332bd99,0x00b33e7d},{0x0203f5e4,0x003627b5,0x00018af8,0x01478581,0x004a2218,0x002e3bb7,0x039384d0,0x0146ea62,0x020b9693,0x0017155f}},
{{0x03c97e6f,0x00738c47,0x03b5db1f,0x01808fcf,0x01e8fc98,0x01ed25dd,0x01bf5045,0x00eb5c2b,0x0178fe98,0x01b85530},{0x01c20eb0,0x01aeec22,0x030b9eee,0x01b7d07e,0x0187e16f,0x014421fb,0x009fa731,0x0040b6d7,0x00841861,0x00a27fbc},{0x02d69abf,0x0058cdbf,0x0129f9ec,0x013c19ae,0x026c5b93,0x013a7fe7,0x004bb2ba,0x0063226f,0x002a95ca,0x01abefd9}},
{{0x02f5d2c1,0x00378318,0x03734fb5,0x01258073,0x0263f0f6,0x01ad70e0,0x01b56d06,0x01188fbd,0x011b9503,0x0036d2e1},{0x0113a8cc,0x01541c3e,0x02ac2bbc,0x01d95867,0x01f47459,0x00ead489,0x00ab5b48,0x01db3b45,0x00edb801,0x004b024f},{0x00b8190f,0x011fe4c2,0x00621f82,0x010508d7,0x001a5a76,0x00c7d7fd,0x03aab96d,0x019cd9dc,0x019c6635,0x00ceaa1e}},
{{0x01085cf2,0x01fd47af,0x03e3f5e1,0x004b3e99,0x01e3d46a,0x0060033c,0x015ff0a8,0x0150cdd8,0x029e8e21,0x008cf1bc},{0x00156cb1,0x003d623f,0x01a4f069,0x00d8d053,0x01b68aea,0x01ca5ab6,0x0316ae43,0x0134dc44,0x001c8d58,0x0084b343},{0x0318c781,0x0135441f,0x03a51a5e,0x019293f4,0x0048bb37,0x013d3341,0x0143151e,0x019c74e1,0x00911914,0x0076ddde}},
{{0x006bc26f,0x00d48e5f,0x00227bbe,0x00629ea8,0x01ea5f8b,0x0179a330,0x027a1d5f,0x01bf8f8e,0x02d26e2a,0x00c6b65e},{0x01701ab6,0x0051da77,0x01b4b667,0x00a0ce7c,0x038ae37b,0x012ac852,0x03a0b0fe,0x0097c2bb,0x00a017d2,0x01eb8b2a},{0x0120b962,0x0005fb42,0x0353b6fd,0x0061f8ce,0x007a1463,0x01560a64,0x00e0a792,0x01907c92,0x013a6622,0x007b47f1}}
};
// *************** modm-donna-32bit.h *************** //
const bignum256modm modm_m = {
0x1cf5d3ed, 0x20498c69, 0x2f79cd65, 0x37be77a8,
0x00000014, 0x00000000, 0x00000000, 0x00000000,
0x00001000
};
const bignum256modm modm_mu = {
0x0a2c131b, 0x3673968c, 0x06329a7e, 0x01885742,
0x3fffeb21, 0x3fffffff, 0x3fffffff, 0x3fffffff,
0x000fffff
};
/* multiples of p */
const word32 twoP0 = 0x07ffffda;
const word32 twoP13579 = 0x03fffffe;
const word32 twoP2468 = 0x07fffffe;
const word32 fourP0 = 0x0fffffb4;
const word32 fourP13579 = 0x07fffffc;
const word32 fourP2468 = 0x0ffffffc;
// *************** ed25519-donna-basepoint-table.h *************** //
/* multiples of the base point in packed {ysubx, xaddy, t2d} form */
ALIGN(16) const byte ge25519_niels_base_multiples[256][96] = {
{0x3e,0x91,0x40,0xd7,0x05,0x39,0x10,0x9d,0xb3,0xbe,0x40,0xd1,0x05,0x9f,0x39,0xfd,0x09,0x8a,0x8f,0x68,0x34,0x84,0xc1,0xa5,0x67,0x12,0xf8,0x98,0x92,0x2f,0xfd,0x44,0x85,0x3b,0x8c,0xf5,0xc6,0x93,0xbc,0x2f,0x19,0x0e,0x8c,0xfb,0xc6,0x2d,0x93,0xcf,0xc2,0x42,0x3d,0x64,0x98,0x48,0x0b,0x27,0x65,0xba,0xd4,0x33,0x3a,0x9d,0xcf,0x07,0x59,0xbb,0x6f,0x4b,0x67,0x15,0xbd,0xdb,0xea,0xa5,0xa2,0xee,0x00,0x3f,0xe1,0x41,0xfa,0xc6,0x57,0xc9,0x1c,0x9d,0xd4,0xcd,0xca,0xec,0x16,0xaf,0x1f,0xbe,0x0e,0x4f},
{0xa8,0xd5,0xb4,0x42,0x60,0xa5,0x99,0x8a,0xf6,0xac,0x60,0x4e,0x0c,0x81,0x2b,0x8f,0xaa,0x37,0x6e,0xb1,0x6b,0x23,0x9e,0xe0,0x55,0x25,0xc9,0x69,0xa6,0x95,0xb5,0x6b,0xd7,0x71,0x3c,0x93,0xfc,0xe7,0x24,0x92,0xb5,0xf5,0x0f,0x7a,0x96,0x9d,0x46,0x9f,0x02,0x07,0xd6,0xe1,0x65,0x9a,0xa6,0x5a,0x2e,0x2e,0x7d,0xa8,0x3f,0x06,0x0c,0x59,0x02,0x68,0xd3,0xda,0xaa,0x7e,0x34,0x6e,0x05,0x48,0xee,0x83,0x93,0x59,0xf3,0xba,0x26,0x68,0x07,0xe6,0x10,0xbe,0xca,0x3b,0xb8,0xd1,0x5e,0x16,0x0a,0x4f,0x31,0x49},
{0x65,0xd2,0xfc,0xa4,0xe8,0x1f,0x61,0x56,0x7d,0xba,0xc1,0xe5,0xfd,0x53,0xd3,0x3b,0xbd,0xd6,0x4b,0x21,0x1a,0xf3,0x31,0x81,0x62,0xda,0x5b,0x55,0x87,0x15,0xb9,0x2a,0x30,0x97,0xee,0x4c,0xa8,0xb0,0x25,0xaf,0x8a,0x4b,0x86,0xe8,0x30,0x84,0x5a,0x02,0x32,0x67,0x01,0x9f,0x02,0x50,0x1b,0xc1,0xf4,0xf8,0x80,0x9a,0x1b,0x4e,0x16,0x7a,0x34,0x48,0x67,0xf1,0xf4,0x11,0xf2,0x9b,0x95,0xf8,0x2d,0xf6,0x17,0x6b,0x4e,0xb8,0x4e,0x2a,0x72,0x5b,0x07,0x6f,0xde,0xd7,0x21,0x2a,0xbb,0x63,0xb9,0x04,0x9a,0x54},
{0xbf,0x18,0x68,0x05,0x0a,0x05,0xfe,0x95,0xa9,0xfa,0x60,0x56,0x71,0x89,0x7e,0x32,0x73,0x50,0xa0,0x06,0xcd,0xe3,0xe8,0xc3,0x9a,0xa4,0x45,0x74,0x4c,0x3f,0x93,0x27,0x9f,0x09,0xfc,0x8e,0xb9,0x51,0x73,0x28,0x38,0x25,0xfd,0x7d,0xf4,0xc6,0x65,0x67,0x65,0x92,0x0a,0xfb,0x3d,0x8d,0x34,0xca,0x27,0x87,0xe5,0x21,0x03,0x91,0x0e,0x68,0xb0,0x26,0x14,0xe5,0xec,0x45,0x1e,0xbf,0x94,0x0f,0xba,0x6d,0x3d,0xc6,0x2b,0xe3,0xc0,0x52,0xf8,0x8c,0xd5,0x74,0x29,0xe4,0x18,0x4c,0xe6,0xb0,0xb1,0x79,0xf0,0x44},
{0xba,0xd6,0x47,0xa4,0xc3,0x82,0x91,0x7f,0xb7,0x29,0x27,0x4b,0xd1,0x14,0x00,0xd5,0x87,0xa0,0x64,0xb8,0x1c,0xf1,0x3c,0xe3,0xf3,0x55,0x1b,0xeb,0x73,0x7e,0x4a,0x15,0x33,0xbb,0xa5,0x08,0x44,0xbc,0x12,0xa2,0x02,0xed,0x5e,0xc7,0xc3,0x48,0x50,0x8d,0x44,0xec,0xbf,0x5a,0x0c,0xeb,0x1b,0xdd,0xeb,0x06,0xe2,0x46,0xf1,0xcc,0x45,0x29,0xb3,0x03,0xd0,0xe7,0x79,0xa1,0x32,0xc8,0x7e,0x4d,0x12,0x00,0x0a,0x9d,0x72,0x5f,0xf3,0x8f,0x6d,0x0e,0xa1,0xd4,0xc1,0x62,0x98,0x7a,0xb2,0x38,0x59,0xac,0xb8,0x68},
{0xa4,0x8c,0x7d,0x7b,0xb6,0x06,0x98,0x49,0x39,0x27,0xd2,0x27,0x84,0xe2,0x5b,0x57,0xb9,0x53,0x45,0x20,0xe7,0x5c,0x08,0xbb,0x84,0x78,0x41,0xae,0x41,0x4c,0xb6,0x38,0x31,0x71,0x15,0x77,0xeb,0xee,0x0c,0x3a,0x88,0xaf,0xc8,0x00,0x89,0x15,0x27,0x9b,0x36,0xa7,0x59,0xda,0x68,0xb6,0x65,0x80,0xbd,0x38,0xcc,0xa2,0xb6,0x7b,0xe5,0x51,0xa4,0xe3,0x9d,0x68,0x91,0xad,0x9d,0x8f,0x37,0x91,0xfb,0xf8,0x28,0x24,0x5f,0x17,0x88,0xb9,0xcf,0x9f,0x32,0xb5,0x0a,0x05,0x9f,0xc0,0x54,0x13,0xa2,0xdf,0x65,0x78},
{0xb1,0x21,0x32,0xaa,0x9a,0x2c,0x6f,0xba,0xa7,0x23,0xba,0x3b,0x53,0x21,0xa0,0x6c,0x3a,0x2c,0x19,0x92,0x4f,0x76,0xea,0x9d,0xe0,0x17,0x53,0x2e,0x5d,0xdd,0x6e,0x1d,0xbf,0xa3,0x4e,0x94,0xd0,0x5c,0x1a,0x6b,0xd2,0xc0,0x9d,0xb3,0x3a,0x35,0x70,0x74,0x49,0x2e,0x54,0x28,0x82,0x52,0xb2,0x71,0x7e,0x92,0x3c,0x28,0x69,0xea,0x1b,0x46,0x36,0xda,0x0f,0xab,0xac,0x8a,0x7a,0x21,0xc8,0x49,0x35,0x3d,0x54,0xc6,0x28,0xa5,0x68,0x75,0xab,0x13,0x8b,0x5b,0xd0,0x37,0x37,0xbc,0x2c,0x3a,0x62,0xef,0x3c,0x23},
{0xd9,0x34,0x92,0xf3,0xed,0x5d,0xa7,0xe2,0xf9,0x58,0xb5,0xe1,0x80,0x76,0x3d,0x96,0xfb,0x23,0x3c,0x6e,0xac,0x41,0x27,0x2c,0xc3,0x01,0x0e,0x32,0xa1,0x24,0x90,0x3a,0x8f,0x3e,0xdd,0x04,0x66,0x59,0xb7,0x59,0x2c,0x70,0x88,0xe2,0x77,0x03,0xb3,0x6c,0x23,0xc3,0xd9,0x5e,0x66,0x9c,0x33,0xb1,0x2f,0xe5,0xbc,0x61,0x60,0xe7,0x15,0x09,0x7e,0xa3,0x34,0xa8,0x35,0xe8,0x7d,0xdf,0xea,0x57,0x98,0x68,0xda,0x9c,0xe1,0x8b,0x26,0xb3,0x67,0x71,0x36,0x85,0x11,0x2c,0xc2,0xd5,0xef,0xdb,0xd9,0xb3,0x9e,0x58},
{0x5e,0x51,0xaa,0x49,0x54,0x63,0x5b,0xed,0x3a,0x82,0xc6,0x0b,0x9f,0xc4,0x65,0xa8,0xc4,0xd1,0x42,0x5b,0xe9,0x1f,0x0c,0x85,0xb9,0x15,0xd3,0x03,0x6f,0x6d,0xd7,0x30,0x1d,0x9c,0x2f,0x63,0x0e,0xdd,0xcc,0x2e,0x15,0x31,0x89,0x76,0x96,0xb6,0xd0,0x51,0x58,0x7a,0x63,0xa8,0x6b,0xb7,0xdf,0x52,0x39,0xef,0x0e,0xa0,0x49,0x7d,0xd3,0x6d,0xc7,0xe4,0x06,0x21,0x17,0x44,0x44,0x6c,0x69,0x7f,0x8d,0x92,0x80,0xd6,0x53,0xfb,0x26,0x3f,0x4d,0x69,0xa4,0x9e,0x73,0xb4,0xb0,0x4b,0x86,0x2e,0x11,0x97,0xc6,0x10},
{0xde,0x5f,0xbe,0x7d,0x27,0xc4,0x93,0x64,0xa2,0x7e,0xad,0x19,0xad,0x4f,0x5d,0x26,0x90,0x45,0x30,0x46,0xc8,0xdf,0x00,0x0e,0x09,0xfe,0x66,0xed,0xab,0x1c,0xe6,0x25,0x05,0xc8,0x58,0x83,0xa0,0x2a,0xa6,0x0c,0x47,0x42,0x20,0x7a,0xe3,0x4a,0x3d,0x6a,0xdc,0xed,0x11,0x3b,0xa6,0xd3,0x64,0x74,0xef,0x06,0x08,0x55,0xaf,0x9b,0xbf,0x03,0x04,0x66,0x58,0xcc,0x28,0xe1,0x13,0x3f,0x7e,0x74,0x59,0xb4,0xec,0x73,0x58,0x6f,0xf5,0x68,0x12,0xcc,0xed,0x3d,0xb6,0xa0,0x2c,0xe2,0x86,0x45,0x63,0x78,0x6d,0x56},
{0x34,0x08,0xc1,0x9c,0x9f,0xa4,0x37,0x16,0x51,0xc4,0x9b,0xa8,0xd5,0x56,0x8e,0xbc,0xdb,0xd2,0x7f,0x7f,0x0f,0xec,0xb5,0x1c,0xd9,0x35,0xcc,0x5e,0xca,0x5b,0x97,0x33,0xd0,0x2f,0x5a,0xc6,0x85,0x42,0x05,0xa1,0xc3,0x67,0x16,0xf3,0x2a,0x11,0x64,0x6c,0x58,0xee,0x1a,0x73,0x40,0xe2,0x0a,0x68,0x2a,0xb2,0x93,0x47,0xf3,0xa5,0xfb,0x14,0xd4,0xf7,0x85,0x69,0x16,0x46,0xd7,0x3c,0x57,0x00,0xc8,0xc9,0x84,0x5e,0x3e,0x59,0x1e,0x13,0x61,0x7b,0xb6,0xf2,0xc3,0x2f,0x6c,0x52,0xfc,0x83,0xea,0x9c,0x82,0x14},
{0xc2,0x95,0xdd,0x97,0x84,0x7b,0x43,0xff,0xa7,0xb5,0x4e,0xaa,0x30,0x4e,0x74,0x6c,0x8b,0xe8,0x85,0x3c,0x61,0x5d,0x0c,0x9e,0x73,0x81,0x75,0x5f,0x1e,0xc7,0xd9,0x2f,0xb8,0xec,0x71,0x4e,0x2f,0x0b,0xe7,0x21,0xe3,0x77,0xa4,0x40,0xb9,0xdd,0x56,0xe6,0x80,0x4f,0x1d,0xce,0xce,0x56,0x65,0xbf,0x7e,0x7b,0x5d,0x53,0xc4,0x3b,0xfc,0x05,0xdd,0xde,0xaf,0x52,0xae,0xb3,0xb8,0x24,0xcf,0x30,0x3b,0xed,0x8c,0x63,0x95,0x34,0x95,0x81,0xbe,0xa9,0x83,0xbc,0xa4,0x33,0x04,0x1f,0x65,0x5c,0x47,0x67,0x37,0x37},
{0xd9,0xad,0xd1,0x40,0xfd,0x99,0xba,0x2f,0x27,0xd0,0xf4,0x96,0x6f,0x16,0x07,0xb3,0xae,0x3b,0xf0,0x15,0x52,0xf0,0x63,0x43,0x99,0xf9,0x18,0x3b,0x6c,0xa5,0xbe,0x1f,0x90,0x65,0x24,0x14,0xcb,0x95,0x40,0x63,0x35,0x55,0xc1,0x16,0x40,0x14,0x12,0xef,0x60,0xbc,0x10,0x89,0x0c,0x14,0x38,0x9e,0x8c,0x7c,0x90,0x30,0x57,0x90,0xf5,0x6b,0x8a,0x5b,0x41,0xe1,0xf1,0x78,0xa7,0x0f,0x7e,0xa7,0xc3,0xba,0xf7,0x9f,0x40,0x06,0x50,0x9a,0xa2,0x9a,0xb8,0xd7,0x52,0x6f,0x56,0x5a,0x63,0x7a,0xf6,0x1c,0x52,0x02},
{0x94,0x52,0x9d,0x0a,0x0b,0xee,0x3f,0x51,0x66,0x5a,0xdf,0x0f,0x5c,0xe7,0x98,0x8f,0xce,0x07,0xe1,0xbf,0x88,0x86,0x61,0xd4,0xed,0x2c,0x38,0x71,0x7e,0x0a,0xa0,0x3f,0xe4,0x5e,0x2f,0x77,0x20,0x67,0x14,0xb1,0xce,0x9a,0x07,0x96,0xb1,0x94,0xf8,0xe8,0x4a,0x82,0xac,0x00,0x4d,0x22,0xf8,0x4a,0xc4,0x6c,0xcd,0xf7,0xd9,0x53,0x17,0x00,0x34,0xdb,0x3d,0x96,0x2d,0x23,0x69,0x3c,0x58,0x38,0x97,0xb4,0xda,0x87,0xde,0x1d,0x85,0xf2,0x91,0xa0,0xf9,0xd1,0xd7,0xaa,0xb6,0xed,0x48,0xa0,0x2f,0xfe,0xb5,0x12},
{0x4d,0xe3,0xfc,0x96,0xc4,0xfb,0xf0,0x71,0xed,0x5b,0xf3,0xad,0x6b,0x82,0xb9,0x73,0x61,0xc5,0x28,0xff,0x61,0x72,0x04,0xd2,0x6f,0x20,0xb1,0x6f,0xf9,0x76,0x9b,0x74,0x92,0x1e,0x6f,0xad,0x26,0x7c,0x2b,0xdf,0x13,0x89,0x4b,0x50,0x23,0xd3,0x66,0x4b,0xc3,0x8b,0x1c,0x75,0xc0,0x9d,0x40,0x8c,0xb8,0xc7,0x96,0x07,0xc2,0x93,0x7e,0x6f,0x05,0xae,0xa6,0xae,0x04,0xf6,0x5a,0x1f,0x99,0x9c,0xe4,0xbe,0xf1,0x51,0x23,0xc1,0x66,0x6b,0xff,0xee,0xb5,0x08,0xa8,0x61,0x51,0x21,0xe0,0x01,0x0f,0xc1,0xce,0x0f},
{0x44,0x1e,0xfe,0x49,0xa6,0x58,0x4d,0x64,0x7e,0x77,0xad,0x31,0xa2,0xae,0xfc,0x21,0xd2,0xd0,0x7f,0x88,0x5a,0x1c,0x44,0x02,0xf3,0x11,0xc5,0x83,0x71,0xaa,0x01,0x49,0x45,0x4e,0x24,0xc4,0x9d,0xd2,0xf2,0x3d,0x0a,0xde,0xd8,0x93,0x74,0x0e,0x02,0x2b,0x4d,0x21,0x0c,0x82,0x7e,0x06,0xc8,0x6c,0x0a,0xb9,0xea,0x6f,0x16,0x79,0x37,0x41,0xf0,0xf8,0x1a,0x8c,0x54,0xb7,0xb1,0x08,0xb4,0x99,0x62,0x24,0x7c,0x7a,0x0f,0xce,0x39,0xd9,0x06,0x1e,0xf9,0xb0,0x60,0xf7,0x13,0x12,0x6d,0x72,0x7b,0x88,0xbb,0x41},
{0xbe,0x46,0x43,0x74,0x44,0x7d,0xe8,0x40,0x25,0x2b,0xb5,0x15,0xd4,0xda,0x48,0x1d,0x3e,0x60,0x3b,0xa1,0x18,0x8a,0x3a,0x7c,0xf7,0xbd,0xcd,0x2f,0xc1,0x28,0xb7,0x4e,0xae,0x91,0x66,0x7c,0x59,0x4c,0x23,0x7e,0xc8,0xb4,0x85,0x0a,0x3d,0x9d,0x88,0x64,0xe7,0xfa,0x4a,0x35,0x0c,0xc9,0xe2,0xda,0x1d,0x9e,0x6a,0x0c,0x07,0x1e,0x87,0x0a,0x89,0x89,0xbc,0x4b,0x99,0xb5,0x01,0x33,0x60,0x42,0xdd,0x5b,0x3a,0xae,0x6b,0x73,0x3c,0x9e,0xd5,0x19,0xe2,0xad,0x61,0x0d,0x64,0xd4,0x85,0x26,0x0f,0x30,0xe7,0x3e},
{0xb7,0xd6,0x7d,0x9e,0xe4,0x55,0xd2,0xf5,0xac,0x1e,0x0b,0x61,0x5c,0x11,0x16,0x80,0xca,0x87,0xe1,0x92,0x5d,0x97,0x99,0x3c,0xc2,0x25,0x91,0x97,0x62,0x57,0x81,0x13,0x18,0x75,0x1e,0x84,0x47,0x79,0xfa,0x43,0xd7,0x46,0x9c,0x63,0x59,0xfa,0xc6,0xe5,0x74,0x2b,0x05,0xe3,0x1d,0x5e,0x06,0xa1,0x30,0x90,0xb8,0xcf,0xa2,0xc6,0x47,0x7d,0xe0,0xd6,0xf0,0x8e,0x14,0xd0,0xda,0x3f,0x3c,0x6f,0x54,0x91,0x9a,0x74,0x3e,0x9d,0x57,0x81,0xbb,0x26,0x10,0x62,0xec,0x71,0x80,0xec,0xc9,0x34,0x8d,0xf5,0x8c,0x14},
{0x27,0xf0,0x34,0x79,0xf6,0x92,0xa4,0x46,0xa9,0x0a,0x84,0xf6,0xbe,0x84,0x99,0x46,0x54,0x18,0x61,0x89,0x2a,0xbc,0xa1,0x5c,0xd4,0xbb,0x5d,0xbd,0x1e,0xfa,0xf2,0x3f,0x6d,0x75,0xe4,0x9a,0x7d,0x2f,0x57,0xe2,0x7f,0x48,0xf3,0x88,0xbb,0x45,0xc3,0x56,0x8d,0xa8,0x60,0x69,0x6d,0x0b,0xd1,0x9f,0xb9,0xa1,0xae,0x4e,0xad,0xeb,0x8f,0x27,0x66,0x39,0x93,0x8c,0x1f,0x68,0xaa,0xb1,0x98,0x0c,0x29,0x20,0x9c,0x94,0x21,0x8c,0x52,0x3c,0x9d,0x21,0x91,0x52,0x11,0x39,0x7b,0x67,0x9c,0xfe,0x02,0xdd,0x04,0x41},
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{0xc3,0x05,0xfa,0xba,0x60,0x75,0x1c,0x7d,0x61,0x5e,0xe5,0xc6,0xa0,0xa0,0xe1,0xb3,0x73,0x64,0xd6,0xc0,0x18,0x97,0x52,0xe3,0x86,0x34,0x0c,0xc2,0x11,0x6b,0x54,0x41,0xbd,0xbd,0x96,0xd5,0xcd,0x72,0x21,0xb4,0x40,0xfc,0xee,0x98,0x43,0x45,0xe0,0x93,0xb5,0x09,0x41,0xb4,0x47,0x53,0xb1,0x9f,0x34,0xae,0x66,0x02,0x99,0xd3,0x6b,0x73,0xb4,0xb3,0x34,0x93,0x50,0x2d,0x53,0x85,0x73,0x65,0x81,0x60,0x4b,0x11,0xfd,0x46,0x75,0x83,0x5c,0x42,0x30,0x5f,0x5f,0xcc,0x5c,0xab,0x7f,0xb8,0xa2,0x95,0x22,0x41},
{0xe9,0xd6,0x7e,0xf5,0x88,0x9b,0xc9,0x19,0x25,0xc8,0xf8,0x6d,0x26,0xcb,0x93,0x53,0x73,0xd2,0x0a,0xb3,0x13,0x32,0xee,0x5c,0x34,0x2e,0x2d,0xb5,0xeb,0x53,0xe1,0x14,0xc6,0xea,0x93,0xe2,0x61,0x52,0x65,0x2e,0xdb,0xac,0x33,0x21,0x03,0x92,0x5a,0x84,0x6b,0x99,0x00,0x79,0xcb,0x75,0x09,0x46,0x80,0xdd,0x5a,0x19,0x8d,0xbb,0x60,0x07,0x8a,0x81,0xe6,0xcd,0x17,0x1a,0x3e,0x41,0x84,0xa0,0x69,0xed,0xa9,0x6d,0x15,0x57,0xb1,0xcc,0xca,0x46,0x8f,0x26,0xbf,0x2c,0xf2,0xc5,0x3a,0xc3,0x9b,0xbe,0x34,0x6b},
{0xb2,0xc0,0x78,0x3a,0x64,0x2f,0xdf,0xf3,0x7c,0x02,0x2e,0xf2,0x1e,0x97,0x3e,0x4c,0xa3,0xb5,0xc1,0x49,0x5e,0x1c,0x7d,0xec,0x2d,0xdd,0x22,0x09,0x8f,0xc1,0x12,0x20,0xd3,0xf2,0x71,0x65,0x65,0x69,0xfc,0x11,0x7a,0x73,0x0e,0x53,0x45,0xe8,0xc9,0xc6,0x35,0x50,0xfe,0xd4,0xa2,0xe7,0x3a,0xe3,0x0b,0xd3,0x6d,0x2e,0xb6,0xc7,0xb9,0x01,0x29,0x9d,0xc8,0x5a,0xe5,0x55,0x0b,0x88,0x63,0xa7,0xa0,0x45,0x1f,0x24,0x83,0x14,0x1f,0x6c,0xe7,0xc2,0xdf,0xef,0x36,0x3d,0xe8,0xad,0x4b,0x4e,0x78,0x5b,0xaf,0x08},
{0x33,0x25,0x1f,0x88,0xdc,0x99,0x34,0x28,0xb6,0x23,0x93,0x77,0xda,0x25,0x05,0x9d,0xf4,0x41,0x34,0x67,0xfb,0xdd,0x7a,0x89,0x8d,0x16,0x3a,0x16,0x71,0x9d,0xb7,0x32,0x4b,0x2c,0xcc,0x89,0xd2,0x14,0x73,0xe2,0x8d,0x17,0x87,0xa2,0x11,0xbd,0xe4,0x4b,0xce,0x64,0x33,0xfa,0xd6,0x28,0xd5,0x18,0x6e,0x82,0xd9,0xaf,0xd5,0xc1,0x23,0x64,0x6a,0xb3,0xfc,0xed,0xd9,0xf8,0x85,0xcc,0xf9,0xe5,0x46,0x37,0x8f,0xc2,0xbc,0x22,0xcd,0xd3,0xe5,0xf9,0x38,0xe3,0x9d,0xe4,0xcc,0x2d,0x3e,0xc1,0xfb,0x5e,0x0a,0x48},
{0x71,0x20,0x62,0x01,0x0b,0xe7,0x51,0x0b,0xc5,0xaf,0x1d,0x8b,0xcf,0x05,0xb5,0x06,0xcd,0xab,0x5a,0xef,0x61,0xb0,0x6b,0x2c,0x31,0xbf,0xb7,0x0c,0x60,0x27,0xaa,0x47,0x1f,0x22,0xce,0x42,0xe4,0x4c,0x61,0xb6,0x28,0x39,0x05,0x4c,0xcc,0x9d,0x19,0x6e,0x03,0xbe,0x1c,0xdc,0xa4,0xb4,0x3f,0x66,0x06,0x8e,0x1c,0x69,0x47,0x1d,0xb3,0x24,0xc3,0xf8,0x15,0xc0,0xed,0x1e,0x54,0x2a,0x7c,0x3f,0x69,0x7c,0x7e,0xfe,0xa4,0x11,0xd6,0x78,0xa2,0x4e,0x13,0x66,0xaf,0xf0,0x94,0xa0,0xdd,0x14,0x5d,0x58,0x5b,0x54},
{0x0f,0x3a,0xd4,0xa0,0x5e,0x27,0xbf,0x67,0xbe,0xee,0x9b,0x08,0x34,0x8e,0xe6,0xad,0x2e,0xe7,0x79,0xd4,0x4c,0x13,0x89,0x42,0x54,0x54,0xba,0x32,0xc3,0xf9,0x62,0x0f,0xe1,0x21,0xb3,0xe3,0xd0,0xe4,0x04,0x62,0x95,0x1e,0xff,0x28,0x7a,0x63,0xaa,0x3b,0x9e,0xbd,0x99,0x5b,0xfd,0xcf,0x0c,0x0b,0x71,0xd0,0xc8,0x64,0x3e,0xdc,0x22,0x4d,0x39,0x5f,0x3b,0xd6,0x89,0x65,0xb4,0xfc,0x61,0xcf,0xcb,0x57,0x3f,0x6a,0xae,0x5c,0x05,0xfa,0x3a,0x95,0xd2,0xc2,0xba,0xfe,0x36,0x14,0x37,0x36,0x1a,0xa0,0x0f,0x1c},
{0xff,0x3d,0x94,0x22,0xb6,0x04,0xc6,0xd2,0xa0,0xb3,0xcf,0x44,0xce,0xbe,0x8c,0xbc,0x78,0x86,0x80,0x97,0xf3,0x4f,0x25,0x5d,0xbf,0xa6,0x1c,0x3b,0x4f,0x61,0xa3,0x0f,0x50,0x6a,0x93,0x8c,0x0e,0x2b,0x08,0x69,0xb6,0xc5,0xda,0xc1,0x35,0xa0,0xc9,0xf9,0x34,0xb6,0xdf,0xc4,0x54,0x3e,0xb7,0x6f,0x40,0xc1,0x2b,0x1d,0x9b,0x41,0x05,0x40,0xf0,0x82,0xbe,0xb9,0xbd,0xfe,0x03,0xa0,0x90,0xac,0x44,0x3a,0xaf,0xc1,0x89,0x20,0x8e,0xfa,0x54,0x19,0x91,0x9f,0x49,0xf8,0x42,0xab,0x40,0xef,0x8a,0x21,0xba,0x1f},
{0x3e,0xf5,0xc8,0xfa,0x48,0x94,0x54,0xab,0x41,0x37,0xa6,0x7b,0x9a,0xe8,0xf6,0x81,0x01,0x5e,0x2b,0x6c,0x7d,0x6c,0xfd,0x74,0x42,0x6e,0xc8,0xa8,0xca,0x3a,0x2e,0x39,0x94,0x01,0x7b,0x3e,0x04,0x57,0x3e,0x4f,0x7f,0xaf,0xda,0x08,0xee,0x3e,0x1d,0xa8,0xf1,0xde,0xdc,0x99,0xab,0xc6,0x39,0xc8,0xd5,0x61,0x77,0xff,0x13,0x5d,0x53,0x6c,0xaf,0x35,0x8a,0x3e,0xe9,0x34,0xbd,0x4c,0x16,0xe8,0x87,0x58,0x44,0x81,0x07,0x2e,0xab,0xb0,0x9a,0xf2,0x76,0x9c,0x31,0x19,0x3b,0xc1,0x0a,0xd5,0xe4,0x7f,0xe1,0x25},
{0x76,0xf6,0x04,0x1e,0xd7,0x9b,0x28,0x0a,0x95,0x0f,0x42,0xd6,0x52,0x1c,0x8e,0x20,0xab,0x1f,0x69,0x34,0xb0,0xd8,0x86,0x51,0x51,0xb3,0x9f,0x2a,0x44,0x51,0x57,0x25,0xa7,0x21,0xf1,0x76,0xf5,0x7f,0x5f,0x91,0xe3,0x87,0xcd,0x2f,0x27,0x32,0x4a,0xc3,0x26,0xe5,0x1b,0x4d,0xde,0x2f,0xba,0xcc,0x9b,0x89,0x69,0x89,0x8f,0x82,0xba,0x6b,0x01,0x39,0xfe,0x90,0x66,0xbc,0xd1,0xe2,0xd5,0x7a,0x99,0xa0,0x18,0x4a,0xb5,0x4c,0xd4,0x60,0x84,0xaf,0x14,0x69,0x1d,0x97,0xe4,0x7b,0x6b,0x7f,0x4f,0x50,0x9d,0x55},
{0xd5,0x54,0xeb,0xb3,0x78,0x83,0x73,0xa7,0x7c,0x3c,0x55,0xa5,0x66,0xd3,0x69,0x1d,0xba,0x00,0x28,0xf9,0x62,0xcf,0x26,0x0a,0x17,0x32,0x7e,0x80,0xd5,0x12,0xab,0x01,0xfd,0x66,0xd2,0xf6,0xe7,0x91,0x48,0x9c,0x1b,0x78,0x07,0x03,0x9b,0xa1,0x44,0x07,0x3b,0xe2,0x61,0x60,0x1d,0x8f,0x38,0x88,0x0e,0xd5,0x4b,0x35,0xa3,0xa6,0x3e,0x12,0x96,0x2d,0xe3,0x41,0x90,0x18,0x8d,0x11,0x48,0x58,0x31,0xd8,0xc2,0xe3,0xed,0xb9,0xd9,0x45,0x32,0xd8,0x71,0x42,0xab,0x1e,0x54,0xa1,0x18,0xc9,0xe2,0x61,0x39,0x4a},
{0xa0,0xbb,0xe6,0xf8,0xe0,0x3b,0xdc,0x71,0x0a,0xe3,0xff,0x7e,0x34,0xf8,0xce,0xd6,0x6a,0x47,0x3a,0xe1,0x5f,0x42,0x92,0xa9,0x63,0xb7,0x1d,0xfb,0xe3,0xbc,0xd6,0x2c,0x1e,0x3f,0x23,0xf3,0x44,0xd6,0x27,0x03,0x16,0xf0,0xfc,0x34,0x0e,0x26,0x9a,0x49,0x79,0xb9,0xda,0xf2,0x16,0xa7,0xb5,0x83,0x1f,0x11,0xd4,0x9b,0xad,0xee,0xac,0x68,0x10,0xc2,0xd7,0xf3,0x0e,0xc9,0xb4,0x38,0x0c,0x04,0xad,0xb7,0x24,0x6e,0x8e,0x30,0x23,0x3e,0xe7,0xb7,0xf1,0xd9,0x60,0x38,0x97,0xf5,0x08,0xb5,0xd5,0x60,0x57,0x59},
{0x97,0x63,0xaa,0x04,0xe1,0xbf,0x29,0x61,0xcb,0xfc,0xa7,0xa4,0x08,0x00,0x96,0x8f,0x58,0x94,0x90,0x7d,0x89,0xc0,0x8b,0x3f,0xa9,0x91,0xb2,0xdc,0x3e,0xa4,0x9f,0x70,0x90,0x27,0x02,0xfd,0xeb,0xcb,0x2a,0x88,0x60,0x57,0x11,0xc4,0x05,0x33,0xaf,0x89,0xf4,0x73,0x34,0x7d,0xe3,0x92,0xf4,0x65,0x2b,0x5a,0x51,0x54,0xdf,0xc5,0xb2,0x2c,0xca,0x2a,0xfd,0x63,0x8c,0x5d,0x0a,0xeb,0xff,0x4e,0x69,0x2e,0x66,0xc1,0x2b,0xd2,0x3a,0xb0,0xcb,0xf8,0x6e,0xf3,0x23,0x27,0x1f,0x13,0xc8,0xf0,0xec,0x29,0xf0,0x70},
{0x33,0x3e,0xed,0x2e,0xb3,0x07,0x13,0x46,0xe7,0x81,0x55,0xa4,0x33,0x2f,0x04,0xae,0x66,0x03,0x5f,0x19,0xd3,0x49,0x44,0xc9,0x58,0x48,0x31,0x6c,0x8a,0x5d,0x7d,0x0b,0xb9,0xb0,0x10,0x5e,0xaa,0xaf,0x6a,0x2a,0xa9,0x1a,0x04,0xef,0x70,0xa3,0xf0,0x78,0x1f,0xd6,0x3a,0xaa,0x77,0xfb,0x3e,0x77,0xe1,0xd9,0x4b,0xa7,0xa2,0xa5,0xec,0x44,0x43,0xd5,0x95,0x7b,0x32,0x48,0xd4,0x25,0x1d,0x0f,0x34,0xa3,0x00,0x83,0xd3,0x70,0x2b,0xc5,0xe1,0x60,0x1c,0x53,0x1c,0xde,0xe4,0xe9,0x7d,0x2c,0x51,0x24,0x22,0x27},
{0x2e,0x34,0xc5,0x49,0xaf,0x92,0xbc,0x1a,0xd0,0xfa,0xe6,0xb2,0x11,0xd8,0xee,0xff,0x29,0x4e,0xc8,0xfc,0x8d,0x8c,0xa2,0xef,0x43,0xc5,0x4c,0xa4,0x18,0xdf,0xb5,0x11,0xfc,0x75,0xa9,0x42,0x8a,0xbb,0x7b,0xbf,0x58,0xa3,0xad,0x96,0x77,0x39,0x5c,0x8c,0x48,0xaa,0xed,0xcd,0x6f,0xc7,0x7f,0xe2,0xa6,0x20,0xbc,0xf6,0xd7,0x5f,0x73,0x19,0x66,0x42,0xc8,0x42,0xd0,0x90,0xab,0xe3,0x7e,0x54,0x19,0x7f,0x0f,0x8e,0x84,0xeb,0xb9,0x97,0xa4,0x65,0xd0,0xa1,0x03,0x25,0x5f,0x89,0xdf,0x91,0x11,0x91,0xef,0x0f}
};
NAMESPACE_END // Arch32
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_DONNA_32_H

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donna_64.cpp
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// donna_64.h - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// This source file multiplexes two different repos using namespaces. This
// was a little easier from a project management standpoint. We only need
// two files per architecture at the expense of namespaces and bloat.
#ifndef CRYPTOPP_DONNA_64_H
#define CRYPTOPP_DONNA_64_H
#include "config.h"
#if defined(_MSC_VER)
# include <intrin.h>
# pragma intrinsic(_umul128)
# pragma intrinsic(__shiftright128)
#endif
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(Arch64)
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::word64;
// ******************** x25519 Agreement ************************* //
#define ALIGN(n) CRYPTOPP_ALIGN_DATA(n)
typedef word64 bignum25519[5];
const byte basePoint[32] = {9};
const word64 reduce_mask_40 = ((word64)1 << 40) - 1;
const word64 reduce_mask_51 = ((word64)1 << 51) - 1;
const word64 reduce_mask_52 = ((word64)1 << 52) - 1;
const word64 reduce_mask_56 = ((word64)1 << 56) - 1;
const word64 two54m152 = (((word64)1) << 54) - 152;
const word64 two54m8 = (((word64)1) << 54) - 8;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
using CryptoPP::word128;
# define lo128(a) ((word64)a)
# define hi128(a) ((word64)(a >> 64))
# define add128(a,b) a += b;
# define add128_64(a,b) a += (word64)b;
# define mul64x64_128(out,a,b) out = (word128)a * b;
# define shr128(out,in,shift) out = (word64)(in >> (shift));
# define shl128(out,in,shift) out = (word64)((in << shift) >> 64);
#elif defined(_MSC_VER)
struct word128 { word64 lo, hi; };
# define mul64x64_128(out,a,b) out.lo = _umul128(a,b,&out.hi);
# define shr128_pair(out,hi,lo,shift) out = __shiftright128(lo, hi, shift);
# define shl128_pair(out,hi,lo,shift) out = __shiftleft128(lo, hi, shift);
# define shr128(out,in,shift) shr128_pair(out, in.hi, in.lo, shift)
# define shl128(out,in,shift) shl128_pair(out, in.hi, in.lo, shift)
# define add128(a,b) { word64 p = a.lo; a.lo += b.lo; a.hi += b.hi + (a.lo < p); }
# define add128_64(a,b) { word64 p = a.lo; a.lo += b; a.hi += (a.lo < p); }
# define lo128(a) (a.lo)
# define hi128(a) (a.hi)
#elif defined(__GNUC__)
struct word128 { word64 lo, hi; };
# define mul64x64_128(out,a,b) __asm__ ("mulq %3" : "=a" (out.lo), "=d" (out.hi) : "a" (a), "rm" (b));
# define shr128_pair(out,hi,lo,shift) __asm__ ("shrdq %2,%1,%0" : "+r" (lo) : "r" (hi), "J" (shift)); out = lo;
# define shl128_pair(out,hi,lo,shift) __asm__ ("shldq %2,%1,%0" : "+r" (hi) : "r" (lo), "J" (shift)); out = hi;
# define shr128(out,in,shift) shr128_pair(out,in.hi, in.lo, shift)
# define shl128(out,in,shift) shl128_pair(out,in.hi, in.lo, shift)
# define add128(a,b) __asm__ ("addq %4,%2; adcq %5,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b.lo), "rm" (b.hi) : "cc");
# define add128_64(a,b) __asm__ ("addq %4,%2; adcq $0,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b) : "cc");
# define lo128(a) (a.lo)
# define hi128(a) (a.hi)
#else
// https://groups.google.com/forum/#!forum/cryptopp-users
# error "Unsupported platform"
#endif
// ****************** ed25519 Signatures *********************** //
typedef byte hash_512bits[64];
const int bignum256modm_bits_per_limb = 56;
const int bignum256modm_limb_size = 5;
typedef word64 bignum256modm_element_t;
typedef bignum256modm_element_t bignum256modm[5];
/* multiples of p */
const word64 twoP0 = 0x0fffffffffffda;
const word64 twoP1234 = 0x0ffffffffffffe;
const word64 fourP0 = 0x1fffffffffffb4;
const word64 fourP1234 = 0x1ffffffffffffc;
struct ge25519 {
bignum25519 x, y, z, t;
};
struct ge25519_p1p1 {
bignum25519 x, y, z, t;
};
struct ge25519_niels {
bignum25519 ysubx, xaddy, t2d;
};
struct ge25519_pniels {
bignum25519 ysubx, xaddy, z, t2d;
};
#define S1_SWINDOWSIZE 5
#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
#define S2_SWINDOWSIZE 7
#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
// *************** ed25519-donna-64bit-tables.h *************** //
const ge25519 ge25519_basepoint = {
{0x00062d608f25d51a,0x000412a4b4f6592a,0x00075b7171a4b31d,0x0001ff60527118fe,0x000216936d3cd6e5},
{0x0006666666666658,0x0004cccccccccccc,0x0001999999999999,0x0003333333333333,0x0006666666666666},
{0x0000000000000001,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000},
{0x00068ab3a5b7dda3,0x00000eea2a5eadbb,0x0002af8df483c27e,0x000332b375274732,0x00067875f0fd78b7}
};
const bignum25519 ge25519_ecd = {
0x00034dca135978a3,0x0001a8283b156ebd,0x0005e7a26001c029,0x000739c663a03cbb,0x00052036cee2b6ff
};
const bignum25519 ge25519_ec2d = {
0x00069b9426b2f159,0x00035050762add7a,0x0003cf44c0038052,0x0006738cc7407977,0x0002406d9dc56dff
};
const bignum25519 ge25519_sqrtneg1 = {
0x00061b274a0ea0b0,0x0000d5a5fc8f189d,0x0007ef5e9cbd0c60,0x00078595a6804c9e,0x0002b8324804fc1d
};
const ge25519_niels ge25519_niels_sliding_multiples[32] = {
{{0x00003905d740913e,0x0000ba2817d673a2,0x00023e2827f4e67c,0x000133d2e0c21a34,0x00044fd2f9298f81},{0x000493c6f58c3b85,0x0000df7181c325f7,0x0000f50b0b3e4cb7,0x0005329385a44c32,0x00007cf9d3a33d4b},{0x00011205877aaa68,0x000479955893d579,0x00050d66309b67a0,0x0002d42d0dbee5ee,0x0006f117b689f0c6}},
{{0x00011fe8a4fcd265,0x0007bcb8374faacc,0x00052f5af4ef4d4f,0x0005314098f98d10,0x0002ab91587555bd},{0x0005b0a84cee9730,0x00061d10c97155e4,0x0004059cc8096a10,0x00047a608da8014f,0x0007a164e1b9a80f},{0x0006933f0dd0d889,0x00044386bb4c4295,0x0003cb6d3162508c,0x00026368b872a2c6,0x0005a2826af12b9b}},
{{0x000182c3a447d6ba,0x00022964e536eff2,0x000192821f540053,0x0002f9f19e788e5c,0x000154a7e73eb1b5},{0x0002bc4408a5bb33,0x000078ebdda05442,0x0002ffb112354123,0x000375ee8df5862d,0x0002945ccf146e20},{0x0003dbf1812a8285,0x0000fa17ba3f9797,0x0006f69cb49c3820,0x00034d5a0db3858d,0x00043aabe696b3bb}},
{{0x00072c9aaa3221b1,0x000267774474f74d,0x000064b0e9b28085,0x0003f04ef53b27c9,0x0001d6edd5d2e531},{0x00025cd0944ea3bf,0x00075673b81a4d63,0x000150b925d1c0d4,0x00013f38d9294114,0x000461bea69283c9},{0x00036dc801b8b3a2,0x0000e0a7d4935e30,0x0001deb7cecc0d7d,0x000053a94e20dd2c,0x0007a9fbb1c6a0f9}},
{{0x0006217e039d8064,0x0006dea408337e6d,0x00057ac112628206,0x000647cb65e30473,0x00049c05a51fadc9},{0x0006678aa6a8632f,0x0005ea3788d8b365,0x00021bd6d6994279,0x0007ace75919e4e3,0x00034b9ed338add7},{0x0004e8bf9045af1b,0x000514e33a45e0d6,0x0007533c5b8bfe0f,0x000583557b7e14c9,0x00073c172021b008}},
{{0x00075b0249864348,0x00052ee11070262b,0x000237ae54fb5acd,0x0003bfd1d03aaab5,0x00018ab598029d5c},{0x000700848a802ade,0x0001e04605c4e5f7,0x0005c0d01b9767fb,0x0007d7889f42388b,0x0004275aae2546d8},{0x00032cc5fd6089e9,0x000426505c949b05,0x00046a18880c7ad2,0x0004a4221888ccda,0x0003dc65522b53df}},
{{0x0007013b327fbf93,0x0001336eeded6a0d,0x0002b565a2bbf3af,0x000253ce89591955,0x0000267882d17602},{0x0000c222a2007f6d,0x000356b79bdb77ee,0x00041ee81efe12ce,0x000120a9bd07097d,0x000234fd7eec346f},{0x0000a119732ea378,0x00063bf1ba8e2a6c,0x00069f94cc90df9a,0x000431d1779bfc48,0x000497ba6fdaa097}},
{{0x0003cd86468ccf0b,0x00048553221ac081,0x0006c9464b4e0a6e,0x00075fba84180403,0x00043b5cd4218d05},{0x0006cc0313cfeaa0,0x0001a313848da499,0x0007cb534219230a,0x00039596dedefd60,0x00061e22917f12de},{0x0002762f9bd0b516,0x0001c6e7fbddcbb3,0x00075909c3ace2bd,0x00042101972d3ec9,0x000511d61210ae4d}},
{{0x000386484420de87,0x0002d6b25db68102,0x000650b4962873c0,0x0004081cfd271394,0x00071a7fe6fe2482},{0x000676ef950e9d81,0x0001b81ae089f258,0x00063c4922951883,0x0002f1d54d9b3237,0x0006d325924ddb85},{0x000182b8a5c8c854,0x00073fcbe5406d8e,0x0005de3430cff451,0x000554b967ac8c41,0x0004746c4b6559ee}},
{{0x000546c864741147,0x0003a1df99092690,0x0001ca8cc9f4d6bb,0x00036b7fc9cd3b03,0x000219663497db5e},{0x00077b3c6dc69a2b,0x0004edf13ec2fa6e,0x0004e85ad77beac8,0x0007dba2b28e7bda,0x0005c9a51de34fe9},{0x0000f1cf79f10e67,0x00043ccb0a2b7ea2,0x00005089dfff776a,0x0001dd84e1d38b88,0x0004804503c60822}},
{{0x000021d23a36d175,0x0004fd3373c6476d,0x00020e291eeed02a,0x00062f2ecf2e7210,0x000771e098858de4},{0x00049ed02ca37fc7,0x000474c2b5957884,0x0005b8388e816683,0x0004b6c454b76be4,0x000553398a516506},{0x0002f5d278451edf,0x000730b133997342,0x0006965420eb6975,0x000308a3bfa516cf,0x0005a5ed1d68ff5a}},
{{0x0005e0c558527359,0x0003395b73afd75c,0x000072afa4e4b970,0x00062214329e0f6d,0x000019b60135fefd},{0x0005122afe150e83,0x0004afc966bb0232,0x0001c478833c8268,0x00017839c3fc148f,0x00044acb897d8bf9},{0x000068145e134b83,0x0001e4860982c3cc,0x000068fb5f13d799,0x0007c9283744547e,0x000150c49fde6ad2}},
{{0x0001863c9cdca868,0x0003770e295a1709,0x0000d85a3720fd13,0x0005e0ff1f71ab06,0x00078a6d7791e05f},{0x0003f29509471138,0x000729eeb4ca31cf,0x00069c22b575bfbc,0x0004910857bce212,0x0006b2b5a075bb99},{0x0007704b47a0b976,0x0002ae82e91aab17,0x00050bd6429806cd,0x00068055158fd8ea,0x000725c7ffc4ad55}},
{{0x00002bf71cd098c0,0x00049dabcc6cd230,0x00040a6533f905b2,0x000573efac2eb8a4,0x0004cd54625f855f},{0x00026715d1cf99b2,0x0002205441a69c88,0x000448427dcd4b54,0x0001d191e88abdc5,0x000794cc9277cb1f},{0x0006c426c2ac5053,0x0005a65ece4b095e,0x0000c44086f26bb6,0x0007429568197885,0x0007008357b6fcc8}},
{{0x00039fbb82584a34,0x00047a568f257a03,0x00014d88091ead91,0x0002145b18b1ce24,0x00013a92a3669d6d},{0x0000672738773f01,0x000752bf799f6171,0x0006b4a6dae33323,0x0007b54696ead1dc,0x00006ef7e9851ad0},{0x0003771cc0577de5,0x0003ca06bb8b9952,0x00000b81c5d50390,0x00043512340780ec,0x0003c296ddf8a2af}},
{{0x00034d2ebb1f2541,0x0000e815b723ff9d,0x000286b416e25443,0x0000bdfe38d1bee8,0x0000a892c7007477},{0x000515f9d914a713,0x00073191ff2255d5,0x00054f5cc2a4bdef,0x0003dd57fc118bcf,0x0007a99d393490c7},{0x0002ed2436bda3e8,0x00002afd00f291ea,0x0000be7381dea321,0x0003e952d4b2b193,0x000286762d28302f}},
{{0x00058e2bce2ef5bd,0x00068ce8f78c6f8a,0x0006ee26e39261b2,0x00033d0aa50bcf9d,0x0007686f2a3d6f17},{0x000036093ce35b25,0x0003b64d7552e9cf,0x00071ee0fe0b8460,0x00069d0660c969e5,0x00032f1da046a9d9},{0x000512a66d597c6a,0x0000609a70a57551,0x000026c08a3c464c,0x0004531fc8ee39e1,0x000561305f8a9ad2}},
{{0x0002cc28e7b0c0d5,0x00077b60eb8a6ce4,0x0004042985c277a6,0x000636657b46d3eb,0x000030a1aef2c57c},{0x0004978dec92aed1,0x000069adae7ca201,0x00011ee923290f55,0x00069641898d916c,0x00000aaec53e35d4},{0x0001f773003ad2aa,0x000005642cc10f76,0x00003b48f82cfca6,0x0002403c10ee4329,0x00020be9c1c24065}},
{{0x0000e44ae2025e60,0x0005f97b9727041c,0x0005683472c0ecec,0x000188882eb1ce7c,0x00069764c545067e},{0x000387d8249673a6,0x0005bea8dc927c2a,0x0005bd8ed5650ef0,0x0000ef0e3fcd40e1,0x000750ab3361f0ac},{0x00023283a2f81037,0x000477aff97e23d1,0x0000b8958dbcbb68,0x0000205b97e8add6,0x00054f96b3fb7075}},
{{0x0005afc616b11ecd,0x00039f4aec8f22ef,0x0003b39e1625d92e,0x0005f85bd4508873,0x00078e6839fbe85d},{0x0005f20429669279,0x00008fafae4941f5,0x00015d83c4eb7688,0x0001cf379eca4146,0x0003d7fe9c52bb75},{0x00032df737b8856b,0x0000608342f14e06,0x0003967889d74175,0x0001211907fba550,0x00070f268f350088}},
{{0x0004112070dcf355,0x0007dcff9c22e464,0x00054ada60e03325,0x00025cd98eef769a,0x000404e56c039b8c},{0x00064583b1805f47,0x00022c1baf832cd0,0x000132c01bd4d717,0x0004ecf4c3a75b8f,0x0007c0d345cfad88},{0x00071f4b8c78338a,0x00062cfc16bc2b23,0x00017cf51280d9aa,0x0003bbae5e20a95a,0x00020d754762aaec}},
{{0x0004feb135b9f543,0x00063bd192ad93ae,0x00044e2ea612cdf7,0x000670f4991583ab,0x00038b8ada8790b4},{0x0007c36fc73bb758,0x0004a6c797734bd1,0x0000ef248ab3950e,0x00063154c9a53ec8,0x0002b8f1e46f3cee},{0x00004a9cdf51f95d,0x0005d963fbd596b8,0x00022d9b68ace54a,0x0004a98e8836c599,0x000049aeb32ceba1}},
{{0x00067d3c63dcfe7e,0x000112f0adc81aee,0x00053df04c827165,0x0002fe5b33b430f0,0x00051c665e0c8d62},{0x00007d0b75fc7931,0x00016f4ce4ba754a,0x0005ace4c03fbe49,0x00027e0ec12a159c,0x000795ee17530f67},{0x00025b0a52ecbd81,0x0005dc0695fce4a9,0x0003b928c575047d,0x00023bf3512686e5,0x0006cd19bf49dc54}},
{{0x0007619052179ca3,0x0000c16593f0afd0,0x000265c4795c7428,0x00031c40515d5442,0x0007520f3db40b2e},{0x0006612165afc386,0x0001171aa36203ff,0x0002642ea820a8aa,0x0001f3bb7b313f10,0x0005e01b3a7429e4},{0x00050be3d39357a1,0x0003ab33d294a7b6,0x0004c479ba59edb3,0x0004c30d184d326f,0x00071092c9ccef3c}},
{{0x0000523f0364918c,0x000687f56d638a7b,0x00020796928ad013,0x0005d38405a54f33,0x0000ea15b03d0257},{0x0003d8ac74051dcf,0x00010ab6f543d0ad,0x0005d0f3ac0fda90,0x0005ef1d2573e5e4,0x0004173a5bb7137a},{0x00056e31f0f9218a,0x0005635f88e102f8,0x0002cbc5d969a5b8,0x000533fbc98b347a,0x0005fc565614a4e3}},
{{0x0006570dc46d7ae5,0x00018a9f1b91e26d,0x000436b6183f42ab,0x000550acaa4f8198,0x00062711c414c454},{0x0002e1e67790988e,0x0001e38b9ae44912,0x000648fbb4075654,0x00028df1d840cd72,0x0003214c7409d466},{0x0001827406651770,0x0004d144f286c265,0x00017488f0ee9281,0x00019e6cdb5c760c,0x0005bea94073ecb8}},
{{0x0005bf0912c89be4,0x00062fadcaf38c83,0x00025ec196b3ce2c,0x00077655ff4f017b,0x0003aacd5c148f61},{0x0000ce63f343d2f8,0x0001e0a87d1e368e,0x000045edbc019eea,0x0006979aed28d0d1,0x0004ad0785944f1b},{0x00063b34c3318301,0x0000e0e62d04d0b1,0x000676a233726701,0x00029e9a042d9769,0x0003aff0cb1d9028}},
{{0x0005c7eb3a20405e,0x0005fdb5aad930f8,0x0004a757e63b8c47,0x00028e9492972456,0x000110e7e86f4cd2},{0x0006430bf4c53505,0x000264c3e4507244,0x00074c9f19a39270,0x00073f84f799bc47,0x0002ccf9f732bd99},{0x0000d89ed603f5e4,0x00051e1604018af8,0x0000b8eedc4a2218,0x00051ba98b9384d0,0x00005c557e0b9693}},
{{0x0001ce311fc97e6f,0x0006023f3fb5db1f,0x0007b49775e8fc98,0x0003ad70adbf5045,0x0006e154c178fe98},{0x0006bbb089c20eb0,0x0006df41fb0b9eee,0x00051087ed87e16f,0x000102db5c9fa731,0x000289fef0841861},{0x00016336fed69abf,0x0004f066b929f9ec,0x0004e9ff9e6c5b93,0x00018c89bc4bb2ba,0x0006afbf642a95ca}},
{{0x0000de0c62f5d2c1,0x00049601cf734fb5,0x0006b5c38263f0f6,0x0004623ef5b56d06,0x0000db4b851b9503},{0x00055070f913a8cc,0x000765619eac2bbc,0x0003ab5225f47459,0x00076ced14ab5b48,0x00012c093cedb801},{0x00047f9308b8190f,0x000414235c621f82,0x00031f5ff41a5a76,0x0006736773aab96d,0x00033aa8799c6635}},
{{0x0007f51ebd085cf2,0x00012cfa67e3f5e1,0x0001800cf1e3d46a,0x00054337615ff0a8,0x000233c6f29e8e21},{0x0000f588fc156cb1,0x000363414da4f069,0x0007296ad9b68aea,0x0004d3711316ae43,0x000212cd0c1c8d58},{0x0004d5107f18c781,0x00064a4fd3a51a5e,0x0004f4cd0448bb37,0x000671d38543151e,0x0001db7778911914}},
{{0x000352397c6bc26f,0x00018a7aa0227bbe,0x0005e68cc1ea5f8b,0x0006fe3e3a7a1d5f,0x00031ad97ad26e2a},{0x00014769dd701ab6,0x00028339f1b4b667,0x0004ab214b8ae37b,0x00025f0aefa0b0fe,0x0007ae2ca8a017d2},{0x000017ed0920b962,0x000187e33b53b6fd,0x00055829907a1463,0x000641f248e0a792,0x0001ed1fc53a6622}}
};
// ****************** modm-donna-64bit.h *********************** //
const bignum256modm modm_m = {
0x12631a5cf5d3ed, 0xf9dea2f79cd658,
0x000000000014de, 0x00000000000000,
0x00000010000000
};
const bignum256modm modm_mu = {
0x9ce5a30a2c131b, 0x215d086329a7ed,
0xffffffffeb2106, 0xffffffffffffff,
0x00000fffffffff
};
// *************** ed25519-donna-basepoint-table.h *************** //
/* multiples of the base point in packed {ysubx, xaddy, t2d} form */
ALIGN(16) const byte ge25519_niels_base_multiples[256][96] = {
{0x3e,0x91,0x40,0xd7,0x05,0x39,0x10,0x9d,0xb3,0xbe,0x40,0xd1,0x05,0x9f,0x39,0xfd,0x09,0x8a,0x8f,0x68,0x34,0x84,0xc1,0xa5,0x67,0x12,0xf8,0x98,0x92,0x2f,0xfd,0x44,0x85,0x3b,0x8c,0xf5,0xc6,0x93,0xbc,0x2f,0x19,0x0e,0x8c,0xfb,0xc6,0x2d,0x93,0xcf,0xc2,0x42,0x3d,0x64,0x98,0x48,0x0b,0x27,0x65,0xba,0xd4,0x33,0x3a,0x9d,0xcf,0x07,0x59,0xbb,0x6f,0x4b,0x67,0x15,0xbd,0xdb,0xea,0xa5,0xa2,0xee,0x00,0x3f,0xe1,0x41,0xfa,0xc6,0x57,0xc9,0x1c,0x9d,0xd4,0xcd,0xca,0xec,0x16,0xaf,0x1f,0xbe,0x0e,0x4f},
{0xa8,0xd5,0xb4,0x42,0x60,0xa5,0x99,0x8a,0xf6,0xac,0x60,0x4e,0x0c,0x81,0x2b,0x8f,0xaa,0x37,0x6e,0xb1,0x6b,0x23,0x9e,0xe0,0x55,0x25,0xc9,0x69,0xa6,0x95,0xb5,0x6b,0xd7,0x71,0x3c,0x93,0xfc,0xe7,0x24,0x92,0xb5,0xf5,0x0f,0x7a,0x96,0x9d,0x46,0x9f,0x02,0x07,0xd6,0xe1,0x65,0x9a,0xa6,0x5a,0x2e,0x2e,0x7d,0xa8,0x3f,0x06,0x0c,0x59,0x02,0x68,0xd3,0xda,0xaa,0x7e,0x34,0x6e,0x05,0x48,0xee,0x83,0x93,0x59,0xf3,0xba,0x26,0x68,0x07,0xe6,0x10,0xbe,0xca,0x3b,0xb8,0xd1,0x5e,0x16,0x0a,0x4f,0x31,0x49},
{0x65,0xd2,0xfc,0xa4,0xe8,0x1f,0x61,0x56,0x7d,0xba,0xc1,0xe5,0xfd,0x53,0xd3,0x3b,0xbd,0xd6,0x4b,0x21,0x1a,0xf3,0x31,0x81,0x62,0xda,0x5b,0x55,0x87,0x15,0xb9,0x2a,0x30,0x97,0xee,0x4c,0xa8,0xb0,0x25,0xaf,0x8a,0x4b,0x86,0xe8,0x30,0x84,0x5a,0x02,0x32,0x67,0x01,0x9f,0x02,0x50,0x1b,0xc1,0xf4,0xf8,0x80,0x9a,0x1b,0x4e,0x16,0x7a,0x34,0x48,0x67,0xf1,0xf4,0x11,0xf2,0x9b,0x95,0xf8,0x2d,0xf6,0x17,0x6b,0x4e,0xb8,0x4e,0x2a,0x72,0x5b,0x07,0x6f,0xde,0xd7,0x21,0x2a,0xbb,0x63,0xb9,0x04,0x9a,0x54},
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{0x33,0x25,0x1f,0x88,0xdc,0x99,0x34,0x28,0xb6,0x23,0x93,0x77,0xda,0x25,0x05,0x9d,0xf4,0x41,0x34,0x67,0xfb,0xdd,0x7a,0x89,0x8d,0x16,0x3a,0x16,0x71,0x9d,0xb7,0x32,0x4b,0x2c,0xcc,0x89,0xd2,0x14,0x73,0xe2,0x8d,0x17,0x87,0xa2,0x11,0xbd,0xe4,0x4b,0xce,0x64,0x33,0xfa,0xd6,0x28,0xd5,0x18,0x6e,0x82,0xd9,0xaf,0xd5,0xc1,0x23,0x64,0x6a,0xb3,0xfc,0xed,0xd9,0xf8,0x85,0xcc,0xf9,0xe5,0x46,0x37,0x8f,0xc2,0xbc,0x22,0xcd,0xd3,0xe5,0xf9,0x38,0xe3,0x9d,0xe4,0xcc,0x2d,0x3e,0xc1,0xfb,0x5e,0x0a,0x48},
{0x71,0x20,0x62,0x01,0x0b,0xe7,0x51,0x0b,0xc5,0xaf,0x1d,0x8b,0xcf,0x05,0xb5,0x06,0xcd,0xab,0x5a,0xef,0x61,0xb0,0x6b,0x2c,0x31,0xbf,0xb7,0x0c,0x60,0x27,0xaa,0x47,0x1f,0x22,0xce,0x42,0xe4,0x4c,0x61,0xb6,0x28,0x39,0x05,0x4c,0xcc,0x9d,0x19,0x6e,0x03,0xbe,0x1c,0xdc,0xa4,0xb4,0x3f,0x66,0x06,0x8e,0x1c,0x69,0x47,0x1d,0xb3,0x24,0xc3,0xf8,0x15,0xc0,0xed,0x1e,0x54,0x2a,0x7c,0x3f,0x69,0x7c,0x7e,0xfe,0xa4,0x11,0xd6,0x78,0xa2,0x4e,0x13,0x66,0xaf,0xf0,0x94,0xa0,0xdd,0x14,0x5d,0x58,0x5b,0x54},
{0x0f,0x3a,0xd4,0xa0,0x5e,0x27,0xbf,0x67,0xbe,0xee,0x9b,0x08,0x34,0x8e,0xe6,0xad,0x2e,0xe7,0x79,0xd4,0x4c,0x13,0x89,0x42,0x54,0x54,0xba,0x32,0xc3,0xf9,0x62,0x0f,0xe1,0x21,0xb3,0xe3,0xd0,0xe4,0x04,0x62,0x95,0x1e,0xff,0x28,0x7a,0x63,0xaa,0x3b,0x9e,0xbd,0x99,0x5b,0xfd,0xcf,0x0c,0x0b,0x71,0xd0,0xc8,0x64,0x3e,0xdc,0x22,0x4d,0x39,0x5f,0x3b,0xd6,0x89,0x65,0xb4,0xfc,0x61,0xcf,0xcb,0x57,0x3f,0x6a,0xae,0x5c,0x05,0xfa,0x3a,0x95,0xd2,0xc2,0xba,0xfe,0x36,0x14,0x37,0x36,0x1a,0xa0,0x0f,0x1c},
{0xff,0x3d,0x94,0x22,0xb6,0x04,0xc6,0xd2,0xa0,0xb3,0xcf,0x44,0xce,0xbe,0x8c,0xbc,0x78,0x86,0x80,0x97,0xf3,0x4f,0x25,0x5d,0xbf,0xa6,0x1c,0x3b,0x4f,0x61,0xa3,0x0f,0x50,0x6a,0x93,0x8c,0x0e,0x2b,0x08,0x69,0xb6,0xc5,0xda,0xc1,0x35,0xa0,0xc9,0xf9,0x34,0xb6,0xdf,0xc4,0x54,0x3e,0xb7,0x6f,0x40,0xc1,0x2b,0x1d,0x9b,0x41,0x05,0x40,0xf0,0x82,0xbe,0xb9,0xbd,0xfe,0x03,0xa0,0x90,0xac,0x44,0x3a,0xaf,0xc1,0x89,0x20,0x8e,0xfa,0x54,0x19,0x91,0x9f,0x49,0xf8,0x42,0xab,0x40,0xef,0x8a,0x21,0xba,0x1f},
{0x3e,0xf5,0xc8,0xfa,0x48,0x94,0x54,0xab,0x41,0x37,0xa6,0x7b,0x9a,0xe8,0xf6,0x81,0x01,0x5e,0x2b,0x6c,0x7d,0x6c,0xfd,0x74,0x42,0x6e,0xc8,0xa8,0xca,0x3a,0x2e,0x39,0x94,0x01,0x7b,0x3e,0x04,0x57,0x3e,0x4f,0x7f,0xaf,0xda,0x08,0xee,0x3e,0x1d,0xa8,0xf1,0xde,0xdc,0x99,0xab,0xc6,0x39,0xc8,0xd5,0x61,0x77,0xff,0x13,0x5d,0x53,0x6c,0xaf,0x35,0x8a,0x3e,0xe9,0x34,0xbd,0x4c,0x16,0xe8,0x87,0x58,0x44,0x81,0x07,0x2e,0xab,0xb0,0x9a,0xf2,0x76,0x9c,0x31,0x19,0x3b,0xc1,0x0a,0xd5,0xe4,0x7f,0xe1,0x25},
{0x76,0xf6,0x04,0x1e,0xd7,0x9b,0x28,0x0a,0x95,0x0f,0x42,0xd6,0x52,0x1c,0x8e,0x20,0xab,0x1f,0x69,0x34,0xb0,0xd8,0x86,0x51,0x51,0xb3,0x9f,0x2a,0x44,0x51,0x57,0x25,0xa7,0x21,0xf1,0x76,0xf5,0x7f,0x5f,0x91,0xe3,0x87,0xcd,0x2f,0x27,0x32,0x4a,0xc3,0x26,0xe5,0x1b,0x4d,0xde,0x2f,0xba,0xcc,0x9b,0x89,0x69,0x89,0x8f,0x82,0xba,0x6b,0x01,0x39,0xfe,0x90,0x66,0xbc,0xd1,0xe2,0xd5,0x7a,0x99,0xa0,0x18,0x4a,0xb5,0x4c,0xd4,0x60,0x84,0xaf,0x14,0x69,0x1d,0x97,0xe4,0x7b,0x6b,0x7f,0x4f,0x50,0x9d,0x55},
{0xd5,0x54,0xeb,0xb3,0x78,0x83,0x73,0xa7,0x7c,0x3c,0x55,0xa5,0x66,0xd3,0x69,0x1d,0xba,0x00,0x28,0xf9,0x62,0xcf,0x26,0x0a,0x17,0x32,0x7e,0x80,0xd5,0x12,0xab,0x01,0xfd,0x66,0xd2,0xf6,0xe7,0x91,0x48,0x9c,0x1b,0x78,0x07,0x03,0x9b,0xa1,0x44,0x07,0x3b,0xe2,0x61,0x60,0x1d,0x8f,0x38,0x88,0x0e,0xd5,0x4b,0x35,0xa3,0xa6,0x3e,0x12,0x96,0x2d,0xe3,0x41,0x90,0x18,0x8d,0x11,0x48,0x58,0x31,0xd8,0xc2,0xe3,0xed,0xb9,0xd9,0x45,0x32,0xd8,0x71,0x42,0xab,0x1e,0x54,0xa1,0x18,0xc9,0xe2,0x61,0x39,0x4a},
{0xa0,0xbb,0xe6,0xf8,0xe0,0x3b,0xdc,0x71,0x0a,0xe3,0xff,0x7e,0x34,0xf8,0xce,0xd6,0x6a,0x47,0x3a,0xe1,0x5f,0x42,0x92,0xa9,0x63,0xb7,0x1d,0xfb,0xe3,0xbc,0xd6,0x2c,0x1e,0x3f,0x23,0xf3,0x44,0xd6,0x27,0x03,0x16,0xf0,0xfc,0x34,0x0e,0x26,0x9a,0x49,0x79,0xb9,0xda,0xf2,0x16,0xa7,0xb5,0x83,0x1f,0x11,0xd4,0x9b,0xad,0xee,0xac,0x68,0x10,0xc2,0xd7,0xf3,0x0e,0xc9,0xb4,0x38,0x0c,0x04,0xad,0xb7,0x24,0x6e,0x8e,0x30,0x23,0x3e,0xe7,0xb7,0xf1,0xd9,0x60,0x38,0x97,0xf5,0x08,0xb5,0xd5,0x60,0x57,0x59},
{0x97,0x63,0xaa,0x04,0xe1,0xbf,0x29,0x61,0xcb,0xfc,0xa7,0xa4,0x08,0x00,0x96,0x8f,0x58,0x94,0x90,0x7d,0x89,0xc0,0x8b,0x3f,0xa9,0x91,0xb2,0xdc,0x3e,0xa4,0x9f,0x70,0x90,0x27,0x02,0xfd,0xeb,0xcb,0x2a,0x88,0x60,0x57,0x11,0xc4,0x05,0x33,0xaf,0x89,0xf4,0x73,0x34,0x7d,0xe3,0x92,0xf4,0x65,0x2b,0x5a,0x51,0x54,0xdf,0xc5,0xb2,0x2c,0xca,0x2a,0xfd,0x63,0x8c,0x5d,0x0a,0xeb,0xff,0x4e,0x69,0x2e,0x66,0xc1,0x2b,0xd2,0x3a,0xb0,0xcb,0xf8,0x6e,0xf3,0x23,0x27,0x1f,0x13,0xc8,0xf0,0xec,0x29,0xf0,0x70},
{0x33,0x3e,0xed,0x2e,0xb3,0x07,0x13,0x46,0xe7,0x81,0x55,0xa4,0x33,0x2f,0x04,0xae,0x66,0x03,0x5f,0x19,0xd3,0x49,0x44,0xc9,0x58,0x48,0x31,0x6c,0x8a,0x5d,0x7d,0x0b,0xb9,0xb0,0x10,0x5e,0xaa,0xaf,0x6a,0x2a,0xa9,0x1a,0x04,0xef,0x70,0xa3,0xf0,0x78,0x1f,0xd6,0x3a,0xaa,0x77,0xfb,0x3e,0x77,0xe1,0xd9,0x4b,0xa7,0xa2,0xa5,0xec,0x44,0x43,0xd5,0x95,0x7b,0x32,0x48,0xd4,0x25,0x1d,0x0f,0x34,0xa3,0x00,0x83,0xd3,0x70,0x2b,0xc5,0xe1,0x60,0x1c,0x53,0x1c,0xde,0xe4,0xe9,0x7d,0x2c,0x51,0x24,0x22,0x27},
{0x2e,0x34,0xc5,0x49,0xaf,0x92,0xbc,0x1a,0xd0,0xfa,0xe6,0xb2,0x11,0xd8,0xee,0xff,0x29,0x4e,0xc8,0xfc,0x8d,0x8c,0xa2,0xef,0x43,0xc5,0x4c,0xa4,0x18,0xdf,0xb5,0x11,0xfc,0x75,0xa9,0x42,0x8a,0xbb,0x7b,0xbf,0x58,0xa3,0xad,0x96,0x77,0x39,0x5c,0x8c,0x48,0xaa,0xed,0xcd,0x6f,0xc7,0x7f,0xe2,0xa6,0x20,0xbc,0xf6,0xd7,0x5f,0x73,0x19,0x66,0x42,0xc8,0x42,0xd0,0x90,0xab,0xe3,0x7e,0x54,0x19,0x7f,0x0f,0x8e,0x84,0xeb,0xb9,0x97,0xa4,0x65,0xd0,0xa1,0x03,0x25,0x5f,0x89,0xdf,0x91,0x11,0x91,0xef,0x0f}
};
NAMESPACE_END // Arch64
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_DONNA_64_H

64
donna_sse.cpp
View File

@ -20,10 +20,6 @@
#include "secblock.h"
#include "misc.h"
#if (CRYPTOPP_CURVE25519_SSE2)
# include <emmintrin.h>
#endif
// The data is aligned, but Clang issues warning based on type
// and not the actual alignment of the variable and data.
#if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
@ -35,8 +31,7 @@ extern const char DONNA_SSE_FNAME[] = __FILE__;
#if (CRYPTOPP_CURVE25519_SSE2)
typedef __m128i xmmi;
#define ALIGN(n) CRYPTOPP_ALIGN_DATA(n)
#include "donna_sse.h"
ANONYMOUS_NAMESPACE_BEGIN
@ -45,62 +40,11 @@ using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;
typedef union packedelem8_t {
byte u[16];
xmmi v;
} packedelem8;
typedef union packedelem32_t {
word32 u[4];
xmmi v;
} packedelem32;
typedef union packedelem64_t {
word64 u[2];
xmmi v;
} packedelem64;
/* 10 elements + an extra 2 to fit in 3 xmm registers */
typedef word32 bignum25519[12];
typedef packedelem32 packed32bignum25519[5];
typedef packedelem64 packed64bignum25519[10];
const word32 reduce_mask_26 = (1 << 26) - 1;
const word32 reduce_mask_25 = (1 << 25) - 1;
const packedelem32 sse2_bot32bitmask = {{0xffffffff, 0x00000000, 0xffffffff, 0x00000000}};
const packedelem32 sse2_top32bitmask = {{0x00000000, 0xffffffff, 0x00000000, 0xffffffff}};
const packedelem32 sse2_top64bitmask = {{0x00000000, 0x00000000, 0xffffffff, 0xffffffff}};
const packedelem32 sse2_bot64bitmask = {{0xffffffff, 0xffffffff, 0x00000000, 0x00000000}};
/* reduction masks */
const packedelem64 packedmask26 = {{0x03ffffff, 0x03ffffff}};
const packedelem64 packedmask25 = {{0x01ffffff, 0x01ffffff}};
const packedelem32 packedmask2625 = {{0x3ffffff,0,0x1ffffff,0}};
const packedelem32 packedmask26262626 = {{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff}};
const packedelem32 packedmask25252525 = {{0x01ffffff, 0x01ffffff, 0x01ffffff, 0x01ffffff}};
/* multipliers */
const packedelem64 packednineteen = {{19, 19}};
const packedelem64 packednineteenone = {{19, 1}};
const packedelem64 packedthirtyeight = {{38, 38}};
const packedelem64 packed3819 = {{19*2,19}};
const packedelem64 packed9638 = {{19*4,19*2}};
/* 121666,121665 */
const packedelem64 packed121666121665 = {{121666, 121665}};
/* 2*(2^255 - 19) = 0 mod p */
const packedelem32 packed2p0 = {{0x7ffffda,0x3fffffe,0x7fffffe,0x3fffffe}};
const packedelem32 packed2p1 = {{0x7fffffe,0x3fffffe,0x7fffffe,0x3fffffe}};
const packedelem32 packed2p2 = {{0x7fffffe,0x3fffffe,0x0000000,0x0000000}};
const packedelem32 packed32zeromodp0 = {{0x7ffffda,0x7ffffda,0x3fffffe,0x3fffffe}};
const packedelem32 packed32zeromodp1 = {{0x7fffffe,0x7fffffe,0x3fffffe,0x3fffffe}};
// Bring in all the symbols from the SSE header
using namespace CryptoPP::Donna::ArchSSE;
/* Copy a bignum to another: out = in */
inline void
@ -1103,7 +1047,7 @@ ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
int curve25519_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
int curve25519_mult_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
{
FixedSizeSecBlock<byte, 32> e;
for (size_t i = 0;i < 32;++i)

84
donna_sse.h Normal file
View File

@ -0,0 +1,84 @@
// donna_sse.h - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// This source file multiplexes two different repos using namespaces. This
// was a little easier from a project management standpoint. We only need
// two files per architecture at the expense of namespaces and bloat.
#ifndef CRYPTOPP_DONNA_SSE_H
#define CRYPTOPP_DONNA_SSE_H
#include "config.h"
#include <emmintrin.h>
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(ArchSSE)
using CryptoPP::byte;
using CryptoPP::word32;
typedef __m128i xmmi;
#define ALIGN(n) CRYPTOPP_ALIGN_DATA(n)
typedef union packedelem8_t {
byte u[16];
xmmi v;
} packedelem8;
typedef union packedelem32_t {
word32 u[4];
xmmi v;
} packedelem32;
typedef union packedelem64_t {
word64 u[2];
xmmi v;
} packedelem64;
/* 10 elements + an extra 2 to fit in 3 xmm registers */
typedef word32 bignum25519[12];
typedef packedelem32 packed32bignum25519[5];
typedef packedelem64 packed64bignum25519[10];
const word32 reduce_mask_26 = (1 << 26) - 1;
const word32 reduce_mask_25 = (1 << 25) - 1;
const packedelem32 sse2_bot32bitmask = {{0xffffffff, 0x00000000, 0xffffffff, 0x00000000}};
const packedelem32 sse2_top32bitmask = {{0x00000000, 0xffffffff, 0x00000000, 0xffffffff}};
const packedelem32 sse2_top64bitmask = {{0x00000000, 0x00000000, 0xffffffff, 0xffffffff}};
const packedelem32 sse2_bot64bitmask = {{0xffffffff, 0xffffffff, 0x00000000, 0x00000000}};
/* reduction masks */
const packedelem64 packedmask26 = {{0x03ffffff, 0x03ffffff}};
const packedelem64 packedmask25 = {{0x01ffffff, 0x01ffffff}};
const packedelem32 packedmask2625 = {{0x3ffffff,0,0x1ffffff,0}};
const packedelem32 packedmask26262626 = {{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff}};
const packedelem32 packedmask25252525 = {{0x01ffffff, 0x01ffffff, 0x01ffffff, 0x01ffffff}};
/* multipliers */
const packedelem64 packednineteen = {{19, 19}};
const packedelem64 packednineteenone = {{19, 1}};
const packedelem64 packedthirtyeight = {{38, 38}};
const packedelem64 packed3819 = {{19*2,19}};
const packedelem64 packed9638 = {{19*4,19*2}};
/* 121666,121665 */
const packedelem64 packed121666121665 = {{121666, 121665}};
/* 2*(2^255 - 19) = 0 mod p */
const packedelem32 packed2p0 = {{0x7ffffda,0x3fffffe,0x7fffffe,0x3fffffe}};
const packedelem32 packed2p1 = {{0x7fffffe,0x3fffffe,0x7fffffe,0x3fffffe}};
const packedelem32 packed2p2 = {{0x7fffffe,0x3fffffe,0x0000000,0x0000000}};
const packedelem32 packed32zeromodp0 = {{0x7ffffda,0x7ffffda,0x3fffffe,0x3fffffe}};
const packedelem32 packed32zeromodp1 = {{0x7fffffe,0x7fffffe,0x3fffffe,0x3fffffe}};
NAMESPACE_END // ArchSSE
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_DONNA_SSE_H

4
eccrypto.cpp
View File

@ -490,7 +490,7 @@ bool DL_GroupParameters_EC<EC>::GetVoidValue(const char *name, const std::type_i
{
if (strcmp(name, Name::GroupOID()) == 0)
{
if (m_oid.GetValues().empty())
if (m_oid.Empty())
return false;
this->ThrowIfTypeMismatch(name, typeid(OID), valueType);
@ -568,7 +568,7 @@ void DL_GroupParameters_EC<EC>::BERDecode(BufferedTransformation &bt)
template <class EC>
void DL_GroupParameters_EC<EC>::DEREncode(BufferedTransformation &bt) const
{
if (m_encodeAsOID && !m_oid.GetValues().empty())
if (m_encodeAsOID && !m_oid.Empty())
m_oid.DEREncode(bt);
else
{

4
pubkey.h
View File

@ -1050,7 +1050,7 @@ public:
CRYPTOPP_GET_FUNCTION_ENTRY(PublicElement);
}
/// \brief Initialize or reinitialize this this key
/// \brief Initialize or reinitialize this key
/// \param source NameValuePairs to assign
void AssignFrom(const NameValuePairs &source);
@ -1135,7 +1135,7 @@ public:
CRYPTOPP_GET_FUNCTION_ENTRY(PrivateExponent);
}
/// \brief Initialize or reinitialize this this key
/// \brief Initialize or reinitialize this key
/// \param source NameValuePairs to assign
void AssignFrom(const NameValuePairs &source)
{

4
validat3.cpp
View File

@ -87,7 +87,7 @@ bool ValidateAll(bool thorough)
pass=TestCompressors() && pass;
pass=TestSharing() && pass;
pass=TestEncryptors() && pass;
pass=TestCurve25519() && pass;
pass=TestX25519() && pass;
#endif
pass=ValidateCRC32() && pass;
@ -193,6 +193,8 @@ bool ValidateAll(bool thorough)
pass=ValidateECGDSA(thorough) && pass;
pass=ValidateESIGN() && pass;
pass=ValidateX25519() && pass;
pass=ValidateEd25519() && pass;
pass=ValidateNaCl() && pass;
if (pass)

2
validat6.cpp
View File

@ -143,7 +143,7 @@ bool SignatureValidate(PK_Signer &priv, PK_Verifier &pub, bool thorough)
std::cout << (fail ? "FAILED " : "passed ");
std::cout << "signature key validation\n";
const byte *message = (byte *)"test message";
const byte message[] = "test message";
const int messageLen = 12;
SecByteBlock signature(priv.MaxSignatureLength());

125
validat7.cpp
View File

@ -356,10 +356,10 @@ bool ValidateEC2N_Agreement()
return pass;
}
// TestCurve25519 is slighty more comprehensive than ValidateX25519
// TestX25519 is slighty more comprehensive than ValidateX25519
// because it cross-validates against Bernstein's NaCL library.
// TestCurve25519 called in Debug builds.
bool TestCurve25519()
// TestX25519 called in Debug builds.
bool TestX25519()
{
std::cout << "\nTesting curve25519 Key Agreements...\n\n";
const unsigned int AGREE_COUNT = 64;
@ -375,11 +375,11 @@ bool TestCurve25519()
priv2[0] &= 248; priv2[31] &= 127; priv2[31] |= 64;
// Andrew Moon's curve25519-donna
Donna::curve25519(pub1, priv1);
Donna::curve25519(pub2, priv2);
Donna::curve25519_mult(pub1, priv1);
Donna::curve25519_mult(pub2, priv2);
int ret1 = Donna::curve25519(share1, priv1, pub2);
int ret2 = Donna::curve25519(share2, priv2, pub1);
int ret1 = Donna::curve25519_mult(share1, priv1, pub2);
int ret2 = Donna::curve25519_mult(share2, priv2, pub1);
int ret3 = std::memcmp(share1, share2, 32);
#if defined(NO_OS_DEPENDENCE)
@ -388,7 +388,7 @@ bool TestCurve25519()
// Bernstein's NaCl requires DefaultAutoSeededRNG.
NaCl::crypto_box_keypair(pub2, priv2);
int ret4 = Donna::curve25519(share1, priv1, pub2);
int ret4 = Donna::curve25519_mult(share1, priv1, pub2);
int ret5 = NaCl::crypto_scalarmult(share2, priv2, pub1);
int ret6 = std::memcmp(share1, share2, 32);
#endif
@ -406,5 +406,114 @@ bool TestCurve25519()
return pass;
}
// TestEd25519 is slighty more comprehensive than ValidateEd25519
// because it cross-validates against Bernstein's NaCL library.
// TestEd25519 called in Debug builds.
bool TestEd25519()
{
std::cout << "\nTesting ed25519 Signatures...\n\n";
const unsigned int SIGN_COUNT = 64, MSG_SIZE=128;
const unsigned int NACL_EXTRA=NaCl::crypto_sign_BYTES;
bool pass = true;
// Test key conversion
byte seed[32], sk1[64], sk2[64], pk1[32], pk2[32];
for (unsigned int i = 0; i<SIGN_COUNT; ++i)
{
GlobalRNG().GenerateBlock(seed, 32);
std::memcpy(sk1, seed, 32);
std::memcpy(sk2, seed, 32);
int ret1 = NaCl::crypto_sign_sk2pk(pk1, sk1);
int ret2 = Donna::ed25519_publickey(pk2, sk2);
int ret3 = std::memcmp(pk1, pk2, 32);
bool fail = ret1 != 0 || ret2 != 0 || ret3 != 0;
pass = pass && !fail;
}
if (pass)
std::cout << "passed:";
else
std::cout << "FAILED:";
std::cout << " " << SIGN_COUNT << " public keys" << std::endl;
// Test signature generation
for (unsigned int i = 0; i<SIGN_COUNT; ++i)
{
// Fresh keypair
(void)NaCl::crypto_sign_keypair(pk1, sk1);
std::memcpy(sk2, sk1, 32);
std::memcpy(pk2, pk1, 32);
// Message and signatures
byte msg[MSG_SIZE], sig1[MSG_SIZE+NACL_EXTRA], sig2[64];
GlobalRNG().GenerateBlock(msg, MSG_SIZE);
// Spike the signatures
sig1[1] = 1; sig2[2] = 2;
word64 smlen = sizeof(sig1);
int ret1 = NaCl::crypto_sign(sig1, &smlen, msg, MSG_SIZE, sk1);
int ret2 = Donna::ed25519_sign(msg, MSG_SIZE, sk2, pk2, sig2);
int ret3 = std::memcmp(sig1, sig2, 64);
bool fail = ret1 != 0 || ret2 != 0 || ret3 != 0;
pass = pass && !fail;
}
if (pass)
std::cout << "passed:";
else
std::cout << "FAILED:";
std::cout << " " << SIGN_COUNT << " signatures" << std::endl;
// Test signature verification
for (unsigned int i = 0; i<SIGN_COUNT; ++i)
{
// Fresh keypair
(void)NaCl::crypto_sign_keypair(pk1, sk1);
std::memcpy(sk2, sk1, 32);
std::memcpy(pk2, pk1, 32);
// Message and signatures
byte msg1[MSG_SIZE+NACL_EXTRA], msg2[MSG_SIZE];
byte sig1[MSG_SIZE+NACL_EXTRA], sig2[64];
GlobalRNG().GenerateBlock(msg1, MSG_SIZE);
std::memcpy(msg2, msg1, MSG_SIZE);
// Spike the signatures
sig1[1] = 1; sig2[2] = 2;
word64 smlen = sizeof(sig1);
int ret1 = NaCl::crypto_sign(sig1, &smlen, msg1, MSG_SIZE, sk1);
int ret2 = Donna::ed25519_sign(msg2, MSG_SIZE, sk2, pk2, sig2);
int ret3 = std::memcmp(sig1, sig2, 64);
bool tamper = !!GlobalRNG().GenerateBit();
if (tamper)
{
sig1[1] ^= 1;
sig2[1] ^= 1;
}
// Verify the other's signature using the other's key
word64 mlen = MSG_SIZE+NACL_EXTRA;
int ret4 = NaCl::crypto_sign_open(msg1, &mlen, sig1, smlen, pk2);
int ret5 = Donna::ed25519_sign_open(msg2, MSG_SIZE, pk1, sig2);
bool fail = ret1 != 0 || ret2 != 0 || ret3 != 0 || ((ret4 != 0) ^ tamper) || ((ret5 != 0) ^ tamper);
pass = pass && !fail;
}
if (pass)
std::cout << "passed:";
else
std::cout << "FAILED:";
std::cout << " " << SIGN_COUNT << " verifications" << std::endl;
return pass;
}
NAMESPACE_END // Test
NAMESPACE_END // CryptoPP

33
validat9.cpp
View File

@ -32,6 +32,11 @@
#include "pubkey.h"
#include "eccrypto.h"
// Curve25519
#include "xed25519.h"
#include "donna.h"
#include "naclite.h"
#include <iostream>
#include <iomanip>
#include <sstream>
@ -667,5 +672,33 @@ bool ValidateESIGN()
return pass;
}
bool ValidateEd25519()
{
std::cout << "\ned25519 validation suite running...\n\n";
bool pass = true, fail;
const char plain[] = "test";
const byte signature[] =
"\x91\x12\x44\x91\xA5\x99\xF8\x49\xBA\xB2\xC4\xF2\xBA\x0B\xAA\x99"
"\xC8\xC5\xF5\x19\xDC\x07\xD4\x4C\xF7\x31\xDE\x2F\x2B\x81\xB2\x81"
"\xF6\xA7\xDE\x33\x29\xCA\x45\xAC\x69\x2A\x80\xB7\xDB\x7F\x07\x37"
"\x77\xC4\xBF\xC5\x45\x79\x3A\xAC\xB5\x16\xAE\x4E\xD9\x16\x95\x0E";
FileSource keys(DataDir("TestData/ed25519.dat").c_str(), true, new HexDecoder);
ed25519::Signer signer(keys);
ed25519::Verifier verifier(signer);
fail = !SignatureValidate(signer, verifier);
pass = pass && !fail;
fail = !verifier.VerifyMessage((byte *)plain, strlen(plain), signature, verifier.SignatureLength());
pass = pass && !fail;
std::cout << (fail ? "FAILED " : "passed ");
std::cout << "verification check against test vector\n";
return pass;
}
NAMESPACE_END // Test
NAMESPACE_END // CryptoPP

6
validate.h
View File

@ -109,7 +109,6 @@ bool ValidateCMAC();
bool ValidateBBS();
bool ValidateDH();
bool ValidateX25519();
bool ValidateMQV();
bool ValidateHMQV();
bool ValidateFHMQV();
@ -134,7 +133,10 @@ bool ValidateESIGN();
bool ValidateHashDRBG();
bool ValidateHmacDRBG();
bool TestCurve25519();
bool TestX25519();
bool TestEd25519();
bool ValidateX25519();
bool ValidateEd25519();
bool ValidateNaCl();
// If CRYPTOPP_DEBUG or CRYPTOPP_COVERAGE is in effect, then perform additional tests

810
xed25519.cpp
View File

@ -1,7 +1,8 @@
// xed25519.cpp - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna. Also see
// https://github.com/floodyberry/curve25519-donna.
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
#include "pch.h"
@ -9,6 +10,7 @@
#include "asn.h"
#include "integer.h"
#include "filters.h"
#include "stdcpp.h"
#include "xed25519.h"
#include "donna.h"
@ -43,23 +45,81 @@ const byte blacklist[][32] = {
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff },
{ 0xdb, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff }
};
};
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
bool x25519::IsClamped(const byte x[32])
// ******************** x25519 Agreement ************************* //
x25519::x25519(const byte y[PUBLIC_KEYLENGTH], const byte x[SECRET_KEYLENGTH])
{
std::memcpy(m_pk, y, SECRET_KEYLENGTH);
std::memcpy(m_sk, x, PUBLIC_KEYLENGTH);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(const byte x[SECRET_KEYLENGTH])
{
std::memcpy(m_sk, x, SECRET_KEYLENGTH);
Donna::curve25519_mult(m_pk, m_sk);
}
x25519::x25519(const Integer &y, const Integer &x)
{
CRYPTOPP_ASSERT(y.MinEncodedSize() <= PUBLIC_KEYLENGTH);
CRYPTOPP_ASSERT(x.MinEncodedSize() <= SECRET_KEYLENGTH);
y.Encode(m_pk, PUBLIC_KEYLENGTH); std::reverse(m_pk+0, m_pk+PUBLIC_KEYLENGTH);
x.Encode(m_sk, SECRET_KEYLENGTH); std::reverse(m_sk+0, m_sk+SECRET_KEYLENGTH);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(const Integer &x)
{
CRYPTOPP_ASSERT(x.MinEncodedSize() <= SECRET_KEYLENGTH);
x.Encode(m_sk, SECRET_KEYLENGTH);
std::reverse(m_sk+0, m_sk+SECRET_KEYLENGTH);
Donna::curve25519_mult(m_pk, m_sk);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(RandomNumberGenerator &rng)
{
rng.GenerateBlock(m_sk, SECRET_KEYLENGTH);
m_sk[0] &= 248; m_sk[31] &= 127; m_sk[31] |= 64;
Donna::curve25519_mult(m_pk, m_sk);
}
x25519::x25519(BufferedTransformation &params)
{
Load(params);
}
void x25519::ClampKeys(byte y[PUBLIC_KEYLENGTH], byte x[SECRET_KEYLENGTH]) const
{
x[0] &= 248; x[31] &= 127; x[31] |= 64;
Donna::curve25519_mult(y, x);
}
bool x25519::IsClamped(const byte x[SECRET_KEYLENGTH]) const
{
return (x[0] & 248) == x[0] && (x[31] & 127) == x[31] && (x[31] | 64) == x[31];
}
// See the comments for the code in tweetnacl.cpp
bool x25519::IsSmallOrder(const byte y[32])
bool x25519::IsSmallOrder(const byte y[PUBLIC_KEYLENGTH]) const
{
// The magic 12 is the count of blaklisted points
byte c[12] = { 0 };
for (size_t j = 0; j < 32; j++) {
for (size_t j = 0; j < PUBLIC_KEYLENGTH; j++) {
for (size_t i = 0; i < COUNTOF(blacklist); i++) {
c[i] |= y[j] ^ blacklist[i][j];
}
@ -70,120 +130,120 @@ bool x25519::IsSmallOrder(const byte y[32])
k |= (c[i] - 1);
}
return (bool) ((k >> 8) & 1);
return (bool)((k >> 8) & 1);
}
void x25519::ClampKey(byte x[32])
void x25519::BERDecodeAndCheckAlgorithmID(BufferedTransformation &bt)
{
x[0] &= 248;
x[31] &= 127;
x[31] |= 64;
// We have not yet determined the OID to use for this object.
// We can't use OID's decoder because it throws BERDecodeError
// if the OIDs do not match.
OID oid(bt);
if (!m_oid.Empty() && m_oid != oid)
BERDecodeError(); // Only accept user specified OID
else if (oid == ASN1::curve25519() || oid == ASN1::X25519())
m_oid = oid; // Accept any of the x25519 OIDs
else
BERDecodeError();
}
x25519::x25519(const byte y[32], const byte x[32])
void x25519::BERDecode(BufferedTransformation &bt)
{
std::memcpy(m_pk, y, 32);
std::memcpy(m_sk, x, 32);
// https://tools.ietf.org/html/rfc8410, section 7 and
// https://www.cryptopp.com/wiki/curve25519_keys
BERSequenceDecoder privateKeyInfo(bt);
word32 version;
BERDecodeUnsigned<word32>(privateKeyInfo, version, INTEGER, 0, 1); // check version
BERSequenceDecoder algorithm(privateKeyInfo);
// GetAlgorithmID().BERDecodeAndCheck(algorithm);
BERDecodeAndCheckAlgorithmID(algorithm);
algorithm.MessageEnd();
BERGeneralDecoder octetString(privateKeyInfo, OCTET_STRING);
BERDecodePrivateKey(octetString, false, (size_t)privateKeyInfo.RemainingLength());
octetString.MessageEnd();
bool generatePublicKey = true;
if (version == 1)
{
BERGeneralDecoder publicKey(privateKeyInfo, CONTEXT_SPECIFIC | CONSTRUCTED | 1);
SecByteBlock subjectPublicKey;
unsigned int unusedBits;
BERDecodeBitString(publicKey, subjectPublicKey, unusedBits);
CRYPTOPP_ASSERT(unusedBits == 0);
CRYPTOPP_ASSERT(subjectPublicKey.size() == PUBLIC_KEYLENGTH);
if (subjectPublicKey.size() != PUBLIC_KEYLENGTH)
BERDecodeError();
std::memcpy(m_pk.begin(), subjectPublicKey, PUBLIC_KEYLENGTH);
generatePublicKey = false;
publicKey.MessageEnd();
}
privateKeyInfo.MessageEnd();
if (generatePublicKey)
Donna::curve25519_mult(m_pk, m_sk);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(const byte x[32])
void x25519::DEREncode(BufferedTransformation &bt, int version) const
{
std::memcpy(m_sk, x, 32);
GeneratePublicKey(NullRNG(), m_sk, m_pk);
// https://tools.ietf.org/html/rfc8410, section 7 and
// https://www.cryptopp.com/wiki/curve25519_keys
CRYPTOPP_ASSERT(version == 0 || version == 1);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
DERSequenceEncoder privateKeyInfo(bt);
DEREncodeUnsigned<word32>(privateKeyInfo, version);
DERSequenceEncoder algorithm(privateKeyInfo);
GetAlgorithmID().DEREncode(algorithm);
algorithm.MessageEnd();
DERGeneralEncoder octetString(privateKeyInfo, OCTET_STRING);
DEREncodePrivateKey(octetString);
octetString.MessageEnd();
if (version == 1)
{
DERGeneralEncoder publicKey(privateKeyInfo, CONTEXT_SPECIFIC | CONSTRUCTED | 1);
DEREncodeBitString(publicKey, m_pk, PUBLIC_KEYLENGTH);
publicKey.MessageEnd();
}
privateKeyInfo.MessageEnd();
}
x25519::x25519(const Integer &y, const Integer &x)
void x25519::BERDecodePrivateKey(BufferedTransformation &bt, bool parametersPresent, size_t /*size*/)
{
ArraySink ys(m_pk, 32);
y.Encode(ys, 32);
// https://tools.ietf.org/html/rfc8410 and
// https://www.cryptopp.com/wiki/curve25519_keys
ArraySink xs(m_sk, 32);
x.Encode(xs, 32);
BERGeneralDecoder privateKey(bt, OCTET_STRING);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
if (!privateKey.IsDefiniteLength())
BERDecodeError();
size_t size = privateKey.Get(m_sk, SECRET_KEYLENGTH);
if (size != SECRET_KEYLENGTH)
BERDecodeError();
// We don't know how to decode them
if (parametersPresent)
BERDecodeError();
privateKey.MessageEnd();
}
x25519::x25519(const Integer &x)
void x25519::DEREncodePrivateKey(BufferedTransformation &bt) const
{
ArraySink xs(m_sk, 32);
x.Encode(xs, 32);
GeneratePublicKey(NullRNG(), m_sk, m_pk);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(RandomNumberGenerator &rng)
{
GeneratePrivateKey(rng, m_sk);
GeneratePublicKey(NullRNG(), m_sk, m_pk);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
x25519::x25519(BufferedTransformation &params)
{
// TODO: Fix the on-disk format once we determine what it is.
BERSequenceDecoder seq(params);
size_t read; byte unused;
BERSequenceDecoder sk(seq, BIT_STRING);
CRYPTOPP_ASSERT(sk.MaxRetrievable() >= 33);
read = sk.Get(unused); // unused bits
CRYPTOPP_ASSERT(read == 1 && unused == 0);
read = sk.Get(m_sk, 32);
sk.MessageEnd();
if (read != 32)
throw BERDecodeErr();
if (seq.EndReached())
{
GeneratePublicKey(NullRNG(), m_sk, m_pk);
}
else
{
BERSequenceDecoder pk(seq, OCTET_STRING);
CRYPTOPP_ASSERT(pk.MaxRetrievable() >= 32);
read = pk.Get(m_pk, 32);
pk.MessageEnd();
if (read != 32)
throw BERDecodeErr();
}
seq.MessageEnd();
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
CRYPTOPP_ASSERT(IsSmallOrder(m_pk) == false);
}
void x25519::DEREncode(BufferedTransformation &params) const
{
// TODO: Fix the on-disk format once we determine what it is.
DERSequenceEncoder seq(params);
DERSequenceEncoder sk(seq, BIT_STRING);
sk.Put((byte)0); // unused bits
sk.Put(m_sk, 32);
sk.MessageEnd();
DERSequenceEncoder pk(seq, OCTET_STRING);
pk.Put(m_pk, 32);
pk.MessageEnd();
seq.MessageEnd();
// https://tools.ietf.org/html/rfc8410
DERGeneralEncoder privateKey(bt, OCTET_STRING);
privateKey.Put(m_sk, SECRET_KEYLENGTH);
privateKey.MessageEnd();
}
bool x25519::Validate(RandomNumberGenerator &rng, unsigned int level) const
@ -202,18 +262,28 @@ bool x25519::Validate(RandomNumberGenerator &rng, unsigned int level) const
bool x25519::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
if (valueType == typeid(ConstByteArrayParameter))
if (std::strcmp(name, Name::PrivateExponent()) == 0 || std::strcmp(name, "SecretKey") == 0)
{
if (std::strcmp(name, "SecretKey") == 0)
{
std::memcpy(pValue, m_sk, 32);
return true;
}
else if (std::strcmp(name, "PublicKey") == 0)
{
std::memcpy(pValue, m_pk, 32);
return true;
}
this->ThrowIfTypeMismatch(name, typeid(ConstByteArrayParameter), valueType);
reinterpret_cast<ConstByteArrayParameter*>(pValue)->Assign(m_sk, SECRET_KEYLENGTH, false);
return true;
}
if (std::strcmp(name, Name::PublicElement()) == 0)
{
this->ThrowIfTypeMismatch(name, typeid(ConstByteArrayParameter), valueType);
reinterpret_cast<ConstByteArrayParameter*>(pValue)->Assign(m_pk, PUBLIC_KEYLENGTH, false);
return true;
}
if (std::strcmp(name, Name::GroupOID()) == 0)
{
if (m_oid.Empty())
return false;
this->ThrowIfTypeMismatch(name, typeid(OID), valueType);
*reinterpret_cast<OID *>(pValue) = m_oid;
return true;
}
return false;
@ -222,27 +292,44 @@ bool x25519::GetVoidValue(const char *name, const std::type_info &valueType, voi
void x25519::AssignFrom(const NameValuePairs &source)
{
ConstByteArrayParameter val;
if (source.GetValue("SecretKey", val))
if (source.GetValue(Name::PrivateExponent(), val) || source.GetValue("SecretKey", val))
{
std::memcpy(m_sk, val.begin(), 32);
std::memcpy(m_sk, val.begin(), SECRET_KEYLENGTH);
}
else if (source.GetValue("PublicKey", val))
if (source.GetValue(Name::PublicElement(), val))
{
std::memcpy(m_pk, val.begin(), 32);
std::memcpy(m_pk, val.begin(), PUBLIC_KEYLENGTH);
}
OID oid;
if (source.GetValue(Name::GroupOID(), oid))
{
m_oid = oid;
}
}
void x25519::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params)
{
ConstByteArrayParameter seed;
if (params.GetValue(Name::Seed(), seed) && rng.CanIncorporateEntropy())
rng.IncorporateEntropy(seed.begin(), seed.size());
rng.GenerateBlock(m_sk, SECRET_KEYLENGTH);
m_sk[0] &= 248; m_sk[31] &= 127; m_sk[31] |= 64;
Donna::curve25519_mult(m_pk, m_sk);
}
void x25519::GeneratePrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
{
rng.GenerateBlock(privateKey, 32);
ClampKey(privateKey);
rng.GenerateBlock(privateKey, SECRET_KEYLENGTH);
privateKey[0] &= 248; privateKey[31] &= 127; privateKey[31] |= 64;
}
void x25519::GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
{
CRYPTOPP_UNUSED(rng);
(void)Donna::curve25519(publicKey, privateKey);
Donna::curve25519_mult(publicKey, privateKey);
}
bool x25519::Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey) const
@ -253,7 +340,490 @@ bool x25519::Agree(byte *agreedValue, const byte *privateKey, const byte *otherP
if (validateOtherPublicKey && IsSmallOrder(otherPublicKey))
return false;
return Donna::curve25519(agreedValue, privateKey, otherPublicKey) == 0;
return Donna::curve25519_mult(agreedValue, privateKey, otherPublicKey) == 0;
}
// ******************** ed25519 Signer ************************* //
void ed25519PrivateKey::ClampKeys(byte y[PUBLIC_KEYLENGTH], byte x[SECRET_KEYLENGTH]) const
{
x[0] &= 248; x[31] &= 127; x[31] |= 64;
int ret = Donna::ed25519_publickey(y, x);
CRYPTOPP_ASSERT(ret == 0);
}
bool ed25519PrivateKey::IsClamped(const byte x[SECRET_KEYLENGTH]) const
{
return (x[0] & 248) == x[0] && (x[31] & 127) == x[31] && (x[31] | 64) == x[31];
}
bool ed25519PrivateKey::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
CRYPTOPP_UNUSED(rng); CRYPTOPP_UNUSED(level);
return true;
}
bool ed25519PrivateKey::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
if (std::strcmp(name, Name::PrivateExponent()) == 0 || std::strcmp(name, "SecretKey") == 0)
{
this->ThrowIfTypeMismatch(name, typeid(ConstByteArrayParameter), valueType);
reinterpret_cast<ConstByteArrayParameter*>(pValue)->Assign(m_sk, SECRET_KEYLENGTH, false);
return true;
}
if (std::strcmp(name, Name::PublicElement()) == 0)
{
this->ThrowIfTypeMismatch(name, typeid(ConstByteArrayParameter), valueType);
reinterpret_cast<ConstByteArrayParameter*>(pValue)->Assign(m_pk, PUBLIC_KEYLENGTH, false);
return true;
}
if (std::strcmp(name, Name::GroupOID()) == 0)
{
if (m_oid.Empty())
return false;
this->ThrowIfTypeMismatch(name, typeid(OID), valueType);
*reinterpret_cast<OID *>(pValue) = m_oid;
return true;
}
return false;
}
void ed25519PrivateKey::AssignFrom(const NameValuePairs &source)
{
ConstByteArrayParameter val;
if (source.GetValue(Name::PrivateExponent(), val) || source.GetValue("SecretKey", val))
{
CRYPTOPP_ASSERT(val.size() == SECRET_KEYLENGTH);
std::memcpy(m_sk, val.begin(), SECRET_KEYLENGTH);
}
if (source.GetValue(Name::PublicElement(), val))
{
CRYPTOPP_ASSERT(val.size() == PUBLIC_KEYLENGTH);
std::memcpy(m_pk, val.begin(), PUBLIC_KEYLENGTH);
}
OID oid;
if (source.GetValue(Name::GroupOID(), oid))
{
m_oid = oid;
}
bool clamp = false;
if (source.GetValue("Clamp", clamp) && clamp == true)
ClampKeys(m_pk, m_sk);
}
void ed25519PrivateKey::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
{
ConstByteArrayParameter seed;
if (params.GetValue(Name::Seed(), seed) && rng.CanIncorporateEntropy())
rng.IncorporateEntropy(seed.begin(), seed.size());
rng.GenerateBlock(m_sk, 32);
m_sk[0] &= 248; m_sk[31] &= 127; m_sk[31] |= 64;
int ret = Donna::ed25519_publickey(m_pk, m_sk);
CRYPTOPP_ASSERT(ret == 0);
}
void ed25519PrivateKey::MakePublicKey (PublicKey &pub) const
{
pub.AssignFrom(MakeParameters
(Name::PublicElement(), ConstByteArrayParameter(m_pk.begin(), PUBLIC_KEYLENGTH))
(Name::GroupOID(), GetAlgorithmID()));
}
void ed25519PrivateKey::BERDecodeAndCheckAlgorithmID(BufferedTransformation &bt)
{
// We have not yet determined the OID to use for this object.
// We can't use OID's decoder because it throws BERDecodeError
// if the OIDs do not match.
OID oid(bt);
if (!m_oid.Empty() && m_oid != oid)
BERDecodeError(); // Only accept user specified OID
else if (oid == ASN1::curve25519() || oid == ASN1::Ed25519())
m_oid = oid; // Accept any of the ed25519PrivateKey OIDs
else
BERDecodeError();
}
void ed25519PrivateKey::BERDecode(BufferedTransformation &bt)
{
// https://tools.ietf.org/html/rfc8410, section 7 and
// https://www.cryptopp.com/wiki/curve25519_keys
BERSequenceDecoder privateKeyInfo(bt);
word32 version;
BERDecodeUnsigned<word32>(privateKeyInfo, version, INTEGER, 0, 1); // check version
BERSequenceDecoder algorithm(privateKeyInfo);
// GetAlgorithmID().BERDecodeAndCheck(algorithm);
BERDecodeAndCheckAlgorithmID(algorithm);
algorithm.MessageEnd();
BERGeneralDecoder octetString(privateKeyInfo, OCTET_STRING);
BERDecodePrivateKey(octetString, false, (size_t)privateKeyInfo.RemainingLength());
octetString.MessageEnd();
bool generatePublicKey = true;
if (version == 1)
{
BERGeneralDecoder publicKey(privateKeyInfo, CONTEXT_SPECIFIC | CONSTRUCTED | 1);
SecByteBlock subjectPublicKey;
unsigned int unusedBits;
BERDecodeBitString(publicKey, subjectPublicKey, unusedBits);
CRYPTOPP_ASSERT(unusedBits == 0);
CRYPTOPP_ASSERT(subjectPublicKey.size() == PUBLIC_KEYLENGTH);
if (subjectPublicKey.size() != PUBLIC_KEYLENGTH)
BERDecodeError();
std::memcpy(m_pk.begin(), subjectPublicKey, PUBLIC_KEYLENGTH);
generatePublicKey = false;
publicKey.MessageEnd();
}
privateKeyInfo.MessageEnd();
if (generatePublicKey)
Donna::ed25519_publickey(m_pk, m_sk);
CRYPTOPP_ASSERT(IsClamped(m_sk) == true);
}
void ed25519PrivateKey::DEREncode(BufferedTransformation &bt, int version) const
{
// https://tools.ietf.org/html/rfc8410, section 7 and
// https://www.cryptopp.com/wiki/curve25519_keys
CRYPTOPP_ASSERT(version == 0 || version == 1);
DERSequenceEncoder privateKeyInfo(bt);
DEREncodeUnsigned<word32>(privateKeyInfo, version);
DERSequenceEncoder algorithm(privateKeyInfo);
GetAlgorithmID().DEREncode(algorithm);
algorithm.MessageEnd();
DERGeneralEncoder octetString(privateKeyInfo, OCTET_STRING);
DEREncodePrivateKey(octetString);
octetString.MessageEnd();
if (version == 1)
{
DERGeneralEncoder publicKey(privateKeyInfo, CONTEXT_SPECIFIC | CONSTRUCTED | 1);
DEREncodeBitString(publicKey, m_pk, PUBLIC_KEYLENGTH);
publicKey.MessageEnd();
}
privateKeyInfo.MessageEnd();
}
void ed25519PrivateKey::BERDecodePrivateKey(BufferedTransformation &bt, bool parametersPresent, size_t /*size*/)
{
// https://tools.ietf.org/html/rfc8410 and
// https://www.cryptopp.com/wiki/curve25519_keys
BERGeneralDecoder privateKey(bt, OCTET_STRING);
if (!privateKey.IsDefiniteLength())
BERDecodeError();
size_t size = privateKey.Get(m_sk, SECRET_KEYLENGTH);
if (size != SECRET_KEYLENGTH)
BERDecodeError();
// We don't know how to decode them
if (parametersPresent)
BERDecodeError();
privateKey.MessageEnd();
}
void ed25519PrivateKey::DEREncodePrivateKey(BufferedTransformation &bt) const
{
// https://tools.ietf.org/html/rfc8410
DERGeneralEncoder privateKey(bt, OCTET_STRING);
privateKey.Put(m_sk, SECRET_KEYLENGTH);
privateKey.MessageEnd();
}
void ed25519PrivateKey::SetPrivateExponent (const byte x[SECRET_KEYLENGTH])
{
AssignFrom(MakeParameters
(Name::PrivateExponent(), ConstByteArrayParameter(x, SECRET_KEYLENGTH))
("Clamp", true));
}
void ed25519PrivateKey::SetPrivateExponent (const Integer &x)
{
CRYPTOPP_ASSERT(x.MinEncodedSize() <= SECRET_KEYLENGTH);
SecByteBlock bx(SECRET_KEYLENGTH);
x.Encode(bx, SECRET_KEYLENGTH); std::reverse(bx+0, bx+SECRET_KEYLENGTH);
AssignFrom(MakeParameters
(Name::PrivateExponent(), ConstByteArrayParameter(bx, SECRET_KEYLENGTH, false))
("Clamp", true));
}
const Integer& ed25519PrivateKey::GetPrivateExponent() const
{
m_x = Integer(m_sk, SECRET_KEYLENGTH, Integer::UNSIGNED, LITTLE_ENDIAN_ORDER);
return m_x;
}
////////////////////////
ed25519Signer::ed25519Signer(const byte y[PUBLIC_KEYLENGTH], const byte x[SECRET_KEYLENGTH])
{
AccessPrivateKey().AssignFrom(MakeParameters
(Name::PrivateExponent(), ConstByteArrayParameter(x, SECRET_KEYLENGTH, false))
(Name::PublicElement(), ConstByteArrayParameter(y, PUBLIC_KEYLENGTH, false)));
}
ed25519Signer::ed25519Signer(const byte x[SECRET_KEYLENGTH])
{
AccessPrivateKey().AssignFrom(MakeParameters
(Name::PrivateExponent(), ConstByteArrayParameter(x, SECRET_KEYLENGTH, false))
("Clamp", true));
}
ed25519Signer::ed25519Signer(const Integer &y, const Integer &x)
{
CRYPTOPP_ASSERT(y.MinEncodedSize() <= PUBLIC_KEYLENGTH);
CRYPTOPP_ASSERT(x.MinEncodedSize() <= SECRET_KEYLENGTH);
SecByteBlock by(PUBLIC_KEYLENGTH), bx(SECRET_KEYLENGTH);
y.Encode(by, PUBLIC_KEYLENGTH); std::reverse(by+0, by+PUBLIC_KEYLENGTH);
x.Encode(bx, SECRET_KEYLENGTH); std::reverse(bx+0, bx+SECRET_KEYLENGTH);
AccessPrivateKey().AssignFrom(MakeParameters
(Name::PublicElement(), ConstByteArrayParameter(by, PUBLIC_KEYLENGTH, false))
(Name::PrivateExponent(), ConstByteArrayParameter(bx, SECRET_KEYLENGTH, false)));
}
ed25519Signer::ed25519Signer(const Integer &x)
{
CRYPTOPP_ASSERT(x.MinEncodedSize() <= SECRET_KEYLENGTH);
SecByteBlock bx(SECRET_KEYLENGTH);
x.Encode(bx, SECRET_KEYLENGTH); std::reverse(bx+0, bx+SECRET_KEYLENGTH);
AccessPrivateKey().AssignFrom(MakeParameters
(Name::PrivateExponent(), ConstByteArrayParameter(bx, SECRET_KEYLENGTH, false))
("Clamp", true));
}
ed25519Signer::ed25519Signer(RandomNumberGenerator &rng)
{
AccessPrivateKey().GenerateRandom(rng);
}
ed25519Signer::ed25519Signer(BufferedTransformation &params)
{
ed25519PrivateKey& key = static_cast<ed25519PrivateKey&>(AccessPrivateKey());
key.BERDecode(params);
}
size_t ed25519Signer::SignAndRestart(RandomNumberGenerator &rng, PK_MessageAccumulator &messageAccumulator, byte *signature, bool restart) const
{
CRYPTOPP_ASSERT(signature != NULLPTR); CRYPTOPP_UNUSED(rng);
ed25519_MessageAccumulator& accum = static_cast<ed25519_MessageAccumulator&>(messageAccumulator);
const ed25519PrivateKey& pk = static_cast<const ed25519PrivateKey&>(GetPrivateKey());
int ret = Donna::ed25519_sign(accum.data(), accum.size(), pk.m_sk, pk.m_pk, signature);
CRYPTOPP_ASSERT(ret == 0);
if (restart)
accum.Restart();
return ret == 0 ? SIGNATURE_LENGTH : 0;
}
// ******************** ed25519 Verifier ************************* //
bool ed25519PublicKey::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
if (std::strcmp(name, Name::PublicElement()) == 0)
{
this->ThrowIfTypeMismatch(name, typeid(ConstByteArrayParameter), valueType);
reinterpret_cast<ConstByteArrayParameter*>(pValue)->Assign(m_pk, PUBLIC_KEYLENGTH, false);
return true;
}
if (std::strcmp(name, Name::GroupOID()) == 0)
{
if (m_oid.Empty())
return false;
this->ThrowIfTypeMismatch(name, typeid(OID), valueType);
*reinterpret_cast<OID *>(pValue) = m_oid;
return true;
}
return false;
}
void ed25519PublicKey::AssignFrom(const NameValuePairs &source)
{
ConstByteArrayParameter ba;
if (source.GetValue(Name::PublicElement(), ba))
{
std::memcpy(m_pk, ba.begin(), PUBLIC_KEYLENGTH);
}
OID oid;
if (source.GetValue(Name::GroupOID(), oid))
{
m_oid = oid;
}
}
void ed25519PublicKey::BERDecodeAndCheckAlgorithmID(BufferedTransformation& bt)
{
// We have not yet determined the OID to use for this object.
// We can't use OID's decoder because it throws BERDecodeError
// if the OIDs do not match.
OID oid(bt);
if (!m_oid.Empty() && m_oid != oid)
BERDecodeError(); // Only accept user specified OID
else if (oid == ASN1::curve25519() || oid == ASN1::Ed25519())
m_oid = oid; // Accept any of the ed25519PublicKey OIDs
else
BERDecodeError();
}
void ed25519PublicKey::BERDecode(BufferedTransformation &bt)
{
BERSequenceDecoder publicKeyInfo(bt);
BERSequenceDecoder algorithm(publicKeyInfo);
// GetAlgorithmID().BERDecodeAndCheck(algorithm);
BERDecodeAndCheckAlgorithmID(algorithm);
algorithm.MessageEnd();
BERDecodePublicKey(publicKeyInfo, false, (size_t)publicKeyInfo.RemainingLength());
publicKeyInfo.MessageEnd();
}
void ed25519PublicKey::DEREncode(BufferedTransformation &bt) const
{
DERSequenceEncoder publicKeyInfo(bt);
DERSequenceEncoder algorithm(publicKeyInfo);
GetAlgorithmID().DEREncode(algorithm);
algorithm.MessageEnd();
DEREncodePublicKey(publicKeyInfo);
publicKeyInfo.MessageEnd();
}
void ed25519PublicKey::BERDecodePublicKey(BufferedTransformation &bt, bool parametersPresent, size_t /*size*/)
{
// We don't know how to decode them
if (parametersPresent)
BERDecodeError();
SecByteBlock subjectPublicKey;
unsigned int unusedBits;
BERDecodeBitString(bt, subjectPublicKey, unusedBits);
CRYPTOPP_ASSERT(unusedBits == 0);
CRYPTOPP_ASSERT(subjectPublicKey.size() == PUBLIC_KEYLENGTH);
if (subjectPublicKey.size() != PUBLIC_KEYLENGTH)
BERDecodeError();
std::memcpy(m_pk.begin(), subjectPublicKey, PUBLIC_KEYLENGTH);
}
void ed25519PublicKey::DEREncodePublicKey(BufferedTransformation &bt) const
{
DEREncodeBitString(bt, m_pk, PUBLIC_KEYLENGTH);
}
void ed25519PublicKey::SetPublicElement (const byte y[PUBLIC_KEYLENGTH])
{
std::memcpy(m_pk, y, PUBLIC_KEYLENGTH);
}
void ed25519PublicKey::SetPublicElement (const Integer &y)
{
CRYPTOPP_ASSERT(y.MinEncodedSize() <= PUBLIC_KEYLENGTH);
SecByteBlock by(PUBLIC_KEYLENGTH);
y.Encode(by, PUBLIC_KEYLENGTH); std::reverse(by+0, by+PUBLIC_KEYLENGTH);
std::memcpy(m_pk, by, PUBLIC_KEYLENGTH);
}
const Integer& ed25519PublicKey::GetPublicElement() const
{
m_y = Integer(m_pk, PUBLIC_KEYLENGTH, Integer::UNSIGNED, LITTLE_ENDIAN_ORDER);
return m_y;
}
bool ed25519PublicKey::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
CRYPTOPP_UNUSED(rng); CRYPTOPP_UNUSED(level);
return true;
}
////////////////////////
ed25519Verifier::ed25519Verifier(const byte y[PUBLIC_KEYLENGTH])
{
AccessPublicKey().AssignFrom(MakeParameters
(Name::PublicElement(), ConstByteArrayParameter(y, PUBLIC_KEYLENGTH)));
}
ed25519Verifier::ed25519Verifier(const Integer &y)
{
CRYPTOPP_ASSERT(y.MinEncodedSize() <= PUBLIC_KEYLENGTH);
SecByteBlock by(PUBLIC_KEYLENGTH);
y.Encode(by, PUBLIC_KEYLENGTH); std::reverse(by+0, by+PUBLIC_KEYLENGTH);
AccessPublicKey().AssignFrom(MakeParameters
(Name::PublicElement(), ConstByteArrayParameter(by, PUBLIC_KEYLENGTH, false)));
}
ed25519Verifier::ed25519Verifier(BufferedTransformation &params)
{
// TODO: Fix the on-disk format once we determine what it is.
BERSequenceDecoder seq(params);
size_t read;
BERSequenceDecoder pk(seq, OCTET_STRING);
CRYPTOPP_ASSERT(pk.MaxRetrievable() >= PUBLIC_KEYLENGTH);
read = pk.Get(m_key.m_pk, PUBLIC_KEYLENGTH);
pk.MessageEnd();
if (read != PUBLIC_KEYLENGTH)
throw BERDecodeErr();
seq.MessageEnd();
}
ed25519Verifier::ed25519Verifier(const ed25519Signer& signer)
{
const ed25519PrivateKey& priv = static_cast<const ed25519PrivateKey&>(signer.GetPrivateKey());
priv.MakePublicKey(AccessPublicKey());
}
bool ed25519Verifier::VerifyAndRestart(PK_MessageAccumulator &messageAccumulator) const
{
ed25519_MessageAccumulator& accum = static_cast<ed25519_MessageAccumulator&>(messageAccumulator);
const ed25519PublicKey& pk = static_cast<const ed25519PublicKey&>(GetPublicKey());
int ret = Donna::ed25519_sign_open(accum.data(), accum.size(), pk.m_pk.begin(), accum.signature());
accum.Restart();
return ret == 0;
}
NAMESPACE_END // CryptoPP

531
xed25519.h
View File

@ -1,46 +1,63 @@
// xed25519.h - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna. Also see
// https://github.com/floodyberry/curve25519-donna.
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// Typically the key agreement classes encapsulate their data more
// than x25519 does below. We made them a little more accessible
// due to crypto_box operations. Once the library cuts-in the
// crypto_box operations the x25519 class will be more restricted.
// than x25519 does below. They are a little more accessible
// due to crypto_box operations.
/// \file xed25519.h
/// \brief Classes for x25519 and ed25519 operations
/// \details This implementation integrates Andrew Moon's public domain
/// curve25519-donna.
/// \sa Andrew Moon's GitHub <A
/// HREF="https://github.com/floodyberry/curve25519-donna">curve25519-donna</A>
/// \details This implementation integrates Andrew Moon's public domain code
/// for curve25519-donna and ed25519-donna.
/// \details Moving keys into and out of the library proceeds as follows.
/// If an Integer class is accepted or returned, then the data is in big
/// endian format. That is, the MSB is at byte position 0, and the LSB
/// is at byte position 31. The Integer will work as expected, just like
/// an int or a long.
/// \details If a byte array is accepted, then the byte array is in little
/// endian format. That is, the LSB is at byte position 0, and the MSB is
/// at byte position 31. This follows the implementation where byte 0 is
/// clamed with 248. That is my_arr[0] &= 248 to mask the lower 3 bits.
/// \details PKCS8 and X509 keys encoded using ASN.1 follow little endian
/// arrays. The format is specified in <A HREF=
/// "https:///tools.ietf.org/html/draft-ietf-curdle-pkix">draft-ietf-curdle-pkix</A>.
/// \details If you have a little endian array and you want to wrap it in
/// an Integer using big endian then you can perform the following:
/// <pre>Integer x(my_arr, SECRET_KEYLENGTH, UNSIGNED, LITTLE_ENDIAN_ORDER);</pre>
/// \sa Andrew Moon's x22519 GitHub <A
/// HREF="https://github.com/floodyberry/curve25519-donna">curve25519-donna</A>,
/// ed22519 GitHub <A
/// HREF="https://github.com/floodyberry/ed25519-donna">ed25519-donna</A>, and
/// <A HREF="https:///tools.ietf.org/html/draft-ietf-curdle-pkix">draft-ietf-curdle-pkix</A>
/// \since Crypto++ 8.0
#ifndef CRYPTOPP_XED25519_H
#define CRYPTOPP_XED25519_H
#include "cryptlib.h"
#include "pubkey.h"
#include "oids.h"
NAMESPACE_BEGIN(CryptoPP)
class Integer;
struct ed25519Signer;
struct ed25519Verifier;
// ******************** x25519 Agreement ************************* //
/// \brief x25519 with key validation
/// \since Crypto++ 8.0
class x25519 : public SimpleKeyAgreementDomain, public CryptoParameters
class x25519 : public SimpleKeyAgreementDomain, public CryptoParameters, public PKCS8PrivateKey
{
public:
/// \brief Test if a key is clamped
/// \param x private key
static bool IsClamped(const byte x[32]);
/// \brief Test if a key has small order
/// \param y public key
static bool IsSmallOrder(const byte y[32]);
/// \brief Test if a key is clamped
/// \param x private key
static void ClampKey(byte x[32]);
CRYPTOPP_CONSTANT(SECRET_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(PUBLIC_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(SHARED_KEYLENGTH = 32)
virtual ~x25519() {}
@ -49,13 +66,13 @@ public:
/// \param x private key
/// \details This constructor creates a x25519 object using existing parameters.
/// \note The public key is not validated.
x25519(const byte y[32], const byte x[32]);
x25519(const byte y[PUBLIC_KEYLENGTH], const byte x[SECRET_KEYLENGTH]);
/// \brief Create a x25519 object
/// \param x private key
/// \details This constructor creates a x25519 object using existing parameters.
/// The public key is calculated from the private key.
x25519(const byte x[32]);
x25519(const byte x[SECRET_KEYLENGTH]);
/// \brief Create a x25519 object
/// \param y public key
@ -82,28 +99,474 @@ public:
/// \note The public key is not validated.
x25519(BufferedTransformation &params);
/// \brief Decode a x25519 object
/// \param params serialized object
/// \details DEREncode() writes the public and private key as an ASN.1 structure.
/// The private key is written first as a <tt>BIT_STRING</tt>. The public key
/// is written second as an <tt>OCTET_STRING</tt>.
void DEREncode(BufferedTransformation &params) const;
/// \brief Create a x25519 object
/// \param oid an object identifier
/// \details This constructor creates a new x25519 using the specified OID. The public
/// and private points are uninitialized.
x25519(const OID &oid);
/// \brief Clamp a private key
/// \param y public key
/// \param x private key
/// \details ClampKeys() clamps a private key and then regenerates the
/// public key from the private key.
void ClampKeys(byte y[PUBLIC_KEYLENGTH], byte x[SECRET_KEYLENGTH]) const;
/// \brief Test if a key is clamped
/// \param x private key
bool IsClamped(const byte x[SECRET_KEYLENGTH]) const;
/// \brief Test if a key has small order
/// \param y public key
bool IsSmallOrder(const byte y[PUBLIC_KEYLENGTH]) const;
/// \Brief Get the Object Identifier
/// \returns the Object Identifier
/// \details The default OID is from RFC 8410 using id-X25519.
/// The default private key format is RFC 5208.
OID GetAlgorithmID() const {
return m_oid.Empty() ? ASN1::X25519() : m_oid;
}
/// \Brief Set the Object Identifier
/// \param oid the new Object Identifier
void SetAlgorithmID(const OID& oid) {
m_oid = oid;
}
// CryptoParameters
bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
void AssignFrom(const NameValuePairs &source);
// CryptoParameters
CryptoParameters & AccessCryptoParameters() {return *this;}
unsigned int AgreedValueLength() const {return 32;}
unsigned int PrivateKeyLength() const {return 32;}
unsigned int PublicKeyLength() const {return 32;}
/// \brief DER encode ASN.1 object
/// \param bt BufferedTransformation object
/// \details Save() will write the OID associated with algorithm or scheme.
/// In the case of public and private keys, this function writes the
/// subjectPubicKeyInfo parts.
/// \details The default OID is from RFC 8410 using id-X25519.
/// The default private key format is RFC 5208, which is the old format.
/// The old format provides the best interop, and keys will work
/// with OpenSSL.
void Save(BufferedTransformation &bt) const {
DEREncode(bt, 0);
}
/// \brief DER encode ASN.1 object
/// \param bt BufferedTransformation object
/// \param v0 flag indicating v0
/// \details Save() will write the OID associated with algorithm or scheme.
/// In the case of public and private keys, this function writes the
/// subjectPubicKeyInfo parts.
/// \details The default OID is from RFC 8410 using id-X25519.
/// The default private key format is RFC 5208.
/// \details v0 means version 0 INTEGER is written. Version 0 means
/// RFC 5208 format, which is the old format. The old format provides
/// the best interop, and keys will work with OpenSSL. The the other
/// option is using version 1 INTEGER. Version 1 means RFC 5958 format,
/// which is the new format.
void Save(BufferedTransformation &bt, bool v0) const {
DEREncode(bt, v0 ? 0 : 1);
}
/// \brief BER decode ASN.1 object
/// \param bt BufferedTransformation object
void Load(BufferedTransformation &bt) {
BERDecode(bt);
}
// PKCS8PrivateKey
void BERDecode(BufferedTransformation &bt);
void DEREncode(BufferedTransformation &bt) const { DEREncode(bt, 0); }
void DEREncode(BufferedTransformation &bt, int version) const;
void BERDecodePrivateKey(BufferedTransformation &bt, bool parametersPresent, size_t size);
void DEREncodePrivateKey(BufferedTransformation &bt) const;
// Hack because multiple OIDs are available
void BERDecodeAndCheckAlgorithmID(BufferedTransformation& bt);
// DL_PrivateKey
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params);
// SimpleKeyAgreementDomain
unsigned int AgreedValueLength() const {return SHARED_KEYLENGTH;}
unsigned int PrivateKeyLength() const {return SECRET_KEYLENGTH;}
unsigned int PublicKeyLength() const {return PUBLIC_KEYLENGTH;}
// SimpleKeyAgreementDomain
void GeneratePrivateKey(RandomNumberGenerator &rng, byte *privateKey) const;
void GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const;
bool Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey=true) const;
private:
FixedSizeSecBlock<byte, 32> m_sk, m_pk;
protected:
FixedSizeSecBlock<byte, SECRET_KEYLENGTH> m_sk;
FixedSizeSecBlock<byte, PUBLIC_KEYLENGTH> m_pk;
OID m_oid; // preferred OID
};
// ****************** ed25519 Signer *********************** //
struct ed25519_MessageAccumulator : public PK_MessageAccumulator
{
CRYPTOPP_CONSTANT(RESERVE_SIZE=2048+64)
CRYPTOPP_CONSTANT(SIGNATURE_LENGTH=64)
ed25519_MessageAccumulator() {
Restart();
}
ed25519_MessageAccumulator(RandomNumberGenerator &rng) {
CRYPTOPP_UNUSED(rng); Restart();
}
void Update(const byte* msg, size_t len) {
if (msg && len)
m_msg.insert(m_msg.end(), msg, msg+len);
}
void Restart() {
m_msg.reserve(RESERVE_SIZE);
m_msg.resize(SIGNATURE_LENGTH);
}
byte* signature() {
return &m_msg[0];
}
const byte* signature() const {
return &m_msg[0];
}
const byte* data() const {
return &m_msg[0]+SIGNATURE_LENGTH;
}
size_t size() const {
return m_msg.size()-SIGNATURE_LENGTH;
}
protected:
// TODO: Find an equivalent Crypto++ structure.
std::vector<byte, AllocatorWithCleanup<byte> > m_msg;
};
struct ed25519PrivateKey : public PKCS8PrivateKey
{
CRYPTOPP_CONSTANT(SECRET_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(PUBLIC_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(SIGNATURE_LENGTH = 64)
// CryptoMaterial
bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
void AssignFrom(const NameValuePairs &source);
// GroupParameters
OID GetAlgorithmID() const {
return m_oid.Empty() ? ASN1::Ed25519() : m_oid;
}
/// \brief DER encode ASN.1 object
/// \param bt BufferedTransformation object
/// \details Save() will write the OID associated with algorithm or scheme.
/// In the case of public and private keys, this function writes the
/// subjectPubicKeyInfo parts.
/// \details The default OID is from RFC 8410 using id-X25519.
/// The default private key format is RFC 5208, which is the old format.
/// The old format provides the best interop, and keys will work
/// with OpenSSL.
void Save(BufferedTransformation &bt) const {
DEREncode(bt, 0);
}
/// \brief DER encode ASN.1 object
/// \param bt BufferedTransformation object
/// \param v0 flag indicating v0
/// \details Save() will write the OID associated with algorithm or scheme.
/// In the case of public and private keys, this function writes the
/// subjectPubicKeyInfo parts.
/// \details The default OID is from RFC 8410 using id-Ed25519.
/// The default private key format is RFC 5208.
/// \details v0 means version 0 INTEGER is written. Version 0 means
/// RFC 5208 format, which is the old format. The old format provides
/// the best interop, and keys will work with OpenSSL. The the other
/// option is using version 1 INTEGER. Version 1 means RFC 5958 format,
/// which is the new format.
void Save(BufferedTransformation &bt, bool v0) const {
DEREncode(bt, v0 ? 0 : 1);
}
/// \brief BER decode ASN.1 object
/// \param bt BufferedTransformation object
void Load(BufferedTransformation &bt) {
BERDecode(bt);
}
/// \brief Initializes a public key from this key
/// \param pub reference to a public key
void MakePublicKey(PublicKey &pub) const;
// PKCS8PrivateKey
void BERDecode(BufferedTransformation &bt);
void DEREncode(BufferedTransformation &bt) const { DEREncode(bt, 0); }
void DEREncode(BufferedTransformation &bt, int version) const;
void BERDecodePrivateKey(BufferedTransformation &bt, bool parametersPresent, size_t size);
void DEREncodePrivateKey(BufferedTransformation &bt) const;
// Hack because multiple OIDs are available
void BERDecodeAndCheckAlgorithmID(BufferedTransformation& bt);
// PKCS8PrivateKey
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params);
void SetPrivateExponent(const byte x[SECRET_KEYLENGTH]);
void SetPrivateExponent(const Integer &x);
const Integer& GetPrivateExponent() const;
/// \brief Clamp a private key
/// \param y public key
/// \param x private key
/// \details ClampKeys() clamps a private key and then regenerates the
/// public key from the private key.
void ClampKeys(byte y[PUBLIC_KEYLENGTH], byte x[SECRET_KEYLENGTH]) const;
/// \brief Test if a key is clamped
/// \param x private key
bool IsClamped(const byte x[SECRET_KEYLENGTH]) const;
FixedSizeSecBlock<byte, SECRET_KEYLENGTH> m_sk;
FixedSizeSecBlock<byte, PUBLIC_KEYLENGTH> m_pk;
OID m_oid; // preferred OID
mutable Integer m_x; // for DL_PrivateKey
};
/// \brief ed25519 signature algorithm
/// \since Crypto++ 8.0
struct ed25519Signer : public PK_Signer
{
CRYPTOPP_CONSTANT(SECRET_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(PUBLIC_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(SIGNATURE_LENGTH = 64)
typedef Integer Element;
virtual ~ed25519Signer() {}
/// \brief Create a ed25519Signer object
ed25519Signer() {}
/// \brief Create a ed25519Signer object
/// \param y public key
/// \param x private key
/// \details This constructor creates a ed25519Signer object using existing parameters.
/// \note The public key is not validated.
ed25519Signer(const byte y[PUBLIC_KEYLENGTH], const byte x[SECRET_KEYLENGTH]);
/// \brief Create a ed25519Signer object
/// \param x private key
/// \details This constructor creates a ed25519Signer object using existing parameters.
/// The public key is calculated from the private key.
ed25519Signer(const byte x[SECRET_KEYLENGTH]);
/// \brief Create a ed25519Signer object
/// \param y public key
/// \param x private key
/// \details This constructor creates a ed25519Signer object using existing parameters.
/// \note The public key is not validated.
ed25519Signer(const Integer &y, const Integer &x);
/// \brief Create a ed25519Signer object
/// \param x private key
/// \details This constructor creates a ed25519Signer object using existing parameters.
/// The public key is calculated from the private key.
ed25519Signer(const Integer &x);
/// \brief Create a ed25519Signer object
/// \param rng RandomNumberGenerator derived class
/// \details This constructor creates a new ed25519Signer using the random number generator.
ed25519Signer(RandomNumberGenerator &rng);
/// \brief Create a ed25519Signer object
/// \param params public and private key
/// \details This constructor creates a ed25519Signer object using existing parameters.
/// The <tt>params</tt> can be created with <tt>DEREncode</tt>.
/// \note The public key is not validated.
ed25519Signer(BufferedTransformation &params);
// DL_ObjectImplBase
PrivateKey& AccessKey() { return m_key; }
PrivateKey& AccessPrivateKey() { return m_key; }
const PrivateKey& GetKey() const { return m_key; }
const PrivateKey& GetPrivateKey() const { return m_key; }
// DL_SignatureSchemeBase
size_t SignatureLength() const { return SIGNATURE_LENGTH; }
size_t MaxRecoverableLength() const { return 0; }
size_t MaxRecoverableLengthFromSignatureLength(size_t signatureLength) const {
CRYPTOPP_UNUSED(signatureLength); return 0;
}
bool IsProbabilistic() const { return false; }
bool AllowNonrecoverablePart() const { return false; }
bool RecoverablePartFirst() const { return false; }
PK_MessageAccumulator* NewSignatureAccumulator(RandomNumberGenerator &rng) const {
return new ed25519_MessageAccumulator(rng);
}
void InputRecoverableMessage(PK_MessageAccumulator &messageAccumulator, const byte *recoverableMessage, size_t recoverableMessageLength) const {
CRYPTOPP_UNUSED(messageAccumulator); CRYPTOPP_UNUSED(recoverableMessage);
CRYPTOPP_UNUSED(recoverableMessageLength);
throw NotImplemented("ed25519Signer: this object does not support recoverable messages");
}
size_t SignAndRestart(RandomNumberGenerator &rng, PK_MessageAccumulator &messageAccumulator, byte *signature, bool restart) const;
protected:
ed25519PrivateKey m_key;
};
// ****************** ed25519 Verifier *********************** //
struct ed25519PublicKey : public X509PublicKey
{
CRYPTOPP_CONSTANT(PUBLIC_KEYLENGTH = 32)
typedef Integer Element;
OID GetAlgorithmID() const {
return m_oid.Empty() ? ASN1::Ed25519() : m_oid;
}
/// \brief DER encode ASN.1 object
/// \param bt BufferedTransformation object
/// \details Save() will write the OID associated with algorithm or scheme.
/// In the case of public and private keys, this function writes the
/// subjectPubicKeyInfo parts.
/// \details The default OID is from RFC 8410 using id-X25519.
/// The default private key format is RFC 5208, which is the old format.
/// The old format provides the best interop, and keys will work
/// with OpenSSL.
void Save(BufferedTransformation &bt) const {
BEREncode(bt);
}
/// \brief BER decode ASN.1 object
/// \param bt BufferedTransformation object
void Load(BufferedTransformation &bt) {
BERDecode(bt);
}
// X509PublicKey
void BERDecode(BufferedTransformation &bt);
void DEREncode(BufferedTransformation &bt) const;
void BERDecodePublicKey(BufferedTransformation &bt, bool parametersPresent, size_t size);
void DEREncodePublicKey(BufferedTransformation &bt) const;
// Hack because multiple OIDs are available
void BERDecodeAndCheckAlgorithmID(BufferedTransformation& bt);
bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
void AssignFrom(const NameValuePairs &source);
// DL_PublicKey
void SetPublicElement(const byte y[PUBLIC_KEYLENGTH]);
void SetPublicElement(const Element &y);
const Element& GetPublicElement() const;
FixedSizeSecBlock<byte, PUBLIC_KEYLENGTH> m_pk;
OID m_oid; // preferred OID
mutable Integer m_y; // for DL_PublicKey
};
/// \brief ed25519 signature verification algorithm
/// \since Crypto++ 8.0
struct ed25519Verifier : public PK_Verifier
{
CRYPTOPP_CONSTANT(PUBLIC_KEYLENGTH = 32)
CRYPTOPP_CONSTANT(SIGNATURE_LENGTH = 64)
typedef Integer Element;
virtual ~ed25519Verifier() {}
/// \brief Create a ed25519Verifier object
ed25519Verifier() {}
/// \brief Create a ed25519Verifier object
/// \param y public key
/// \details This constructor creates a ed25519Verifier object using existing parameters.
/// \note The public key is not validated.
ed25519Verifier(const byte y[PUBLIC_KEYLENGTH]);
/// \brief Create a ed25519Verifier object
/// \param y public key
/// \details This constructor creates a ed25519Verifier object using existing parameters.
/// \note The public key is not validated.
ed25519Verifier(const Integer &y);
/// \brief Create a ed25519Verifier object
/// \param params public and private key
/// \details This constructor creates a ed25519Verifier object using existing parameters.
/// The <tt>params</tt> can be created with <tt>DEREncode</tt>.
/// \note The public key is not validated.
ed25519Verifier(BufferedTransformation &params);
/// \brief Create a ed25519Verifier object
/// \param signer ed25519 signer object
/// \details This constructor creates a ed25519Verifier object using existing parameters.
/// The <tt>params</tt> can be created with <tt>DEREncode</tt>.
/// \note The public key is not validated.
ed25519Verifier(const ed25519Signer& signer);
// DL_ObjectImplBase
PublicKey& AccessKey() { return m_key; }
PublicKey& AccessPublicKey() { return m_key; }
const PublicKey& GetKey() const { return m_key; }
const PublicKey& GetPublicKey() const { return m_key; }
// DL_SignatureSchemeBase
size_t SignatureLength() const { return SIGNATURE_LENGTH; }
size_t MaxRecoverableLength() const { return 0; }
size_t MaxRecoverableLengthFromSignatureLength(size_t signatureLength) const {
CRYPTOPP_UNUSED(signatureLength); return 0;
}
bool IsProbabilistic() const { return false; }
bool AllowNonrecoverablePart() const { return false; }
bool RecoverablePartFirst() const { return false; }
ed25519_MessageAccumulator* NewVerificationAccumulator() const {
return new ed25519_MessageAccumulator;
}
void InputSignature(PK_MessageAccumulator &messageAccumulator, const byte *signature, size_t signatureLength) const {
CRYPTOPP_ASSERT(signature != NULLPTR);
CRYPTOPP_ASSERT(signatureLength == SIGNATURE_LENGTH);
ed25519_MessageAccumulator& accum = static_cast<ed25519_MessageAccumulator&>(messageAccumulator);
if (signature && signatureLength)
std::memcpy(accum.signature(), signature, STDMIN((size_t)SIGNATURE_LENGTH, signatureLength));
}
bool VerifyAndRestart(PK_MessageAccumulator &messageAccumulator) const;
DecodingResult RecoverAndRestart(byte *recoveredMessage, PK_MessageAccumulator &messageAccumulator) const {
CRYPTOPP_UNUSED(recoveredMessage); CRYPTOPP_UNUSED(messageAccumulator);
throw NotImplemented("ed25519Verifier: this object does not support recoverable messages");
}
protected:
ed25519PublicKey m_key;
};
/// \brief ed25519 signature scheme
/// \since Crypto++ 8.0
struct ed25519
{
typedef ed25519Signer Signer;
typedef ed25519Verifier Verifier;
};
NAMESPACE_END // CryptoPP