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ext-cryptopp/integer.cpp

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// integer.cpp - written and placed in the public domain by Wei Dai
// contains public domain code contributed by Alister Lee and Leonard Janke
#include "pch.h"
#ifndef CRYPTOPP_IMPORTS
#include "integer.h"
#include "modarith.h"
#include "nbtheory.h"
#include "asn.h"
#include "oids.h"
#include "words.h"
#include "algparam.h"
#include "pubkey.h" // for P1363_KDF2
#include "sha.h"
#include <iostream>
#ifdef SSE2_INTRINSICS_AVAILABLE
#ifdef __GNUC__
#include <xmmintrin.h>
#include <signal.h>
#include <setjmp.h>
#ifdef CRYPTOPP_MEMALIGN_AVAILABLE
#include <malloc.h>
#else
#include <stdlib.h>
#endif
#else
#include <emmintrin.h>
#endif
#elif defined(_MSC_VER) && defined(_M_IX86)
#pragma message("You do not seem to have the Visual C++ Processor Pack installed, so use of SSE2 intrinsics will be disabled.")
#elif defined(__GNUC__) && defined(__i386__)
#warning "You do not have GCC 3.3 or later, or did not specify -msse2 compiler option, so use of SSE2 intrinsics will be disabled."
#endif
NAMESPACE_BEGIN(CryptoPP)
bool FunctionAssignIntToInteger(const std::type_info &valueType, void *pInteger, const void *pInt)
{
if (valueType != typeid(Integer))
return false;
*reinterpret_cast<Integer *>(pInteger) = *reinterpret_cast<const int *>(pInt);
return true;
}
static const char s_RunAtStartup = (AssignIntToInteger = FunctionAssignIntToInteger, 0);
#ifdef SSE2_INTRINSICS_AVAILABLE
template <class T>
CPP_TYPENAME AllocatorBase<T>::pointer AlignedAllocator<T>::allocate(size_type n, const void *)
{
CheckSize(n);
if (n == 0)
return NULL;
if (n >= 4)
{
void *p;
#ifdef CRYPTOPP_MM_MALLOC_AVAILABLE
while (!(p = _mm_malloc(sizeof(T)*n, 16)))
#elif defined(CRYPTOPP_MEMALIGN_AVAILABLE)
while (!(p = memalign(16, sizeof(T)*n)))
#elif defined(CRYPTOPP_MALLOC_ALIGNMENT_IS_16)
while (!(p = malloc(sizeof(T)*n)))
#else
while (!(p = (byte *)malloc(sizeof(T)*n + 8))) // assume malloc alignment is at least 8
#endif
CallNewHandler();
#ifdef CRYPTOPP_NO_ALIGNED_ALLOC
assert(m_pBlock == NULL);
m_pBlock = p;
if (!IsAlignedOn(p, 16))
{
assert(IsAlignedOn(p, 8));
p = (byte *)p + 8;
}
#endif
assert(IsAlignedOn(p, 16));
return (T*)p;
}
return new T[n];
}
template <class T>
void AlignedAllocator<T>::deallocate(void *p, size_type n)
{
memset(p, 0, n*sizeof(T));
if (n >= 4)
{
#ifdef CRYPTOPP_MM_MALLOC_AVAILABLE
_mm_free(p);
#elif defined(CRYPTOPP_NO_ALIGNED_ALLOC)
assert(m_pBlock == p || (byte *)m_pBlock+8 == p);
free(m_pBlock);
m_pBlock = NULL;
#else
free(p);
#endif
}
else
delete [] (T *)p;
}
#endif
static int Compare(const word *A, const word *B, unsigned int N)
{
while (N--)
if (A[N] > B[N])
return 1;
else if (A[N] < B[N])
return -1;
return 0;
}
static word Increment(word *A, unsigned int N, word B=1)
{
assert(N);
word t = A[0];
A[0] = t+B;
if (A[0] >= t)
return 0;
for (unsigned i=1; i<N; i++)
if (++A[i])
return 0;
return 1;
}
static word Decrement(word *A, unsigned int N, word B=1)
{
assert(N);
word t = A[0];
A[0] = t-B;
if (A[0] <= t)
return 0;
for (unsigned i=1; i<N; i++)
if (A[i]--)
return 0;
return 1;
}
static void TwosComplement(word *A, unsigned int N)
{
Decrement(A, N);
for (unsigned i=0; i<N; i++)
A[i] = ~A[i];
}
static word AtomicInverseModPower2(word A)
{
assert(A%2==1);
word R=A%8;
for (unsigned i=3; i<WORD_BITS; i*=2)
R = R*(2-R*A);
assert(R*A==1);
return R;
}
// ********************************************************
class DWord
{
public:
DWord() {}
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
explicit DWord(word low)
{
m_whole = low;
}
#else
explicit DWord(word low)
{
m_halfs.low = low;
m_halfs.high = 0;
}
#endif
DWord(word low, word high)
{
m_halfs.low = low;
m_halfs.high = high;
}
static DWord Multiply(word a, word b)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = (dword)a * b;
#elif defined(__alpha__)
r.m_halfs.low = a*b; __asm__("umulh %1,%2,%0" : "=r" (r.m_halfs.high) : "r" (a), "r" (b));
#elif defined(__ia64__)
r.m_halfs.low = a*b; __asm__("xmpy.hu %0=%1,%2" : "=f" (r.m_halfs.high) : "f" (a), "f" (b));
#elif defined(_ARCH_PPC64)
r.m_halfs.low = a*b; __asm__("mulhdu %0,%1,%2" : "=r" (r.m_halfs.high) : "r" (a), "r" (b) : "cc");
#elif defined(__x86_64__)
__asm__("mulq %3" : "=d" (r.m_halfs.high), "=a" (r.m_halfs.low) : "a" (a), "rm" (b) : "cc");
#elif defined(__mips64)
__asm__("dmultu %2,%3" : "=h" (r.m_halfs.high), "=l" (r.m_halfs.low) : "r" (a), "r" (b));
#elif defined(_M_IX86)
// for testing
word64 t = (word64)a * b;
r.m_halfs.high = ((word32 *)(&t))[1];
r.m_halfs.low = (word32)t;
#else
#error can not implement DWord
#endif
return r;
}
static DWord MultiplyAndAdd(word a, word b, word c)
{
DWord r = Multiply(a, b);
return r += c;
}
DWord & operator+=(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
m_whole = m_whole + a;
#else
m_halfs.low += a;
m_halfs.high += (m_halfs.low < a);
#endif
return *this;
}
DWord operator+(word a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole + a;
#else
r.m_halfs.low = m_halfs.low + a;
r.m_halfs.high = m_halfs.high + (r.m_halfs.low < a);
#endif
return r;
}
DWord operator-(DWord a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole - a.m_whole;
#else
r.m_halfs.low = m_halfs.low - a.m_halfs.low;
r.m_halfs.high = m_halfs.high - a.m_halfs.high - (r.m_halfs.low > m_halfs.low);
#endif
return r;
}
DWord operator-(word a)
{
DWord r;
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
r.m_whole = m_whole - a;
#else
r.m_halfs.low = m_halfs.low - a;
r.m_halfs.high = m_halfs.high - (r.m_halfs.low > m_halfs.low);
#endif
return r;
}
// returns quotient, which must fit in a word
word operator/(word divisor);
word operator%(word a);
bool operator!() const
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return !m_whole;
#else
return !m_halfs.high && !m_halfs.low;
#endif
}
word GetLowHalf() const {return m_halfs.low;}
word GetHighHalf() const {return m_halfs.high;}
word GetHighHalfAsBorrow() const {return 0-m_halfs.high;}
private:
union
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
dword m_whole;
#endif
struct
{
#ifdef IS_LITTLE_ENDIAN
word low;
word high;
#else
word high;
word low;
#endif
} m_halfs;
};
};
class Word
{
public:
Word() {}
Word(word value)
{
m_whole = value;
}
Word(hword low, hword high)
{
m_whole = low | (word(high) << (WORD_BITS/2));
}
static Word Multiply(hword a, hword b)
{
Word r;
r.m_whole = (word)a * b;
return r;
}
Word operator-(Word a)
{
Word r;
r.m_whole = m_whole - a.m_whole;
return r;
}
Word operator-(hword a)
{
Word r;
r.m_whole = m_whole - a;
return r;
}
// returns quotient, which must fit in a word
hword operator/(hword divisor)
{
return hword(m_whole / divisor);
}
bool operator!() const
{
return !m_whole;
}
word GetWhole() const {return m_whole;}
hword GetLowHalf() const {return hword(m_whole);}
hword GetHighHalf() const {return hword(m_whole>>(WORD_BITS/2));}
hword GetHighHalfAsBorrow() const {return 0-hword(m_whole>>(WORD_BITS/2));}
private:
word m_whole;
};
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
template <class S, class D>
S DivideThreeWordsByTwo(S *A, S B0, S B1, D *dummy=NULL)
{
// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a S
assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));
// estimate the quotient: do a 2 S by 1 S divide
S Q;
if (S(B1+1) == 0)
Q = A[2];
else
Q = D(A[1], A[2]) / S(B1+1);
// now subtract Q*B from A
D p = D::Multiply(B0, Q);
D u = (D) A[0] - p.GetLowHalf();
A[0] = u.GetLowHalf();
u = (D) A[1] - p.GetHighHalf() - u.GetHighHalfAsBorrow() - D::Multiply(B1, Q);
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
// Q <= actual quotient, so fix it
while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
{
u = (D) A[0] - B0;
A[0] = u.GetLowHalf();
u = (D) A[1] - B1 - u.GetHighHalfAsBorrow();
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
Q++;
assert(Q); // shouldn't overflow
}
return Q;
}
// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
template <class S, class D>
inline D DivideFourWordsByTwo(S *T, const D &Al, const D &Ah, const D &B)
{
if (!B) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
return D(Ah.GetLowHalf(), Ah.GetHighHalf());
else
{
S Q[2];
T[0] = Al.GetLowHalf();
T[1] = Al.GetHighHalf();
T[2] = Ah.GetLowHalf();
T[3] = Ah.GetHighHalf();
Q[1] = DivideThreeWordsByTwo<S, D>(T+1, B.GetLowHalf(), B.GetHighHalf());
Q[0] = DivideThreeWordsByTwo<S, D>(T, B.GetLowHalf(), B.GetHighHalf());
return D(Q[0], Q[1]);
}
}
// returns quotient, which must fit in a word
inline word DWord::operator/(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return word(m_whole / a);
#else
hword r[4];
return DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a).GetWhole();
#endif
}
inline word DWord::operator%(word a)
{
#ifdef CRYPTOPP_NATIVE_DWORD_AVAILABLE
return word(m_whole % a);
#else
if (a < (word(1) << (WORD_BITS/2)))
{
hword h = hword(a);
word r = m_halfs.high % h;
r = ((m_halfs.low >> (WORD_BITS/2)) + (r << (WORD_BITS/2))) % h;
return hword((hword(m_halfs.low) + (r << (WORD_BITS/2))) % h);
}
else
{
hword r[4];
DivideFourWordsByTwo<hword, Word>(r, m_halfs.low, m_halfs.high, a);
return Word(r[0], r[1]).GetWhole();
}
#endif
}
// ********************************************************
class Portable
{
public:
static word Add(word *C, const word *A, const word *B, unsigned int N);
static word Subtract(word *C, const word *A, const word *B, unsigned int N);
static inline void Multiply2(word *C, const word *A, const word *B);
static inline word Multiply2Add(word *C, const word *A, const word *B);
static void Multiply4(word *C, const word *A, const word *B);
static void Multiply8(word *C, const word *A, const word *B);
static inline unsigned int MultiplyRecursionLimit() {return 8;}
static inline void Multiply2Bottom(word *C, const word *A, const word *B);
static void Multiply4Bottom(word *C, const word *A, const word *B);
static void Multiply8Bottom(word *C, const word *A, const word *B);
static inline unsigned int MultiplyBottomRecursionLimit() {return 8;}
static void Square2(word *R, const word *A);
static void Square4(word *R, const word *A);
static void Square8(word *R, const word *A) {assert(false);}
static inline unsigned int SquareRecursionLimit() {return 4;}
};
word Portable::Add(word *C, const word *A, const word *B, unsigned int N)
{
assert (N%2 == 0);
DWord u(0, 0);
for (unsigned int i = 0; i < N; i+=2)
{
u = DWord(A[i]) + B[i] + u.GetHighHalf();
C[i] = u.GetLowHalf();
u = DWord(A[i+1]) + B[i+1] + u.GetHighHalf();
C[i+1] = u.GetLowHalf();
}
return u.GetHighHalf();
}
word Portable::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
assert (N%2 == 0);
DWord u(0, 0);
for (unsigned int i = 0; i < N; i+=2)
{
u = (DWord) A[i] - B[i] - u.GetHighHalfAsBorrow();
C[i] = u.GetLowHalf();
u = (DWord) A[i+1] - B[i+1] - u.GetHighHalfAsBorrow();
C[i+1] = u.GetLowHalf();
}
return 0-u.GetHighHalf();
}
void Portable::Multiply2(word *C, const word *A, const word *B)
{
/*
word s;
dword d;
if (A1 >= A0)
if (B0 >= B1)
{
s = 0;
d = (dword)(A1-A0)*(B0-B1);
}
else
{
s = (A1-A0);
d = (dword)s*(word)(B0-B1);
}
else
if (B0 > B1)
{
s = (B0-B1);
d = (word)(A1-A0)*(dword)s;
}
else
{
s = 0;
d = (dword)(A0-A1)*(B1-B0);
}
*/
// this segment is the branchless equivalent of above
word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
unsigned int ai = A[1] < A[0];
unsigned int bi = B[0] < B[1];
unsigned int di = ai & bi;
DWord d = DWord::Multiply(D[di], D[di+2]);
D[1] = D[3] = 0;
unsigned int si = ai + !bi;
word s = D[si];
DWord A0B0 = DWord::Multiply(A[0], B[0]);
C[0] = A0B0.GetLowHalf();
DWord A1B1 = DWord::Multiply(A[1], B[1]);
DWord t = (DWord) A0B0.GetHighHalf() + A0B0.GetLowHalf() + d.GetLowHalf() + A1B1.GetLowHalf();
C[1] = t.GetLowHalf();
t = A1B1 + t.GetHighHalf() + A0B0.GetHighHalf() + d.GetHighHalf() + A1B1.GetHighHalf() - s;
C[2] = t.GetLowHalf();
C[3] = t.GetHighHalf();
}
inline void Portable::Multiply2Bottom(word *C, const word *A, const word *B)
{
DWord t = DWord::Multiply(A[0], B[0]);
C[0] = t.GetLowHalf();
C[1] = t.GetHighHalf() + A[0]*B[1] + A[1]*B[0];
}
word Portable::Multiply2Add(word *C, const word *A, const word *B)
{
word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
unsigned int ai = A[1] < A[0];
unsigned int bi = B[0] < B[1];
unsigned int di = ai & bi;
DWord d = DWord::Multiply(D[di], D[di+2]);
D[1] = D[3] = 0;
unsigned int si = ai + !bi;
word s = D[si];
DWord A0B0 = DWord::Multiply(A[0], B[0]);
DWord t = A0B0 + C[0];
C[0] = t.GetLowHalf();
DWord A1B1 = DWord::Multiply(A[1], B[1]);
t = (DWord) t.GetHighHalf() + A0B0.GetLowHalf() + d.GetLowHalf() + A1B1.GetLowHalf() + C[1];
C[1] = t.GetLowHalf();
t = (DWord) t.GetHighHalf() + A1B1.GetLowHalf() + A0B0.GetHighHalf() + d.GetHighHalf() + A1B1.GetHighHalf() - s + C[2];
C[2] = t.GetLowHalf();
t = (DWord) t.GetHighHalf() + A1B1.GetHighHalf() + C[3];
C[3] = t.GetLowHalf();
return t.GetHighHalf();
}
#define MulAcc(x, y) \
p = DWord::MultiplyAndAdd(A[x], B[y], c); \
c = p.GetLowHalf(); \
p = (DWord) d + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e += p.GetHighHalf();
#define SaveMulAcc(s, x, y) \
R[s] = c; \
p = DWord::MultiplyAndAdd(A[x], B[y], d); \
c = p.GetLowHalf(); \
p = (DWord) e + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e = p.GetHighHalf();
#define SquAcc(x, y) \
q = DWord::Multiply(A[x], A[y]); \
p = q + c; \
c = p.GetLowHalf(); \
p = (DWord) d + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e += p.GetHighHalf(); \
p = q + c; \
c = p.GetLowHalf(); \
p = (DWord) d + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e += p.GetHighHalf();
#define SaveSquAcc(s, x, y) \
R[s] = c; \
q = DWord::Multiply(A[x], A[y]); \
p = q + d; \
c = p.GetLowHalf(); \
p = (DWord) e + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e = p.GetHighHalf(); \
p = q + c; \
c = p.GetLowHalf(); \
p = (DWord) d + p.GetHighHalf(); \
d = p.GetLowHalf(); \
e += p.GetHighHalf();
void Portable::Multiply4(word *R, const word *A, const word *B)
{
DWord p;
word c, d, e;
p = DWord::Multiply(A[0], B[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
MulAcc(0, 1);
MulAcc(1, 0);
SaveMulAcc(1, 2, 0);
MulAcc(1, 1);
MulAcc(0, 2);
SaveMulAcc(2, 0, 3);
MulAcc(1, 2);
MulAcc(2, 1);
MulAcc(3, 0);
SaveMulAcc(3, 3, 1);
MulAcc(2, 2);
MulAcc(1, 3);
SaveMulAcc(4, 2, 3);
MulAcc(3, 2);
R[5] = c;
p = DWord::MultiplyAndAdd(A[3], B[3], d);
R[6] = p.GetLowHalf();
R[7] = e + p.GetHighHalf();
}
void Portable::Square2(word *R, const word *A)
{
DWord p, q;
word c, d, e;
p = DWord::Multiply(A[0], A[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
SquAcc(0, 1);
R[1] = c;
p = DWord::MultiplyAndAdd(A[1], A[1], d);
R[2] = p.GetLowHalf();
R[3] = e + p.GetHighHalf();
}
void Portable::Square4(word *R, const word *A)
{
#ifdef _MSC_VER
// VC60 workaround: MSVC 6.0 has an optimization bug that makes
// (dword)A*B where either A or B has been cast to a dword before
// very expensive. Revisit this function when this
// bug is fixed.
Multiply4(R, A, A);
#else
const word *B = A;
DWord p, q;
word c, d, e;
p = DWord::Multiply(A[0], A[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
SquAcc(0, 1);
SaveSquAcc(1, 2, 0);
MulAcc(1, 1);
SaveSquAcc(2, 0, 3);
SquAcc(1, 2);
SaveSquAcc(3, 3, 1);
MulAcc(2, 2);
SaveSquAcc(4, 2, 3);
R[5] = c;
p = DWord::MultiplyAndAdd(A[3], A[3], d);
R[6] = p.GetLowHalf();
R[7] = e + p.GetHighHalf();
#endif
}
void Portable::Multiply8(word *R, const word *A, const word *B)
{
DWord p;
word c, d, e;
p = DWord::Multiply(A[0], B[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
MulAcc(0, 1);
MulAcc(1, 0);
SaveMulAcc(1, 2, 0);
MulAcc(1, 1);
MulAcc(0, 2);
SaveMulAcc(2, 0, 3);
MulAcc(1, 2);
MulAcc(2, 1);
MulAcc(3, 0);
SaveMulAcc(3, 0, 4);
MulAcc(1, 3);
MulAcc(2, 2);
MulAcc(3, 1);
MulAcc(4, 0);
SaveMulAcc(4, 0, 5);
MulAcc(1, 4);
MulAcc(2, 3);
MulAcc(3, 2);
MulAcc(4, 1);
MulAcc(5, 0);
SaveMulAcc(5, 0, 6);
MulAcc(1, 5);
MulAcc(2, 4);
MulAcc(3, 3);
MulAcc(4, 2);
MulAcc(5, 1);
MulAcc(6, 0);
SaveMulAcc(6, 0, 7);
MulAcc(1, 6);
MulAcc(2, 5);
MulAcc(3, 4);
MulAcc(4, 3);
MulAcc(5, 2);
MulAcc(6, 1);
MulAcc(7, 0);
SaveMulAcc(7, 1, 7);
MulAcc(2, 6);
MulAcc(3, 5);
MulAcc(4, 4);
MulAcc(5, 3);
MulAcc(6, 2);
MulAcc(7, 1);
SaveMulAcc(8, 2, 7);
MulAcc(3, 6);
MulAcc(4, 5);
MulAcc(5, 4);
MulAcc(6, 3);
MulAcc(7, 2);
SaveMulAcc(9, 3, 7);
MulAcc(4, 6);
MulAcc(5, 5);
MulAcc(6, 4);
MulAcc(7, 3);
SaveMulAcc(10, 4, 7);
MulAcc(5, 6);
MulAcc(6, 5);
MulAcc(7, 4);
SaveMulAcc(11, 5, 7);
MulAcc(6, 6);
MulAcc(7, 5);
SaveMulAcc(12, 6, 7);
MulAcc(7, 6);
R[13] = c;
p = DWord::MultiplyAndAdd(A[7], B[7], d);
R[14] = p.GetLowHalf();
R[15] = e + p.GetHighHalf();
}
void Portable::Multiply4Bottom(word *R, const word *A, const word *B)
{
DWord p;
word c, d, e;
p = DWord::Multiply(A[0], B[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
MulAcc(0, 1);
MulAcc(1, 0);
SaveMulAcc(1, 2, 0);
MulAcc(1, 1);
MulAcc(0, 2);
R[2] = c;
R[3] = d + A[0] * B[3] + A[1] * B[2] + A[2] * B[1] + A[3] * B[0];
}
void Portable::Multiply8Bottom(word *R, const word *A, const word *B)
{
DWord p;
word c, d, e;
p = DWord::Multiply(A[0], B[0]);
R[0] = p.GetLowHalf();
c = p.GetHighHalf();
d = e = 0;
MulAcc(0, 1);
MulAcc(1, 0);
SaveMulAcc(1, 2, 0);
MulAcc(1, 1);
MulAcc(0, 2);
SaveMulAcc(2, 0, 3);
MulAcc(1, 2);
MulAcc(2, 1);
MulAcc(3, 0);
SaveMulAcc(3, 0, 4);
MulAcc(1, 3);
MulAcc(2, 2);
MulAcc(3, 1);
MulAcc(4, 0);
SaveMulAcc(4, 0, 5);
MulAcc(1, 4);
MulAcc(2, 3);
MulAcc(3, 2);
MulAcc(4, 1);
MulAcc(5, 0);
SaveMulAcc(5, 0, 6);
MulAcc(1, 5);
MulAcc(2, 4);
MulAcc(3, 3);
MulAcc(4, 2);
MulAcc(5, 1);
MulAcc(6, 0);
R[6] = c;
R[7] = d + A[0] * B[7] + A[1] * B[6] + A[2] * B[5] + A[3] * B[4] +
A[4] * B[3] + A[5] * B[2] + A[6] * B[1] + A[7] * B[0];
}
#undef MulAcc
#undef SaveMulAcc
#undef SquAcc
#undef SaveSquAcc
#ifdef CRYPTOPP_X86ASM_AVAILABLE
// ************** x86 feature detection ***************
static bool s_sse2Enabled = true;
static void CpuId(word32 input, word32 *output)
{
#ifdef __GNUC__
__asm__
(
// save ebx in case -fPIC is being used
"push %%ebx; cpuid; mov %%ebx, %%edi; pop %%ebx"
: "=a" (output[0]), "=D" (output[1]), "=c" (output[2]), "=d" (output[3])
: "a" (input)
);
#else
__asm
{
mov eax, input
cpuid
mov edi, output
mov [edi], eax
mov [edi+4], ebx
mov [edi+8], ecx
mov [edi+12], edx
}
#endif
}
#ifdef SSE2_INTRINSICS_AVAILABLE
#ifndef _MSC_VER
static jmp_buf s_env;
static void SigIllHandler(int)
{
longjmp(s_env, 1);
}
#endif
static bool HasSSE2()
{
if (!s_sse2Enabled)
return false;
word32 cpuid[4];
CpuId(1, cpuid);
if ((cpuid[3] & (1 << 26)) == 0)
return false;
#ifdef _MSC_VER
__try
{
__asm xorpd xmm0, xmm0 // executing SSE2 instruction
}
__except (1)
{
return false;
}
return true;
#else
typedef void (*SigHandler)(int);
SigHandler oldHandler = signal(SIGILL, SigIllHandler);
if (oldHandler == SIG_ERR)
return false;
bool result = true;
if (setjmp(s_env))
result = false;
else
__asm __volatile ("xorps %xmm0, %xmm0");
signal(SIGILL, oldHandler);
return result;
#endif
}
#endif
static bool IsP4()
{
word32 cpuid[4];
CpuId(0, cpuid);
std::swap(cpuid[2], cpuid[3]);
if (memcmp(cpuid+1, "GenuineIntel", 12) != 0)
return false;
CpuId(1, cpuid);
return ((cpuid[0] >> 8) & 0xf) == 0xf;
}
// ************** Pentium/P4 optimizations ***************
class PentiumOptimized : public Portable
{
public:
static word CRYPTOPP_CDECL Add(word *C, const word *A, const word *B, unsigned int N);
static word CRYPTOPP_CDECL Subtract(word *C, const word *A, const word *B, unsigned int N);
static void CRYPTOPP_CDECL Multiply4(word *C, const word *A, const word *B);
static void CRYPTOPP_CDECL Multiply8(word *C, const word *A, const word *B);
static void CRYPTOPP_CDECL Multiply8Bottom(word *C, const word *A, const word *B);
};
class P4Optimized
{
public:
static word CRYPTOPP_CDECL Add(word *C, const word *A, const word *B, unsigned int N);
static word CRYPTOPP_CDECL Subtract(word *C, const word *A, const word *B, unsigned int N);
#ifdef SSE2_INTRINSICS_AVAILABLE
static void CRYPTOPP_CDECL Multiply4(word *C, const word *A, const word *B);
static void CRYPTOPP_CDECL Multiply8(word *C, const word *A, const word *B);
static void CRYPTOPP_CDECL Multiply8Bottom(word *C, const word *A, const word *B);
#endif
};
typedef word (CRYPTOPP_CDECL * PAddSub)(word *C, const word *A, const word *B, unsigned int N);
typedef void (CRYPTOPP_CDECL * PMul)(word *C, const word *A, const word *B);
static PAddSub s_pAdd, s_pSub;
#ifdef SSE2_INTRINSICS_AVAILABLE
static PMul s_pMul4, s_pMul8, s_pMul8B;
#endif
static void SetPentiumFunctionPointers()
{
if (IsP4())
{
s_pAdd = &P4Optimized::Add;
s_pSub = &P4Optimized::Subtract;
}
else
{
s_pAdd = &PentiumOptimized::Add;
s_pSub = &PentiumOptimized::Subtract;
}
#ifdef SSE2_INTRINSICS_AVAILABLE
if (HasSSE2())
{
s_pMul4 = &P4Optimized::Multiply4;
s_pMul8 = &P4Optimized::Multiply8;
s_pMul8B = &P4Optimized::Multiply8Bottom;
}
else
{
s_pMul4 = &PentiumOptimized::Multiply4;
s_pMul8 = &PentiumOptimized::Multiply8;
s_pMul8B = &PentiumOptimized::Multiply8Bottom;
}
#endif
}
static const char s_RunAtStartupSetPentiumFunctionPointers = (SetPentiumFunctionPointers(), 0);
void DisableSSE2()
{
s_sse2Enabled = false;
SetPentiumFunctionPointers();
}
class LowLevel : public PentiumOptimized
{
public:
inline static word Add(word *C, const word *A, const word *B, unsigned int N)
{return s_pAdd(C, A, B, N);}
inline static word Subtract(word *C, const word *A, const word *B, unsigned int N)
{return s_pSub(C, A, B, N);}
inline static void Square4(word *R, const word *A)
{Multiply4(R, A, A);}
#ifdef SSE2_INTRINSICS_AVAILABLE
inline static void Multiply4(word *C, const word *A, const word *B)
{s_pMul4(C, A, B);}
inline static void Multiply8(word *C, const word *A, const word *B)
{s_pMul8(C, A, B);}
inline static void Multiply8Bottom(word *C, const word *A, const word *B)
{s_pMul8B(C, A, B);}
#endif
};
// use some tricks to share assembly code between MSVC and GCC
#ifdef _MSC_VER
#define CRYPTOPP_NAKED __declspec(naked)
#define AS1(x) __asm x
#define AS2(x, y) __asm x, y
#define AddPrologue \
__asm push ebp \
__asm push ebx \
__asm push esi \
__asm push edi \
__asm mov ecx, [esp+20] \
__asm mov edx, [esp+24] \
__asm mov ebx, [esp+28] \
__asm mov esi, [esp+32]
#define AddEpilogue \
__asm pop edi \
__asm pop esi \
__asm pop ebx \
__asm pop ebp \
__asm ret
#define MulPrologue \
__asm push ebp \
__asm push ebx \
__asm push esi \
__asm push edi \
__asm mov ecx, [esp+28] \
__asm mov esi, [esp+24] \
__asm push [esp+20]
#define MulEpilogue \
__asm add esp, 4 \
__asm pop edi \
__asm pop esi \
__asm pop ebx \
__asm pop ebp \
__asm ret
#else
#define CRYPTOPP_NAKED
#define AS1(x) #x ";"
#define AS2(x, y) #x ", " #y ";"
#define AddPrologue \
__asm__ __volatile__ \
( \
"push %%ebx;" /* save this manually, in case of -fPIC */ \
"mov %2, %%ebx;" \
".intel_syntax noprefix;" \
"push ebp;"
#define AddEpilogue \
"pop ebp;" \
".att_syntax prefix;" \
"pop %%ebx;" \
: \
: "c" (C), "d" (A), "m" (B), "S" (N) \
: "%edi", "memory", "cc" \
);
#define MulPrologue \
__asm__ __volatile__ \
( \
"push %%ebx;" /* save this manually, in case of -fPIC */ \
"push %%ebp;" \
"push %0;" \
".intel_syntax noprefix;"
#define MulEpilogue \
"add esp, 4;" \
"pop ebp;" \
"pop ebx;" \
".att_syntax prefix;" \
: \
: "rm" (Z), "S" (X), "c" (Y) \
: "%eax", "%edx", "%edi", "memory", "cc" \
);
#endif
CRYPTOPP_NAKED word PentiumOptimized::Add(word *C, const word *A, const word *B, unsigned int N)
{
AddPrologue
// now: ebx = B, ecx = C, edx = A, esi = N
AS2( sub ecx, edx) // hold the distance between C & A so we can add this to A to get C
AS2( xor eax, eax) // clear eax
AS2( sub eax, esi) // eax is a negative index from end of B
AS2( lea ebx, [ebx+4*esi]) // ebx is end of B
AS2( sar eax, 1) // unit of eax is now dwords; this also clears the carry flag
AS1( jz loopendAdd) // if no dwords then nothing to do
AS1(loopstartAdd:)
AS2( mov esi,[edx]) // load lower word of A
AS2( mov ebp,[edx+4]) // load higher word of A
AS2( mov edi,[ebx+8*eax]) // load lower word of B
AS2( lea edx,[edx+8]) // advance A and C
AS2( adc esi,edi) // add lower words
AS2( mov edi,[ebx+8*eax+4]) // load higher word of B
AS2( adc ebp,edi) // add higher words
AS1( inc eax) // advance B
AS2( mov [edx+ecx-8],esi) // store lower word result
AS2( mov [edx+ecx-4],ebp) // store higher word result
AS1( jnz loopstartAdd) // loop until eax overflows and becomes zero
AS1(loopendAdd:)
AS2( adc eax, 0) // store carry into eax (return result register)
AddEpilogue
}
CRYPTOPP_NAKED word PentiumOptimized::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
AddPrologue
// now: ebx = B, ecx = C, edx = A, esi = N
AS2( sub ecx, edx) // hold the distance between C & A so we can add this to A to get C
AS2( xor eax, eax) // clear eax
AS2( sub eax, esi) // eax is a negative index from end of B
AS2( lea ebx, [ebx+4*esi]) // ebx is end of B
AS2( sar eax, 1) // unit of eax is now dwords; this also clears the carry flag
AS1( jz loopendSub) // if no dwords then nothing to do
AS1(loopstartSub:)
AS2( mov esi,[edx]) // load lower word of A
AS2( mov ebp,[edx+4]) // load higher word of A
AS2( mov edi,[ebx+8*eax]) // load lower word of B
AS2( lea edx,[edx+8]) // advance A and C
AS2( sbb esi,edi) // subtract lower words
AS2( mov edi,[ebx+8*eax+4]) // load higher word of B
AS2( sbb ebp,edi) // subtract higher words
AS1( inc eax) // advance B
AS2( mov [edx+ecx-8],esi) // store lower word result
AS2( mov [edx+ecx-4],ebp) // store higher word result
AS1( jnz loopstartSub) // loop until eax overflows and becomes zero
AS1(loopendSub:)
AS2( adc eax, 0) // store carry into eax (return result register)
AddEpilogue
}
// On Pentium 4, the adc and sbb instructions are very expensive, so avoid them.
CRYPTOPP_NAKED word P4Optimized::Add(word *C, const word *A, const word *B, unsigned int N)
{
AddPrologue
// now: ebx = B, ecx = C, edx = A, esi = N
AS2( xor eax, eax)
AS1( neg esi)
AS1( jz loopendAddP4) // if no dwords then nothing to do
AS2( mov edi, [edx])
AS2( mov ebp, [ebx])
AS1( jmp carry1AddP4)
AS1(loopstartAddP4:)
AS2( mov edi, [edx+8])
AS2( add ecx, 8)
AS2( add edx, 8)
AS2( mov ebp, [ebx])
AS2( add edi, eax)
AS1( jc carry1AddP4)
AS2( xor eax, eax)
AS1(carry1AddP4:)
AS2( add edi, ebp)
AS2( mov ebp, 1)
AS2( mov [ecx], edi)
AS2( mov edi, [edx+4])
AS2( cmovc eax, ebp)
AS2( mov ebp, [ebx+4])
AS2( add ebx, 8)
AS2( add edi, eax)
AS1( jc carry2AddP4)
AS2( xor eax, eax)
AS1(carry2AddP4:)
AS2( add edi, ebp)
AS2( mov ebp, 1)
AS2( cmovc eax, ebp)
AS2( mov [ecx+4], edi)
AS2( add esi, 2)
AS1( jnz loopstartAddP4)
AS1(loopendAddP4:)
AddEpilogue
}
CRYPTOPP_NAKED word P4Optimized::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
AddPrologue
// now: ebx = B, ecx = C, edx = A, esi = N
AS2( xor eax, eax)
AS1( neg esi)
AS1( jz loopendSubP4) // if no dwords then nothing to do
AS2( mov edi, [edx])
AS2( mov ebp, [ebx])
AS1( jmp carry1SubP4)
AS1(loopstartSubP4:)
AS2( mov edi, [edx+8])
AS2( add edx, 8)
AS2( add ecx, 8)
AS2( mov ebp, [ebx])
AS2( sub edi, eax)
AS1( jc carry1SubP4)
AS2( xor eax, eax)
AS1(carry1SubP4:)
AS2( sub edi, ebp)
AS2( mov ebp, 1)
AS2( mov [ecx], edi)
AS2( mov edi, [edx+4])
AS2( cmovc eax, ebp)
AS2( mov ebp, [ebx+4])
AS2( add ebx, 8)
AS2( sub edi, eax)
AS1( jc carry2SubP4)
AS2( xor eax, eax)
AS1(carry2SubP4:)
AS2( sub edi, ebp)
AS2( mov ebp, 1)
AS2( cmovc eax, ebp)
AS2( mov [ecx+4], edi)
AS2( add esi, 2)
AS1( jnz loopstartSubP4)
AS1(loopendSubP4:)
AddEpilogue
}
// multiply assembly code originally contributed by Leonard Janke
#define MulStartup \
AS2(xor ebp, ebp) \
AS2(xor edi, edi) \
AS2(xor ebx, ebx)
#define MulShiftCarry \
AS2(mov ebp, edx) \
AS2(mov edi, ebx) \
AS2(xor ebx, ebx)
#define MulAccumulateBottom(i,j) \
AS2(mov eax, [ecx+4*j]) \
AS2(imul eax, dword ptr [esi+4*i]) \
AS2(add ebp, eax)
#define MulAccumulate(i,j) \
AS2(mov eax, [ecx+4*j]) \
AS1(mul dword ptr [esi+4*i]) \
AS2(add ebp, eax) \
AS2(adc edi, edx) \
AS2(adc bl, bh)
#define MulStoreDigit(i) \
AS2(mov edx, edi) \
AS2(mov edi, [esp]) \
AS2(mov [edi+4*i], ebp)
#define MulLastDiagonal(digits) \
AS2(mov eax, [ecx+4*(digits-1)]) \
AS1(mul dword ptr [esi+4*(digits-1)]) \
AS2(add ebp, eax) \
AS2(adc edx, edi) \
AS2(mov edi, [esp]) \
AS2(mov [edi+4*(2*digits-2)], ebp) \
AS2(mov [edi+4*(2*digits-1)], edx)
CRYPTOPP_NAKED void PentiumOptimized::Multiply4(word* Z, const word* X, const word* Y)
{
MulPrologue
// now: [esp] = Z, esi = X, ecx = Y
MulStartup
MulAccumulate(0,0)
MulStoreDigit(0)
MulShiftCarry
MulAccumulate(1,0)
MulAccumulate(0,1)
MulStoreDigit(1)
MulShiftCarry
MulAccumulate(2,0)
MulAccumulate(1,1)
MulAccumulate(0,2)
MulStoreDigit(2)
MulShiftCarry
MulAccumulate(3,0)
MulAccumulate(2,1)
MulAccumulate(1,2)
MulAccumulate(0,3)
MulStoreDigit(3)
MulShiftCarry
MulAccumulate(3,1)
MulAccumulate(2,2)
MulAccumulate(1,3)
MulStoreDigit(4)
MulShiftCarry
MulAccumulate(3,2)
MulAccumulate(2,3)
MulStoreDigit(5)
MulShiftCarry
MulLastDiagonal(4)
MulEpilogue
}
CRYPTOPP_NAKED void PentiumOptimized::Multiply8(word* Z, const word* X, const word* Y)
{
MulPrologue
// now: [esp] = Z, esi = X, ecx = Y
MulStartup
MulAccumulate(0,0)
MulStoreDigit(0)
MulShiftCarry
MulAccumulate(1,0)
MulAccumulate(0,1)
MulStoreDigit(1)
MulShiftCarry
MulAccumulate(2,0)
MulAccumulate(1,1)
MulAccumulate(0,2)
MulStoreDigit(2)
MulShiftCarry
MulAccumulate(3,0)
MulAccumulate(2,1)
MulAccumulate(1,2)
MulAccumulate(0,3)
MulStoreDigit(3)
MulShiftCarry
MulAccumulate(4,0)
MulAccumulate(3,1)
MulAccumulate(2,2)
MulAccumulate(1,3)
MulAccumulate(0,4)
MulStoreDigit(4)
MulShiftCarry
MulAccumulate(5,0)
MulAccumulate(4,1)
MulAccumulate(3,2)
MulAccumulate(2,3)
MulAccumulate(1,4)
MulAccumulate(0,5)
MulStoreDigit(5)
MulShiftCarry
MulAccumulate(6,0)
MulAccumulate(5,1)
MulAccumulate(4,2)
MulAccumulate(3,3)
MulAccumulate(2,4)
MulAccumulate(1,5)
MulAccumulate(0,6)
MulStoreDigit(6)
MulShiftCarry
MulAccumulate(7,0)
MulAccumulate(6,1)
MulAccumulate(5,2)
MulAccumulate(4,3)
MulAccumulate(3,4)
MulAccumulate(2,5)
MulAccumulate(1,6)
MulAccumulate(0,7)
MulStoreDigit(7)
MulShiftCarry
MulAccumulate(7,1)
MulAccumulate(6,2)
MulAccumulate(5,3)
MulAccumulate(4,4)
MulAccumulate(3,5)
MulAccumulate(2,6)
MulAccumulate(1,7)
MulStoreDigit(8)
MulShiftCarry
MulAccumulate(7,2)
MulAccumulate(6,3)
MulAccumulate(5,4)
MulAccumulate(4,5)
MulAccumulate(3,6)
MulAccumulate(2,7)
MulStoreDigit(9)
MulShiftCarry
MulAccumulate(7,3)
MulAccumulate(6,4)
MulAccumulate(5,5)
MulAccumulate(4,6)
MulAccumulate(3,7)
MulStoreDigit(10)
MulShiftCarry
MulAccumulate(7,4)
MulAccumulate(6,5)
MulAccumulate(5,6)
MulAccumulate(4,7)
MulStoreDigit(11)
MulShiftCarry
MulAccumulate(7,5)
MulAccumulate(6,6)
MulAccumulate(5,7)
MulStoreDigit(12)
MulShiftCarry
MulAccumulate(7,6)
MulAccumulate(6,7)
MulStoreDigit(13)
MulShiftCarry
MulLastDiagonal(8)
MulEpilogue
}
CRYPTOPP_NAKED void PentiumOptimized::Multiply8Bottom(word* Z, const word* X, const word* Y)
{
MulPrologue
// now: [esp] = Z, esi = X, ecx = Y
MulStartup
MulAccumulate(0,0)
MulStoreDigit(0)
MulShiftCarry
MulAccumulate(1,0)
MulAccumulate(0,1)
MulStoreDigit(1)
MulShiftCarry
MulAccumulate(2,0)
MulAccumulate(1,1)
MulAccumulate(0,2)
MulStoreDigit(2)
MulShiftCarry
MulAccumulate(3,0)
MulAccumulate(2,1)
MulAccumulate(1,2)
MulAccumulate(0,3)
MulStoreDigit(3)
MulShiftCarry
MulAccumulate(4,0)
MulAccumulate(3,1)
MulAccumulate(2,2)
MulAccumulate(1,3)
MulAccumulate(0,4)
MulStoreDigit(4)
MulShiftCarry
MulAccumulate(5,0)
MulAccumulate(4,1)
MulAccumulate(3,2)
MulAccumulate(2,3)
MulAccumulate(1,4)
MulAccumulate(0,5)
MulStoreDigit(5)
MulShiftCarry
MulAccumulate(6,0)
MulAccumulate(5,1)
MulAccumulate(4,2)
MulAccumulate(3,3)
MulAccumulate(2,4)
MulAccumulate(1,5)
MulAccumulate(0,6)
MulStoreDigit(6)
MulShiftCarry
MulAccumulateBottom(7,0)
MulAccumulateBottom(6,1)
MulAccumulateBottom(5,2)
MulAccumulateBottom(4,3)
MulAccumulateBottom(3,4)
MulAccumulateBottom(2,5)
MulAccumulateBottom(1,6)
MulAccumulateBottom(0,7)
MulStoreDigit(7)
MulEpilogue
}
#undef AS1
#undef AS2
#else // not x86 - no processor specific code at this layer
typedef Portable LowLevel;
#endif
#ifdef SSE2_INTRINSICS_AVAILABLE
#ifdef __GNUC__
#define CRYPTOPP_FASTCALL
#else
#define CRYPTOPP_FASTCALL __fastcall
#endif
static void CRYPTOPP_FASTCALL P4_Mul(__m128i *C, const __m128i *A, const __m128i *B)
{
__m128i a3210 = _mm_load_si128(A);
__m128i b3210 = _mm_load_si128(B);
__m128i sum;
__m128i z = _mm_setzero_si128();
__m128i a2b2_a0b0 = _mm_mul_epu32(a3210, b3210);
C[0] = a2b2_a0b0;
__m128i a3120 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(3, 1, 2, 0));
__m128i b3021 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(3, 0, 2, 1));
__m128i a1b0_a0b1 = _mm_mul_epu32(a3120, b3021);
__m128i a1b0 = _mm_unpackhi_epi32(a1b0_a0b1, z);
__m128i a0b1 = _mm_unpacklo_epi32(a1b0_a0b1, z);
C[1] = _mm_add_epi64(a1b0, a0b1);
__m128i a31 = _mm_srli_epi64(a3210, 32);
__m128i b31 = _mm_srli_epi64(b3210, 32);
__m128i a3b3_a1b1 = _mm_mul_epu32(a31, b31);
C[6] = a3b3_a1b1;
__m128i a1b1 = _mm_unpacklo_epi32(a3b3_a1b1, z);
__m128i b3012 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(3, 0, 1, 2));
__m128i a2b0_a0b2 = _mm_mul_epu32(a3210, b3012);
__m128i a0b2 = _mm_unpacklo_epi32(a2b0_a0b2, z);
__m128i a2b0 = _mm_unpackhi_epi32(a2b0_a0b2, z);
sum = _mm_add_epi64(a1b1, a0b2);
C[2] = _mm_add_epi64(sum, a2b0);
__m128i a2301 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(2, 3, 0, 1));
__m128i b2103 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(2, 1, 0, 3));
__m128i a3b0_a1b2 = _mm_mul_epu32(a2301, b3012);
__m128i a2b1_a0b3 = _mm_mul_epu32(a3210, b2103);
__m128i a3b0 = _mm_unpackhi_epi32(a3b0_a1b2, z);
__m128i a1b2 = _mm_unpacklo_epi32(a3b0_a1b2, z);
__m128i a2b1 = _mm_unpackhi_epi32(a2b1_a0b3, z);
__m128i a0b3 = _mm_unpacklo_epi32(a2b1_a0b3, z);
__m128i sum1 = _mm_add_epi64(a3b0, a1b2);
sum = _mm_add_epi64(a2b1, a0b3);
C[3] = _mm_add_epi64(sum, sum1);
__m128i a3b1_a1b3 = _mm_mul_epu32(a2301, b2103);
__m128i a2b2 = _mm_unpackhi_epi32(a2b2_a0b0, z);
__m128i a3b1 = _mm_unpackhi_epi32(a3b1_a1b3, z);
__m128i a1b3 = _mm_unpacklo_epi32(a3b1_a1b3, z);
sum = _mm_add_epi64(a2b2, a3b1);
C[4] = _mm_add_epi64(sum, a1b3);
__m128i a1302 = _mm_shuffle_epi32(a3210, _MM_SHUFFLE(1, 3, 0, 2));
__m128i b1203 = _mm_shuffle_epi32(b3210, _MM_SHUFFLE(1, 2, 0, 3));
__m128i a3b2_a2b3 = _mm_mul_epu32(a1302, b1203);
__m128i a3b2 = _mm_unpackhi_epi32(a3b2_a2b3, z);
__m128i a2b3 = _mm_unpacklo_epi32(a3b2_a2b3, z);
C[5] = _mm_add_epi64(a3b2, a2b3);
}
void P4Optimized::Multiply4(word *C, const word *A, const word *B)
{
__m128i temp[7];
const word *w = (word *)temp;
const __m64 *mw = (__m64 *)w;
P4_Mul(temp, (__m128i *)A, (__m128i *)B);
C[0] = w[0];
__m64 s1, s2;
__m64 w1 = _mm_cvtsi32_si64(w[1]);
__m64 w4 = mw[2];
__m64 w6 = mw[3];
__m64 w8 = mw[4];
__m64 w10 = mw[5];
__m64 w12 = mw[6];
__m64 w14 = mw[7];
__m64 w16 = mw[8];
__m64 w18 = mw[9];
__m64 w20 = mw[10];
__m64 w22 = mw[11];
__m64 w26 = _mm_cvtsi32_si64(w[26]);
s1 = _mm_add_si64(w1, w4);
C[1] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w6, w8);
s1 = _mm_add_si64(s1, s2);
C[2] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w10, w12);
s1 = _mm_add_si64(s1, s2);
C[3] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w14, w16);
s1 = _mm_add_si64(s1, s2);
C[4] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w18, w20);
s1 = _mm_add_si64(s1, s2);
C[5] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w22, w26);
s1 = _mm_add_si64(s1, s2);
C[6] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
C[7] = _mm_cvtsi64_si32(s1) + w[27];
_mm_empty();
}
void P4Optimized::Multiply8(word *C, const word *A, const word *B)
{
__m128i temp[28];
const word *w = (word *)temp;
const __m64 *mw = (__m64 *)w;
const word *x = (word *)temp+7*4;
const __m64 *mx = (__m64 *)x;
const word *y = (word *)temp+7*4*2;
const __m64 *my = (__m64 *)y;
const word *z = (word *)temp+7*4*3;
const __m64 *mz = (__m64 *)z;
P4_Mul(temp, (__m128i *)A, (__m128i *)B);
P4_Mul(temp+7, (__m128i *)A+1, (__m128i *)B);
P4_Mul(temp+14, (__m128i *)A, (__m128i *)B+1);
P4_Mul(temp+21, (__m128i *)A+1, (__m128i *)B+1);
C[0] = w[0];
__m64 s1, s2, s3, s4;
__m64 w1 = _mm_cvtsi32_si64(w[1]);
__m64 w4 = mw[2];
__m64 w6 = mw[3];
__m64 w8 = mw[4];
__m64 w10 = mw[5];
__m64 w12 = mw[6];
__m64 w14 = mw[7];
__m64 w16 = mw[8];
__m64 w18 = mw[9];
__m64 w20 = mw[10];
__m64 w22 = mw[11];
__m64 w26 = _mm_cvtsi32_si64(w[26]);
__m64 w27 = _mm_cvtsi32_si64(w[27]);
__m64 x0 = _mm_cvtsi32_si64(x[0]);
__m64 x1 = _mm_cvtsi32_si64(x[1]);
__m64 x4 = mx[2];
__m64 x6 = mx[3];
__m64 x8 = mx[4];
__m64 x10 = mx[5];
__m64 x12 = mx[6];
__m64 x14 = mx[7];
__m64 x16 = mx[8];
__m64 x18 = mx[9];
__m64 x20 = mx[10];
__m64 x22 = mx[11];
__m64 x26 = _mm_cvtsi32_si64(x[26]);
__m64 x27 = _mm_cvtsi32_si64(x[27]);
__m64 y0 = _mm_cvtsi32_si64(y[0]);
__m64 y1 = _mm_cvtsi32_si64(y[1]);
__m64 y4 = my[2];
__m64 y6 = my[3];
__m64 y8 = my[4];
__m64 y10 = my[5];
__m64 y12 = my[6];
__m64 y14 = my[7];
__m64 y16 = my[8];
__m64 y18 = my[9];
__m64 y20 = my[10];
__m64 y22 = my[11];
__m64 y26 = _mm_cvtsi32_si64(y[26]);
__m64 y27 = _mm_cvtsi32_si64(y[27]);
__m64 z0 = _mm_cvtsi32_si64(z[0]);
__m64 z1 = _mm_cvtsi32_si64(z[1]);
__m64 z4 = mz[2];
__m64 z6 = mz[3];
__m64 z8 = mz[4];
__m64 z10 = mz[5];
__m64 z12 = mz[6];
__m64 z14 = mz[7];
__m64 z16 = mz[8];
__m64 z18 = mz[9];
__m64 z20 = mz[10];
__m64 z22 = mz[11];
__m64 z26 = _mm_cvtsi32_si64(z[26]);
s1 = _mm_add_si64(w1, w4);
C[1] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w6, w8);
s1 = _mm_add_si64(s1, s2);
C[2] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w10, w12);
s1 = _mm_add_si64(s1, s2);
C[3] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x0, y0);
s2 = _mm_add_si64(w14, w16);
s1 = _mm_add_si64(s1, s3);
s1 = _mm_add_si64(s1, s2);
C[4] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x1, y1);
s4 = _mm_add_si64(x4, y4);
s1 = _mm_add_si64(s1, w18);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, w20);
s1 = _mm_add_si64(s1, s3);
C[5] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x6, y6);
s4 = _mm_add_si64(x8, y8);
s1 = _mm_add_si64(s1, w22);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, w26);
s1 = _mm_add_si64(s1, s3);
C[6] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x10, y10);
s4 = _mm_add_si64(x12, y12);
s1 = _mm_add_si64(s1, w27);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, s3);
C[7] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x14, y14);
s4 = _mm_add_si64(x16, y16);
s1 = _mm_add_si64(s1, z0);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, s3);
C[8] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x18, y18);
s4 = _mm_add_si64(x20, y20);
s1 = _mm_add_si64(s1, z1);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, z4);
s1 = _mm_add_si64(s1, s3);
C[9] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x22, y22);
s4 = _mm_add_si64(x26, y26);
s1 = _mm_add_si64(s1, z6);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, z8);
s1 = _mm_add_si64(s1, s3);
C[10] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x27, y27);
s1 = _mm_add_si64(s1, z10);
s1 = _mm_add_si64(s1, z12);
s1 = _mm_add_si64(s1, s3);
C[11] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(z14, z16);
s1 = _mm_add_si64(s1, s3);
C[12] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(z18, z20);
s1 = _mm_add_si64(s1, s3);
C[13] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(z22, z26);
s1 = _mm_add_si64(s1, s3);
C[14] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
C[15] = z[27] + _mm_cvtsi64_si32(s1);
_mm_empty();
}
void P4Optimized::Multiply8Bottom(word *C, const word *A, const word *B)
{
__m128i temp[21];
const word *w = (word *)temp;
const __m64 *mw = (__m64 *)w;
const word *x = (word *)temp+7*4;
const __m64 *mx = (__m64 *)x;
const word *y = (word *)temp+7*4*2;
const __m64 *my = (__m64 *)y;
P4_Mul(temp, (__m128i *)A, (__m128i *)B);
P4_Mul(temp+7, (__m128i *)A+1, (__m128i *)B);
P4_Mul(temp+14, (__m128i *)A, (__m128i *)B+1);
C[0] = w[0];
__m64 s1, s2, s3, s4;
__m64 w1 = _mm_cvtsi32_si64(w[1]);
__m64 w4 = mw[2];
__m64 w6 = mw[3];
__m64 w8 = mw[4];
__m64 w10 = mw[5];
__m64 w12 = mw[6];
__m64 w14 = mw[7];
__m64 w16 = mw[8];
__m64 w18 = mw[9];
__m64 w20 = mw[10];
__m64 w22 = mw[11];
__m64 w26 = _mm_cvtsi32_si64(w[26]);
__m64 x0 = _mm_cvtsi32_si64(x[0]);
__m64 x1 = _mm_cvtsi32_si64(x[1]);
__m64 x4 = mx[2];
__m64 x6 = mx[3];
__m64 x8 = mx[4];
__m64 y0 = _mm_cvtsi32_si64(y[0]);
__m64 y1 = _mm_cvtsi32_si64(y[1]);
__m64 y4 = my[2];
__m64 y6 = my[3];
__m64 y8 = my[4];
s1 = _mm_add_si64(w1, w4);
C[1] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w6, w8);
s1 = _mm_add_si64(s1, s2);
C[2] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s2 = _mm_add_si64(w10, w12);
s1 = _mm_add_si64(s1, s2);
C[3] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x0, y0);
s2 = _mm_add_si64(w14, w16);
s1 = _mm_add_si64(s1, s3);
s1 = _mm_add_si64(s1, s2);
C[4] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x1, y1);
s4 = _mm_add_si64(x4, y4);
s1 = _mm_add_si64(s1, w18);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, w20);
s1 = _mm_add_si64(s1, s3);
C[5] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
s3 = _mm_add_si64(x6, y6);
s4 = _mm_add_si64(x8, y8);
s1 = _mm_add_si64(s1, w22);
s3 = _mm_add_si64(s3, s4);
s1 = _mm_add_si64(s1, w26);
s1 = _mm_add_si64(s1, s3);
C[6] = _mm_cvtsi64_si32(s1);
s1 = _mm_srli_si64(s1, 32);
C[7] = _mm_cvtsi64_si32(s1) + w[27] + x[10] + y[10] + x[12] + y[12];
_mm_empty();
}
#endif // #ifdef SSE2_INTRINSICS_AVAILABLE
// ********************************************************
#define A0 A
#define A1 (A+N2)
#define B0 B
#define B1 (B+N2)
#define T0 T
#define T1 (T+N2)
#define T2 (T+N)
#define T3 (T+N+N2)
#define R0 R
#define R1 (R+N2)
#define R2 (R+N)
#define R3 (R+N+N2)
// R[2*N] - result = A*B
// T[2*N] - temporary work space
// A[N] --- multiplier
// B[N] --- multiplicant
void RecursiveMultiply(word *R, word *T, const word *A, const word *B, unsigned int N)
{
assert(N>=2 && N%2==0);
if (LowLevel::MultiplyRecursionLimit() >= 8 && N==8)
LowLevel::Multiply8(R, A, B);
else if (LowLevel::MultiplyRecursionLimit() >= 4 && N==4)
LowLevel::Multiply4(R, A, B);
else if (N==2)
LowLevel::Multiply2(R, A, B);
else
{
const unsigned int N2 = N/2;
int carry;
int aComp = Compare(A0, A1, N2);
int bComp = Compare(B0, B1, N2);
switch (2*aComp + aComp + bComp)
{
case -4:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
LowLevel::Subtract(T1, T1, R0, N2);
carry = -1;
break;
case -2:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
carry = 0;
break;
case 2:
LowLevel::Subtract(R0, A0, A1, N2);
LowLevel::Subtract(R1, B1, B0, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
carry = 0;
break;
case 4:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
LowLevel::Subtract(T1, T1, R1, N2);
carry = -1;
break;
default:
SetWords(T0, 0, N);
carry = 0;
}
RecursiveMultiply(R0, T2, A0, B0, N2);
RecursiveMultiply(R2, T2, A1, B1, N2);
// now T[01] holds (A1-A0)*(B0-B1), R[01] holds A0*B0, R[23] holds A1*B1
carry += LowLevel::Add(T0, T0, R0, N);
carry += LowLevel::Add(T0, T0, R2, N);
carry += LowLevel::Add(R1, R1, T0, N);
assert (carry >= 0 && carry <= 2);
Increment(R3, N2, carry);
}
}
// R[2*N] - result = A*A
// T[2*N] - temporary work space
// A[N] --- number to be squared
void RecursiveSquare(word *R, word *T, const word *A, unsigned int N)
{
assert(N && N%2==0);
if (LowLevel::SquareRecursionLimit() >= 8 && N==8)
LowLevel::Square8(R, A);
if (LowLevel::SquareRecursionLimit() >= 4 && N==4)
LowLevel::Square4(R, A);
else if (N==2)
LowLevel::Square2(R, A);
else
{
const unsigned int N2 = N/2;
RecursiveSquare(R0, T2, A0, N2);
RecursiveSquare(R2, T2, A1, N2);
RecursiveMultiply(T0, T2, A0, A1, N2);
word carry = LowLevel::Add(R1, R1, T0, N);
carry += LowLevel::Add(R1, R1, T0, N);
Increment(R3, N2, carry);
}
}
// R[N] - bottom half of A*B
// T[N] - temporary work space
// A[N] - multiplier
// B[N] - multiplicant
void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
{
assert(N>=2 && N%2==0);
if (LowLevel::MultiplyBottomRecursionLimit() >= 8 && N==8)
LowLevel::Multiply8Bottom(R, A, B);
else if (LowLevel::MultiplyBottomRecursionLimit() >= 4 && N==4)
LowLevel::Multiply4Bottom(R, A, B);
else if (N==2)
LowLevel::Multiply2Bottom(R, A, B);
else
{
const unsigned int N2 = N/2;
RecursiveMultiply(R, T, A0, B0, N2);
RecursiveMultiplyBottom(T0, T1, A1, B0, N2);
LowLevel::Add(R1, R1, T0, N2);
RecursiveMultiplyBottom(T0, T1, A0, B1, N2);
LowLevel::Add(R1, R1, T0, N2);
}
}
// R[N] --- upper half of A*B
// T[2*N] - temporary work space
// L[N] --- lower half of A*B
// A[N] --- multiplier
// B[N] --- multiplicant
void RecursiveMultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
{
assert(N>=2 && N%2==0);
if (N==4)
{
LowLevel::Multiply4(T, A, B);
memcpy(R, T+4, 4*WORD_SIZE);
}
else if (N==2)
{
LowLevel::Multiply2(T, A, B);
memcpy(R, T+2, 2*WORD_SIZE);
}
else
{
const unsigned int N2 = N/2;
int carry;
int aComp = Compare(A0, A1, N2);
int bComp = Compare(B0, B1, N2);
switch (2*aComp + aComp + bComp)
{
case -4:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
LowLevel::Subtract(T1, T1, R0, N2);
carry = -1;
break;
case -2:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
carry = 0;
break;
case 2:
LowLevel::Subtract(R0, A0, A1, N2);
LowLevel::Subtract(R1, B1, B0, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
carry = 0;
break;
case 4:
LowLevel::Subtract(R0, A1, A0, N2);
LowLevel::Subtract(R1, B0, B1, N2);
RecursiveMultiply(T0, T2, R0, R1, N2);
LowLevel::Subtract(T1, T1, R1, N2);
carry = -1;
break;
default:
SetWords(T0, 0, N);
carry = 0;
}
RecursiveMultiply(T2, R0, A1, B1, N2);
// now T[01] holds (A1-A0)*(B0-B1), T[23] holds A1*B1
word c2 = LowLevel::Subtract(R0, L+N2, L, N2);
c2 += LowLevel::Subtract(R0, R0, T0, N2);
word t = (Compare(R0, T2, N2) == -1);
carry += t;
carry += Increment(R0, N2, c2+t);
carry += LowLevel::Add(R0, R0, T1, N2);
carry += LowLevel::Add(R0, R0, T3, N2);
assert (carry >= 0 && carry <= 2);
CopyWords(R1, T3, N2);
Increment(R1, N2, carry);
}
}
inline word Add(word *C, const word *A, const word *B, unsigned int N)
{
return LowLevel::Add(C, A, B, N);
}
inline word Subtract(word *C, const word *A, const word *B, unsigned int N)
{
return LowLevel::Subtract(C, A, B, N);
}
inline void Multiply(word *R, word *T, const word *A, const word *B, unsigned int N)
{
RecursiveMultiply(R, T, A, B, N);
}
inline void Square(word *R, word *T, const word *A, unsigned int N)
{
RecursiveSquare(R, T, A, N);
}
inline void MultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
{
RecursiveMultiplyBottom(R, T, A, B, N);
}
inline void MultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
{
RecursiveMultiplyTop(R, T, L, A, B, N);
}
static word LinearMultiply(word *C, const word *A, word B, unsigned int N)
{
word carry=0;
for(unsigned i=0; i<N; i++)
{
DWord p = DWord::MultiplyAndAdd(A[i], B, carry);
C[i] = p.GetLowHalf();
carry = p.GetHighHalf();
}
return carry;
}
// R[NA+NB] - result = A*B
// T[NA+NB] - temporary work space
// A[NA] ---- multiplier
// B[NB] ---- multiplicant
void AsymmetricMultiply(word *R, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
{
if (NA == NB)
{
if (A == B)
Square(R, T, A, NA);
else
Multiply(R, T, A, B, NA);
return;
}
if (NA > NB)
{
std::swap(A, B);
std::swap(NA, NB);
}
assert(NB % NA == 0);
assert((NB/NA)%2 == 0); // NB is an even multiple of NA
if (NA==2 && !A[1])
{
switch (A[0])
{
case 0:
SetWords(R, 0, NB+2);
return;
case 1:
CopyWords(R, B, NB);
R[NB] = R[NB+1] = 0;
return;
default:
R[NB] = LinearMultiply(R, B, A[0], NB);
R[NB+1] = 0;
return;
}
}
Multiply(R, T, A, B, NA);
CopyWords(T+2*NA, R+NA, NA);
unsigned i;
for (i=2*NA; i<NB; i+=2*NA)
Multiply(T+NA+i, T, A, B+i, NA);
for (i=NA; i<NB; i+=2*NA)
Multiply(R+i, T, A, B+i, NA);
if (Add(R+NA, R+NA, T+2*NA, NB-NA))
Increment(R+NB, NA);
}
// R[N] ----- result = A inverse mod 2**(WORD_BITS*N)
// T[3*N/2] - temporary work space
// A[N] ----- an odd number as input
void RecursiveInverseModPower2(word *R, word *T, const word *A, unsigned int N)
{
if (N==2)
{
T[0] = AtomicInverseModPower2(A[0]);
T[1] = 0;
LowLevel::Multiply2Bottom(T+2, T, A);
TwosComplement(T+2, 2);
Increment(T+2, 2, 2);
LowLevel::Multiply2Bottom(R, T, T+2);
}
else
{
const unsigned int N2 = N/2;
RecursiveInverseModPower2(R0, T0, A0, N2);
T0[0] = 1;
SetWords(T0+1, 0, N2-1);
MultiplyTop(R1, T1, T0, R0, A0, N2);
MultiplyBottom(T0, T1, R0, A1, N2);
Add(T0, R1, T0, N2);
TwosComplement(T0, N2);
MultiplyBottom(R1, T1, R0, T0, N2);
}
}
// R[N] --- result = X/(2**(WORD_BITS*N)) mod M
// T[3*N] - temporary work space
// X[2*N] - number to be reduced
// M[N] --- modulus
// U[N] --- multiplicative inverse of M mod 2**(WORD_BITS*N)
void MontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, unsigned int N)
{
MultiplyBottom(R, T, X, U, N);
MultiplyTop(T, T+N, X, R, M, N);
word borrow = Subtract(T, X+N, T, N);
// defend against timing attack by doing this Add even when not needed
word carry = Add(T+N, T, M, N);
assert(carry || !borrow);
CopyWords(R, T + (borrow ? N : 0), N);
}
// R[N] --- result = X/(2**(WORD_BITS*N/2)) mod M
// T[2*N] - temporary work space
// X[2*N] - number to be reduced
// M[N] --- modulus
// U[N/2] - multiplicative inverse of M mod 2**(WORD_BITS*N/2)
// V[N] --- 2**(WORD_BITS*3*N/2) mod M
void HalfMontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, const word *V, unsigned int N)
{
assert(N%2==0 && N>=4);
#define M0 M
#define M1 (M+N2)
#define V0 V
#define V1 (V+N2)
#define X0 X
#define X1 (X+N2)
#define X2 (X+N)
#define X3 (X+N+N2)
const unsigned int N2 = N/2;
Multiply(T0, T2, V0, X3, N2);
int c2 = Add(T0, T0, X0, N);
MultiplyBottom(T3, T2, T0, U, N2);
MultiplyTop(T2, R, T0, T3, M0, N2);
c2 -= Subtract(T2, T1, T2, N2);
Multiply(T0, R, T3, M1, N2);
c2 -= Subtract(T0, T2, T0, N2);
int c3 = -(int)Subtract(T1, X2, T1, N2);
Multiply(R0, T2, V1, X3, N2);
c3 += Add(R, R, T, N);
if (c2>0)
c3 += Increment(R1, N2);
else if (c2<0)
c3 -= Decrement(R1, N2, -c2);
assert(c3>=-1 && c3<=1);
if (c3>0)
Subtract(R, R, M, N);
else if (c3<0)
Add(R, R, M, N);
#undef M0
#undef M1
#undef V0
#undef V1
#undef X0
#undef X1
#undef X2
#undef X3
}
#undef A0
#undef A1
#undef B0
#undef B1
#undef T0
#undef T1
#undef T2
#undef T3
#undef R0
#undef R1
#undef R2
#undef R3
/*
// do a 3 word by 2 word divide, returns quotient and leaves remainder in A
static word SubatomicDivide(word *A, word B0, word B1)
{
// assert {A[2],A[1]} < {B1,B0}, so quotient can fit in a word
assert(A[2] < B1 || (A[2]==B1 && A[1] < B0));
// estimate the quotient: do a 2 word by 1 word divide
word Q;
if (B1+1 == 0)
Q = A[2];
else
Q = DWord(A[1], A[2]).DividedBy(B1+1);
// now subtract Q*B from A
DWord p = DWord::Multiply(B0, Q);
DWord u = (DWord) A[0] - p.GetLowHalf();
A[0] = u.GetLowHalf();
u = (DWord) A[1] - p.GetHighHalf() - u.GetHighHalfAsBorrow() - DWord::Multiply(B1, Q);
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
// Q <= actual quotient, so fix it
while (A[2] || A[1] > B1 || (A[1]==B1 && A[0]>=B0))
{
u = (DWord) A[0] - B0;
A[0] = u.GetLowHalf();
u = (DWord) A[1] - B1 - u.GetHighHalfAsBorrow();
A[1] = u.GetLowHalf();
A[2] += u.GetHighHalf();
Q++;
assert(Q); // shouldn't overflow
}
return Q;
}
// do a 4 word by 2 word divide, returns 2 word quotient in Q0 and Q1
static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
if (!B[0] && !B[1]) // if divisor is 0, we assume divisor==2**(2*WORD_BITS)
{
Q[0] = A[2];
Q[1] = A[3];
}
else
{
word T[4];
T[0] = A[0]; T[1] = A[1]; T[2] = A[2]; T[3] = A[3];
Q[1] = SubatomicDivide(T+1, B[0], B[1]);
Q[0] = SubatomicDivide(T, B[0], B[1]);
#ifndef NDEBUG
// multiply quotient and divisor and add remainder, make sure it equals dividend
assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
word P[4];
LowLevel::Multiply2(P, Q, B);
Add(P, P, T, 4);
assert(memcmp(P, A, 4*WORD_SIZE)==0);
#endif
}
}
*/
static inline void AtomicDivide(word *Q, const word *A, const word *B)
{
word T[4];
DWord q = DivideFourWordsByTwo<word, DWord>(T, DWord(A[0], A[1]), DWord(A[2], A[3]), DWord(B[0], B[1]));
Q[0] = q.GetLowHalf();
Q[1] = q.GetHighHalf();
#ifndef NDEBUG
if (B[0] || B[1])
{
// multiply quotient and divisor and add remainder, make sure it equals dividend
assert(!T[2] && !T[3] && (T[1] < B[1] || (T[1]==B[1] && T[0]<B[0])));
word P[4];
Portable::Multiply2(P, Q, B);
Add(P, P, T, 4);
assert(memcmp(P, A, 4*WORD_SIZE)==0);
}
#endif
}
// for use by Divide(), corrects the underestimated quotient {Q1,Q0}
static void CorrectQuotientEstimate(word *R, word *T, word *Q, const word *B, unsigned int N)
{
assert(N && N%2==0);
if (Q[1])
{
T[N] = T[N+1] = 0;
unsigned i;
for (i=0; i<N; i+=4)
LowLevel::Multiply2(T+i, Q, B+i);
for (i=2; i<N; i+=4)
if (LowLevel::Multiply2Add(T+i, Q, B+i))
T[i+5] += (++T[i+4]==0);
}
else
{
T[N] = LinearMultiply(T, B, Q[0], N);
T[N+1] = 0;
}
word borrow = Subtract(R, R, T, N+2);
assert(!borrow && !R[N+1]);
while (R[N] || Compare(R, B, N) >= 0)
{
R[N] -= Subtract(R, R, B, N);
Q[1] += (++Q[0]==0);
assert(Q[0] || Q[1]); // no overflow
}
}
// R[NB] -------- remainder = A%B
// Q[NA-NB+2] --- quotient = A/B
// T[NA+2*NB+4] - temp work space
// A[NA] -------- dividend
// B[NB] -------- divisor
void Divide(word *R, word *Q, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
{
assert(NA && NB && NA%2==0 && NB%2==0);
assert(B[NB-1] || B[NB-2]);
assert(NB <= NA);
// set up temporary work space
word *const TA=T;
word *const TB=T+NA+2;
word *const TP=T+NA+2+NB;
// copy B into TB and normalize it so that TB has highest bit set to 1
unsigned shiftWords = (B[NB-1]==0);
TB[0] = TB[NB-1] = 0;
CopyWords(TB+shiftWords, B, NB-shiftWords);
unsigned shiftBits = WORD_BITS - BitPrecision(TB[NB-1]);
assert(shiftBits < WORD_BITS);
ShiftWordsLeftByBits(TB, NB, shiftBits);
// copy A into TA and normalize it
TA[0] = TA[NA] = TA[NA+1] = 0;
CopyWords(TA+shiftWords, A, NA);
ShiftWordsLeftByBits(TA, NA+2, shiftBits);
if (TA[NA+1]==0 && TA[NA] <= 1)
{
Q[NA-NB+1] = Q[NA-NB] = 0;
while (TA[NA] || Compare(TA+NA-NB, TB, NB) >= 0)
{
TA[NA] -= Subtract(TA+NA-NB, TA+NA-NB, TB, NB);
++Q[NA-NB];
}
}
else
{
NA+=2;
assert(Compare(TA+NA-NB, TB, NB) < 0);
}
word BT[2];
BT[0] = TB[NB-2] + 1;
BT[1] = TB[NB-1] + (BT[0]==0);
// start reducing TA mod TB, 2 words at a time
for (unsigned i=NA-2; i>=NB; i-=2)
{
AtomicDivide(Q+i-NB, TA+i-2, BT);
CorrectQuotientEstimate(TA+i-NB, TP, Q+i-NB, TB, NB);
}
// copy TA into R, and denormalize it
CopyWords(R, TA+shiftWords, NB);
ShiftWordsRightByBits(R, NB, shiftBits);
}
static inline unsigned int EvenWordCount(const word *X, unsigned int N)
{
while (N && X[N-2]==0 && X[N-1]==0)
N-=2;
return N;
}
// return k
// R[N] --- result = A^(-1) * 2^k mod M
// T[4*N] - temporary work space
// A[NA] -- number to take inverse of
// M[N] --- modulus
unsigned int AlmostInverse(word *R, word *T, const word *A, unsigned int NA, const word *M, unsigned int N)
{
assert(NA<=N && N && N%2==0);
word *b = T;
word *c = T+N;
word *f = T+2*N;
word *g = T+3*N;
unsigned int bcLen=2, fgLen=EvenWordCount(M, N);
unsigned int k=0, s=0;
SetWords(T, 0, 3*N);
b[0]=1;
CopyWords(f, A, NA);
CopyWords(g, M, N);
while (1)
{
word t=f[0];
while (!t)
{
if (EvenWordCount(f, fgLen)==0)
{
SetWords(R, 0, N);
return 0;
}
ShiftWordsRightByWords(f, fgLen, 1);
if (c[bcLen-1]) bcLen+=2;
assert(bcLen <= N);
ShiftWordsLeftByWords(c, bcLen, 1);
k+=WORD_BITS;
t=f[0];
}
unsigned int i=0;
while (t%2 == 0)
{
t>>=1;
i++;
}
k+=i;
if (t==1 && f[1]==0 && EvenWordCount(f, fgLen)==2)
{
if (s%2==0)
CopyWords(R, b, N);
else
Subtract(R, M, b, N);
return k;
}
ShiftWordsRightByBits(f, fgLen, i);
t=ShiftWordsLeftByBits(c, bcLen, i);
if (t)
{
c[bcLen] = t;
bcLen+=2;
assert(bcLen <= N);
}
if (f[fgLen-2]==0 && g[fgLen-2]==0 && f[fgLen-1]==0 && g[fgLen-1]==0)
fgLen-=2;
if (Compare(f, g, fgLen)==-1)
{
std::swap(f, g);
std::swap(b, c);
s++;
}
Subtract(f, f, g, fgLen);
if (Add(b, b, c, bcLen))
{
b[bcLen] = 1;
bcLen+=2;
assert(bcLen <= N);
}
}
}
// R[N] - result = A/(2^k) mod M
// A[N] - input
// M[N] - modulus
void DivideByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
{
CopyWords(R, A, N);
while (k--)
{
if (R[0]%2==0)
ShiftWordsRightByBits(R, N, 1);
else
{
word carry = Add(R, R, M, N);
ShiftWordsRightByBits(R, N, 1);
R[N-1] += carry<<(WORD_BITS-1);
}
}
}
// R[N] - result = A*(2^k) mod M
// A[N] - input
// M[N] - modulus
void MultiplyByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
{
CopyWords(R, A, N);
while (k--)
if (ShiftWordsLeftByBits(R, N, 1) || Compare(R, M, N)>=0)
Subtract(R, R, M, N);
}
// ******************************************************************
static const unsigned int RoundupSizeTable[] = {2, 2, 2, 4, 4, 8, 8, 8, 8};
static inline unsigned int RoundupSize(unsigned int n)
{
if (n<=8)
return RoundupSizeTable[n];
else if (n<=16)
return 16;
else if (n<=32)
return 32;
else if (n<=64)
return 64;
else return 1U << BitPrecision(n-1);
}
Integer::Integer()
: reg(2), sign(POSITIVE)
{
reg[0] = reg[1] = 0;
}
Integer::Integer(const Integer& t)
: reg(RoundupSize(t.WordCount())), sign(t.sign)
{
CopyWords(reg, t.reg, reg.size());
}
Integer::Integer(Sign s, lword value)
: reg(2), sign(s)
{
reg[0] = word(value);
reg[1] = word(SafeRightShift<WORD_BITS>(value));
}
Integer::Integer(signed long value)
: reg(2)
{
if (value >= 0)
sign = POSITIVE;
else
{
sign = NEGATIVE;
value = -value;
}
reg[0] = word(value);
reg[1] = word(SafeRightShift<WORD_BITS>((unsigned long)value));
}
Integer::Integer(Sign s, word high, word low)
: reg(2), sign(s)
{
reg[0] = low;
reg[1] = high;
}
bool Integer::IsConvertableToLong() const
{
if (ByteCount() > sizeof(long))
return false;
unsigned long value = reg[0];
value += SafeLeftShift<WORD_BITS, unsigned long>(reg[1]);
if (sign==POSITIVE)
return (signed long)value >= 0;
else
return -(signed long)value < 0;
}
signed long Integer::ConvertToLong() const
{
assert(IsConvertableToLong());
unsigned long value = reg[0];
value += SafeLeftShift<WORD_BITS, unsigned long>(reg[1]);
return sign==POSITIVE ? value : -(signed long)value;
}
Integer::Integer(BufferedTransformation &encodedInteger, unsigned int byteCount, Signedness s)
{
Decode(encodedInteger, byteCount, s);
}
Integer::Integer(const byte *encodedInteger, unsigned int byteCount, Signedness s)
{
Decode(encodedInteger, byteCount, s);
}
Integer::Integer(BufferedTransformation &bt)
{
BERDecode(bt);
}
Integer::Integer(RandomNumberGenerator &rng, unsigned int bitcount)
{
Randomize(rng, bitcount);
}
Integer::Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv, const Integer &mod)
{
if (!Randomize(rng, min, max, rnType, equiv, mod))
throw Integer::RandomNumberNotFound();
}
Integer Integer::Power2(unsigned int e)
{
Integer r((word)0, BitsToWords(e+1));
r.SetBit(e);
return r;
}
template <long i>
struct NewInteger
{
Integer * operator()() const
{
return new Integer(i);
}
};
const Integer &Integer::Zero()
{
return Singleton<Integer>().Ref();
}
const Integer &Integer::One()
{
return Singleton<Integer, NewInteger<1> >().Ref();
}
const Integer &Integer::Two()
{
return Singleton<Integer, NewInteger<2> >().Ref();
}
bool Integer::operator!() const
{
return IsNegative() ? false : (reg[0]==0 && WordCount()==0);
}
Integer& Integer::operator=(const Integer& t)
{
if (this != &t)
{
reg.New(RoundupSize(t.WordCount()));
CopyWords(reg, t.reg, reg.size());
sign = t.sign;
}
return *this;
}
bool Integer::GetBit(unsigned int n) const
{
if (n/WORD_BITS >= reg.size())
return 0;
else
return bool((reg[n/WORD_BITS] >> (n % WORD_BITS)) & 1);
}
void Integer::SetBit(unsigned int n, bool value)
{
if (value)
{
reg.CleanGrow(RoundupSize(BitsToWords(n+1)));
reg[n/WORD_BITS] |= (word(1) << (n%WORD_BITS));
}
else
{
if (n/WORD_BITS < reg.size())
reg[n/WORD_BITS] &= ~(word(1) << (n%WORD_BITS));
}
}
byte Integer::GetByte(unsigned int n) const
{
if (n/WORD_SIZE >= reg.size())
return 0;
else
return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
}
void Integer::SetByte(unsigned int n, byte value)
{
reg.CleanGrow(RoundupSize(BytesToWords(n+1)));
reg[n/WORD_SIZE] &= ~(word(0xff) << 8*(n%WORD_SIZE));
reg[n/WORD_SIZE] |= (word(value) << 8*(n%WORD_SIZE));
}
unsigned long Integer::GetBits(unsigned int i, unsigned int n) const
{
assert(n <= sizeof(unsigned long)*8);
unsigned long v = 0;
for (unsigned int j=0; j<n; j++)
v |= GetBit(i+j) << j;
return v;
}
Integer Integer::operator-() const
{
Integer result(*this);
result.Negate();
return result;
}
Integer Integer::AbsoluteValue() const
{
Integer result(*this);
result.sign = POSITIVE;
return result;
}
void Integer::swap(Integer &a)
{
reg.swap(a.reg);
std::swap(sign, a.sign);
}
Integer::Integer(word value, unsigned int length)
: reg(RoundupSize(length)), sign(POSITIVE)
{
reg[0] = value;
SetWords(reg+1, 0, reg.size()-1);
}
template <class T>
static Integer StringToInteger(const T *str)
{
word radix;
// GCC workaround
// std::char_traits doesn't exist in GCC 2.x
// std::char_traits<wchar_t>::length() not defined in GCC 3.2 and STLport 4.5.3
unsigned int length;
for (length = 0; str[length] != 0; length++) {}
Integer v;
if (length == 0)
return v;
switch (str[length-1])
{
case 'h':
case 'H':
radix=16;
break;
case 'o':
case 'O':
radix=8;
break;
case 'b':
case 'B':
radix=2;
break;
default:
radix=10;
}
if (length > 2 && str[0] == '0' && str[1] == 'x')
radix = 16;
for (unsigned i=0; i<length; i++)
{
word digit;
if (str[i] >= '0' && str[i] <= '9')
digit = str[i] - '0';
else if (str[i] >= 'A' && str[i] <= 'F')
digit = str[i] - 'A' + 10;
else if (str[i] >= 'a' && str[i] <= 'f')
digit = str[i] - 'a' + 10;
else
digit = radix;
if (digit < radix)
{
v *= radix;
v += digit;
}
}
if (str[0] == '-')
v.Negate();
return v;
}
Integer::Integer(const char *str)
: reg(2), sign(POSITIVE)
{
*this = StringToInteger(str);
}
Integer::Integer(const wchar_t *str)
: reg(2), sign(POSITIVE)
{
*this = StringToInteger(str);
}
unsigned int Integer::WordCount() const
{
return CountWords(reg, reg.size());
}
unsigned int Integer::ByteCount() const
{
unsigned wordCount = WordCount();
if (wordCount)
return (wordCount-1)*WORD_SIZE + BytePrecision(reg[wordCount-1]);
else
return 0;
}
unsigned int Integer::BitCount() const
{
unsigned wordCount = WordCount();
if (wordCount)
return (wordCount-1)*WORD_BITS + BitPrecision(reg[wordCount-1]);
else
return 0;
}
void Integer::Decode(const byte *input, unsigned int inputLen, Signedness s)
{
StringStore store(input, inputLen);
Decode(store, inputLen, s);
}
void Integer::Decode(BufferedTransformation &bt, unsigned int inputLen, Signedness s)
{
assert(bt.MaxRetrievable() >= inputLen);
byte b;
bt.Peek(b);
sign = ((s==SIGNED) && (b & 0x80)) ? NEGATIVE : POSITIVE;
while (inputLen>0 && (sign==POSITIVE ? b==0 : b==0xff))
{
bt.Skip(1);
inputLen--;
bt.Peek(b);
}
reg.CleanNew(RoundupSize(BytesToWords(inputLen)));
for (unsigned int i=inputLen; i > 0; i--)
{
bt.Get(b);
reg[(i-1)/WORD_SIZE] |= word(b) << ((i-1)%WORD_SIZE)*8;
}
if (sign == NEGATIVE)
{
for (unsigned i=inputLen; i<reg.size()*WORD_SIZE; i++)
reg[i/WORD_SIZE] |= word(0xff) << (i%WORD_SIZE)*8;
TwosComplement(reg, reg.size());
}
}
unsigned int Integer::MinEncodedSize(Signedness signedness) const
{
unsigned int outputLen = STDMAX(1U, ByteCount());
if (signedness == UNSIGNED)
return outputLen;
if (NotNegative() && (GetByte(outputLen-1) & 0x80))
outputLen++;
if (IsNegative() && *this < -Power2(outputLen*8-1))
outputLen++;
return outputLen;
}
unsigned int Integer::Encode(byte *output, unsigned int outputLen, Signedness signedness) const
{
ArraySink sink(output, outputLen);
return Encode(sink, outputLen, signedness);
}
unsigned int Integer::Encode(BufferedTransformation &bt, unsigned int outputLen, Signedness signedness) const
{
if (signedness == UNSIGNED || NotNegative())
{
for (unsigned int i=outputLen; i > 0; i--)
bt.Put(GetByte(i-1));
}
else
{
// take two's complement of *this
Integer temp = Integer::Power2(8*STDMAX(ByteCount(), outputLen)) + *this;
for (unsigned i=0; i<outputLen; i++)
bt.Put(temp.GetByte(outputLen-i-1));
}
return outputLen;
}
void Integer::DEREncode(BufferedTransformation &bt) const
{
DERGeneralEncoder enc(bt, INTEGER);
Encode(enc, MinEncodedSize(SIGNED), SIGNED);
enc.MessageEnd();
}
void Integer::BERDecode(const byte *input, unsigned int len)
{
StringStore store(input, len);
BERDecode(store);
}
void Integer::BERDecode(BufferedTransformation &bt)
{
BERGeneralDecoder dec(bt, INTEGER);
if (!dec.IsDefiniteLength() || dec.MaxRetrievable() < dec.RemainingLength())
BERDecodeError();
Decode(dec, dec.RemainingLength(), SIGNED);
dec.MessageEnd();
}
void Integer::DEREncodeAsOctetString(BufferedTransformation &bt, unsigned int length) const
{
DERGeneralEncoder enc(bt, OCTET_STRING);
Encode(enc, length);
enc.MessageEnd();
}
void Integer::BERDecodeAsOctetString(BufferedTransformation &bt, unsigned int length)
{
BERGeneralDecoder dec(bt, OCTET_STRING);
if (!dec.IsDefiniteLength() || dec.RemainingLength() != length)
BERDecodeError();
Decode(dec, length);
dec.MessageEnd();
}
unsigned int Integer::OpenPGPEncode(byte *output, unsigned int len) const
{
ArraySink sink(output, len);
return OpenPGPEncode(sink);
}
unsigned int Integer::OpenPGPEncode(BufferedTransformation &bt) const
{
word16 bitCount = BitCount();
bt.PutWord16(bitCount);
return 2 + Encode(bt, BitsToBytes(bitCount));
}
void Integer::OpenPGPDecode(const byte *input, unsigned int len)
{
StringStore store(input, len);
OpenPGPDecode(store);
}
void Integer::OpenPGPDecode(BufferedTransformation &bt)
{
word16 bitCount;
if (bt.GetWord16(bitCount) != 2 || bt.MaxRetrievable() < BitsToBytes(bitCount))
throw OpenPGPDecodeErr();
Decode(bt, BitsToBytes(bitCount));
}
void Integer::Randomize(RandomNumberGenerator &rng, unsigned int nbits)
{
const unsigned int nbytes = nbits/8 + 1;
SecByteBlock buf(nbytes);
rng.GenerateBlock(buf, nbytes);
if (nbytes)
buf[0] = (byte)Crop(buf[0], nbits % 8);
Decode(buf, nbytes, UNSIGNED);
}
void Integer::Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max)
{
if (min > max)
throw InvalidArgument("Integer: Min must be no greater than Max");
Integer range = max - min;
const unsigned int nbits = range.BitCount();
do
{
Randomize(rng, nbits);
}
while (*this > range);
*this += min;
}
bool Integer::Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv, const Integer &mod)
{
return GenerateRandomNoThrow(rng, MakeParameters("Min", min)("Max", max)("RandomNumberType", rnType)("EquivalentTo", equiv)("Mod", mod));
}
class KDF2_RNG : public RandomNumberGenerator
{
public:
KDF2_RNG(const byte *seed, unsigned int seedSize)
: m_counter(0), m_counterAndSeed(seedSize + 4)
{
memcpy(m_counterAndSeed + 4, seed, seedSize);
}
byte GenerateByte()
{
byte b;
GenerateBlock(&b, 1);
return b;
}
void GenerateBlock(byte *output, unsigned int size)
{
UnalignedPutWord(BIG_ENDIAN_ORDER, m_counterAndSeed, m_counter);
++m_counter;
P1363_KDF2<SHA1>::DeriveKey(output, size, m_counterAndSeed, m_counterAndSeed.size(), NULL, 0);
}
private:
word32 m_counter;
SecByteBlock m_counterAndSeed;
};
bool Integer::GenerateRandomNoThrow(RandomNumberGenerator &i_rng, const NameValuePairs &params)
{
Integer min = params.GetValueWithDefault("Min", Integer::Zero());
Integer max;
if (!params.GetValue("Max", max))
{
int bitLength;
if (params.GetIntValue("BitLength", bitLength))
max = Integer::Power2(bitLength);
else
throw InvalidArgument("Integer: missing Max argument");
}
if (min > max)
throw InvalidArgument("Integer: Min must be no greater than Max");
Integer equiv = params.GetValueWithDefault("EquivalentTo", Integer::Zero());
Integer mod = params.GetValueWithDefault("Mod", Integer::One());
if (equiv.IsNegative() || equiv >= mod)
throw InvalidArgument("Integer: invalid EquivalentTo and/or Mod argument");
Integer::RandomNumberType rnType = params.GetValueWithDefault("RandomNumberType", Integer::ANY);
member_ptr<KDF2_RNG> kdf2Rng;
ConstByteArrayParameter seed;
if (params.GetValue("Seed", seed))
{
ByteQueue bq;
DERSequenceEncoder seq(bq);
min.DEREncode(seq);
max.DEREncode(seq);
equiv.DEREncode(seq);
mod.DEREncode(seq);
DEREncodeUnsigned(seq, rnType);
DEREncodeOctetString(seq, seed.begin(), seed.size());
seq.MessageEnd();
SecByteBlock finalSeed(bq.MaxRetrievable());
bq.Get(finalSeed, finalSeed.size());
kdf2Rng.reset(new KDF2_RNG(finalSeed.begin(), finalSeed.size()));
}
RandomNumberGenerator &rng = kdf2Rng.get() ? (RandomNumberGenerator &)*kdf2Rng : i_rng;
switch (rnType)
{
case ANY:
if (mod == One())
Randomize(rng, min, max);
else
{
Integer min1 = min + (equiv-min)%mod;
if (max < min1)
return false;
Randomize(rng, Zero(), (max - min1) / mod);
*this *= mod;
*this += min1;
}
return true;
case PRIME:
{
const PrimeSelector *pSelector = params.GetValueWithDefault(Name::PointerToPrimeSelector(), (const PrimeSelector *)NULL);
int i;
i = 0;
while (1)
{
if (++i==16)
{
// check if there are any suitable primes in [min, max]
Integer first = min;
if (FirstPrime(first, max, equiv, mod, pSelector))
{
// if there is only one suitable prime, we're done
*this = first;
if (!FirstPrime(first, max, equiv, mod, pSelector))
return true;
}
else
return false;
}
Randomize(rng, min, max);
if (FirstPrime(*this, STDMIN(*this+mod*PrimeSearchInterval(max), max), equiv, mod, pSelector))
return true;
}
}
default:
throw InvalidArgument("Integer: invalid RandomNumberType argument");
}
}
std::istream& operator>>(std::istream& in, Integer &a)
{
char c;
unsigned int length = 0;
SecBlock<char> str(length + 16);
std::ws(in);
do
{
in.read(&c, 1);
str[length++] = c;
if (length >= str.size())
str.Grow(length + 16);
}
while (in && (c=='-' || c=='x' || (c>='0' && c<='9') || (c>='a' && c<='f') || (c>='A' && c<='F') || c=='h' || c=='H' || c=='o' || c=='O' || c==',' || c=='.'));
if (in.gcount())
in.putback(c);
str[length-1] = '\0';
a = Integer(str);
return in;
}
std::ostream& operator<<(std::ostream& out, const Integer &a)
{
// Get relevant conversion specifications from ostream.
long f = out.flags() & std::ios::basefield; // Get base digits.
int base, block;
char suffix;
switch(f)
{
case std::ios::oct :
base = 8;
block = 8;
suffix = 'o';
break;
case std::ios::hex :
base = 16;
block = 4;
suffix = 'h';
break;
default :
base = 10;
block = 3;
suffix = '.';
}
SecBlock<char> s(a.BitCount() / (BitPrecision(base)-1) + 1);
Integer temp1=a, temp2;
unsigned i=0;
const char vec[]="0123456789ABCDEF";
if (a.IsNegative())
{
out << '-';
temp1.Negate();
}
if (!a)
out << '0';
while (!!temp1)
{
word digit;
Integer::Divide(digit, temp2, temp1, base);
s[i++]=vec[digit];
temp1=temp2;
}
while (i--)
{
out << s[i];
// if (i && !(i%block))
// out << ",";
}
return out << suffix;
}
Integer& Integer::operator++()
{
if (NotNegative())
{
if (Increment(reg, reg.size()))
{
reg.CleanGrow(2*reg.size());
reg[reg.size()/2]=1;
}
}
else
{
word borrow = Decrement(reg, reg.size());
assert(!borrow);
if (WordCount()==0)
*this = Zero();
}
return *this;
}
Integer& Integer::operator--()
{
if (IsNegative())
{
if (Increment(reg, reg.size()))
{
reg.CleanGrow(2*reg.size());
reg[reg.size()/2]=1;
}
}
else
{
if (Decrement(reg, reg.size()))
*this = -One();
}
return *this;
}
void PositiveAdd(Integer &sum, const Integer &a, const Integer& b)
{
word carry;
if (a.reg.size() == b.reg.size())
carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
else if (a.reg.size() > b.reg.size())
{
carry = Add(sum.reg, a.reg, b.reg, b.reg.size());
CopyWords(sum.reg+b.reg.size(), a.reg+b.reg.size(), a.reg.size()-b.reg.size());
carry = Increment(sum.reg+b.reg.size(), a.reg.size()-b.reg.size(), carry);
}
else
{
carry = Add(sum.reg, a.reg, b.reg, a.reg.size());
CopyWords(sum.reg+a.reg.size(), b.reg+a.reg.size(), b.reg.size()-a.reg.size());
carry = Increment(sum.reg+a.reg.size(), b.reg.size()-a.reg.size(), carry);
}
if (carry)
{
sum.reg.CleanGrow(2*sum.reg.size());
sum.reg[sum.reg.size()/2] = 1;
}
sum.sign = Integer::POSITIVE;
}
void PositiveSubtract(Integer &diff, const Integer &a, const Integer& b)
{
unsigned aSize = a.WordCount();
aSize += aSize%2;
unsigned bSize = b.WordCount();
bSize += bSize%2;
if (aSize == bSize)
{
if (Compare(a.reg, b.reg, aSize) >= 0)
{
Subtract(diff.reg, a.reg, b.reg, aSize);
diff.sign = Integer::POSITIVE;
}
else
{
Subtract(diff.reg, b.reg, a.reg, aSize);
diff.sign = Integer::NEGATIVE;
}
}
else if (aSize > bSize)
{
word borrow = Subtract(diff.reg, a.reg, b.reg, bSize);
CopyWords(diff.reg+bSize, a.reg+bSize, aSize-bSize);
borrow = Decrement(diff.reg+bSize, aSize-bSize, borrow);
assert(!borrow);
diff.sign = Integer::POSITIVE;
}
else
{
word borrow = Subtract(diff.reg, b.reg, a.reg, aSize);
CopyWords(diff.reg+aSize, b.reg+aSize, bSize-aSize);
borrow = Decrement(diff.reg+aSize, bSize-aSize, borrow);
assert(!borrow);
diff.sign = Integer::NEGATIVE;
}
}
Integer Integer::Plus(const Integer& b) const
{
Integer sum((word)0, STDMAX(reg.size(), b.reg.size()));
if (NotNegative())
{
if (b.NotNegative())
PositiveAdd(sum, *this, b);
else
PositiveSubtract(sum, *this, b);
}
else
{
if (b.NotNegative())
PositiveSubtract(sum, b, *this);
else
{
PositiveAdd(sum, *this, b);
sum.sign = Integer::NEGATIVE;
}
}
return sum;
}
Integer& Integer::operator+=(const Integer& t)
{
reg.CleanGrow(t.reg.size());
if (NotNegative())
{
if (t.NotNegative())
PositiveAdd(*this, *this, t);
else
PositiveSubtract(*this, *this, t);
}
else
{
if (t.NotNegative())
PositiveSubtract(*this, t, *this);
else
{
PositiveAdd(*this, *this, t);
sign = Integer::NEGATIVE;
}
}
return *this;
}
Integer Integer::Minus(const Integer& b) const
{
Integer diff((word)0, STDMAX(reg.size(), b.reg.size()));
if (NotNegative())
{
if (b.NotNegative())
PositiveSubtract(diff, *this, b);
else
PositiveAdd(diff, *this, b);
}
else
{
if (b.NotNegative())
{
PositiveAdd(diff, *this, b);
diff.sign = Integer::NEGATIVE;
}
else
PositiveSubtract(diff, b, *this);
}
return diff;
}
Integer& Integer::operator-=(const Integer& t)
{
reg.CleanGrow(t.reg.size());
if (NotNegative())
{
if (t.NotNegative())
PositiveSubtract(*this, *this, t);
else
PositiveAdd(*this, *this, t);
}
else
{
if (t.NotNegative())
{
PositiveAdd(*this, *this, t);
sign = Integer::NEGATIVE;
}
else
PositiveSubtract(*this, t, *this);
}
return *this;
}
Integer& Integer::operator<<=(unsigned int n)
{
const unsigned int wordCount = WordCount();
const unsigned int shiftWords = n / WORD_BITS;
const unsigned int shiftBits = n % WORD_BITS;
reg.CleanGrow(RoundupSize(wordCount+BitsToWords(n)));
ShiftWordsLeftByWords(reg, wordCount + shiftWords, shiftWords);
ShiftWordsLeftByBits(reg+shiftWords, wordCount+BitsToWords(shiftBits), shiftBits);
return *this;
}
Integer& Integer::operator>>=(unsigned int n)
{
const unsigned int wordCount = WordCount();
const unsigned int shiftWords = n / WORD_BITS;
const unsigned int shiftBits = n % WORD_BITS;
ShiftWordsRightByWords(reg, wordCount, shiftWords);
if (wordCount > shiftWords)
ShiftWordsRightByBits(reg, wordCount-shiftWords, shiftBits);
if (IsNegative() && WordCount()==0) // avoid -0
*this = Zero();
return *this;
}
void PositiveMultiply(Integer &product, const Integer &a, const Integer &b)
{
unsigned aSize = RoundupSize(a.WordCount());
unsigned bSize = RoundupSize(b.WordCount());
product.reg.CleanNew(RoundupSize(aSize+bSize));
product.sign = Integer::POSITIVE;
SecAlignedWordBlock workspace(aSize + bSize);
AsymmetricMultiply(product.reg, workspace, a.reg, aSize, b.reg, bSize);
}
void Multiply(Integer &product, const Integer &a, const Integer &b)
{
PositiveMultiply(product, a, b);
if (a.NotNegative() != b.NotNegative())
product.Negate();
}
Integer Integer::Times(const Integer &b) const
{
Integer product;
Multiply(product, *this, b);
return product;
}
/*
void PositiveDivide(Integer &remainder, Integer &quotient,
const Integer &dividend, const Integer &divisor)
{
remainder.reg.CleanNew(divisor.reg.size());
remainder.sign = Integer::POSITIVE;
quotient.reg.New(0);
quotient.sign = Integer::POSITIVE;
unsigned i=dividend.BitCount();
while (i--)
{
word overflow = ShiftWordsLeftByBits(remainder.reg, remainder.reg.size(), 1);
remainder.reg[0] |= dividend[i];
if (overflow || remainder >= divisor)
{
Subtract(remainder.reg, remainder.reg, divisor.reg, remainder.reg.size());
quotient.SetBit(i);
}
}
}
*/
void PositiveDivide(Integer &remainder, Integer &quotient,
const Integer &a, const Integer &b)
{
unsigned aSize = a.WordCount();
unsigned bSize = b.WordCount();
if (!bSize)
throw Integer::DivideByZero();
if (a.PositiveCompare(b) == -1)
{
remainder = a;
remainder.sign = Integer::POSITIVE;
quotient = Integer::Zero();
return;
}
aSize += aSize%2; // round up to next even number
bSize += bSize%2;
remainder.reg.CleanNew(RoundupSize(bSize));
remainder.sign = Integer::POSITIVE;
quotient.reg.CleanNew(RoundupSize(aSize-bSize+2));
quotient.sign = Integer::POSITIVE;
SecAlignedWordBlock T(aSize+2*bSize+4);
Divide(remainder.reg, quotient.reg, T, a.reg, aSize, b.reg, bSize);
}
void Integer::Divide(Integer &remainder, Integer &quotient, const Integer &dividend, const Integer &divisor)
{
PositiveDivide(remainder, quotient, dividend, divisor);
if (dividend.IsNegative())
{
quotient.Negate();
if (remainder.NotZero())
{
--quotient;
remainder = divisor.AbsoluteValue() - remainder;
}
}
if (divisor.IsNegative())
quotient.Negate();
}
void Integer::DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n)
{
q = a;
q >>= n;
const unsigned int wordCount = BitsToWords(n);
if (wordCount <= a.WordCount())
{
r.reg.resize(RoundupSize(wordCount));
CopyWords(r.reg, a.reg, wordCount);
SetWords(r.reg+wordCount, 0, r.reg.size()-wordCount);
if (n % WORD_BITS != 0)
r.reg[wordCount-1] %= (1 << (n % WORD_BITS));
}
else
{
r.reg.resize(RoundupSize(a.WordCount()));
CopyWords(r.reg, a.reg, r.reg.size());
}
r.sign = POSITIVE;
if (a.IsNegative() && r.NotZero())
{
--q;
r = Power2(n) - r;
}
}
Integer Integer::DividedBy(const Integer &b) const
{
Integer remainder, quotient;
Integer::Divide(remainder, quotient, *this, b);
return quotient;
}
Integer Integer::Modulo(const Integer &b) const
{
Integer remainder, quotient;
Integer::Divide(remainder, quotient, *this, b);
return remainder;
}
void Integer::Divide(word &remainder, Integer &quotient, const Integer &dividend, word divisor)
{
if (!divisor)
throw Integer::DivideByZero();
assert(divisor);
if ((divisor & (divisor-1)) == 0) // divisor is a power of 2
{
quotient = dividend >> (BitPrecision(divisor)-1);
remainder = dividend.reg[0] & (divisor-1);
return;
}
unsigned int i = dividend.WordCount();
quotient.reg.CleanNew(RoundupSize(i));
remainder = 0;
while (i--)
{
quotient.reg[i] = DWord(dividend.reg[i], remainder) / divisor;
remainder = DWord(dividend.reg[i], remainder) % divisor;
}
if (dividend.NotNegative())
quotient.sign = POSITIVE;
else
{
quotient.sign = NEGATIVE;
if (remainder)
{
--quotient;
remainder = divisor - remainder;
}
}
}
Integer Integer::DividedBy(word b) const
{
word remainder;
Integer quotient;
Integer::Divide(remainder, quotient, *this, b);
return quotient;
}
word Integer::Modulo(word divisor) const
{
if (!divisor)
throw Integer::DivideByZero();
assert(divisor);
word remainder;
if ((divisor & (divisor-1)) == 0) // divisor is a power of 2
remainder = reg[0] & (divisor-1);
else
{
unsigned int i = WordCount();
if (divisor <= 5)
{
DWord sum(0, 0);
while (i--)
sum += reg[i];
remainder = sum % divisor;
}
else
{
remainder = 0;
while (i--)
remainder = DWord(reg[i], remainder) % divisor;
}
}
if (IsNegative() && remainder)
remainder = divisor - remainder;
return remainder;
}
void Integer::Negate()
{
if (!!(*this)) // don't flip sign if *this==0
sign = Sign(1-sign);
}
int Integer::PositiveCompare(const Integer& t) const
{
unsigned size = WordCount(), tSize = t.WordCount();
if (size == tSize)
return CryptoPP::Compare(reg, t.reg, size);
else
return size > tSize ? 1 : -1;
}
int Integer::Compare(const Integer& t) const
{
if (NotNegative())
{
if (t.NotNegative())
return PositiveCompare(t);
else
return 1;
}
else
{
if (t.NotNegative())
return -1;
else
return -PositiveCompare(t);
}
}
Integer Integer::SquareRoot() const
{
if (!IsPositive())
return Zero();
// overestimate square root
Integer x, y = Power2((BitCount()+1)/2);
assert(y*y >= *this);
do
{
x = y;
y = (x + *this/x) >> 1;
} while (y<x);
return x;
}
bool Integer::IsSquare() const
{
Integer r = SquareRoot();
return *this == r.Squared();
}
bool Integer::IsUnit() const
{
return (WordCount() == 1) && (reg[0] == 1);
}
Integer Integer::MultiplicativeInverse() const
{
return IsUnit() ? *this : Zero();
}
Integer a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m)
{
return x*y%m;
}
Integer a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m)
{
ModularArithmetic mr(m);
return mr.Exponentiate(x, e);
}
Integer Integer::Gcd(const Integer &a, const Integer &b)
{
return EuclideanDomainOf<Integer>().Gcd(a, b);
}
Integer Integer::InverseMod(const Integer &m) const
{
assert(m.NotNegative());
if (IsNegative() || *this>=m)
return (*this%m).InverseMod(m);
if (m.IsEven())
{
if (!m || IsEven())
return Zero(); // no inverse
if (*this == One())
return One();
Integer u = m.InverseMod(*this);
return !u ? Zero() : (m*(*this-u)+1)/(*this);
}
SecBlock<word> T(m.reg.size() * 4);
Integer r((word)0, m.reg.size());
unsigned k = AlmostInverse(r.reg, T, reg, reg.size(), m.reg, m.reg.size());
DivideByPower2Mod(r.reg, r.reg, k, m.reg, m.reg.size());
return r;
}
word Integer::InverseMod(const word mod) const
{
word g0 = mod, g1 = *this % mod;
word v0 = 0, v1 = 1;
word y;
while (g1)
{
if (g1 == 1)
return v1;
y = g0 / g1;
g0 = g0 % g1;
v0 += y * v1;
if (!g0)
break;
if (g0 == 1)
return mod-v0;
y = g1 / g0;
g1 = g1 % g0;
v1 += y * v0;
}
return 0;
}
// ********************************************************
ModularArithmetic::ModularArithmetic(BufferedTransformation &bt)
{
BERSequenceDecoder seq(bt);
OID oid(seq);
if (oid != ASN1::prime_field())
BERDecodeError();
modulus.BERDecode(seq);
seq.MessageEnd();
result.reg.resize(modulus.reg.size());
}
void ModularArithmetic::DEREncode(BufferedTransformation &bt) const
{
DERSequenceEncoder seq(bt);
ASN1::prime_field().DEREncode(seq);
modulus.DEREncode(seq);
seq.MessageEnd();
}
void ModularArithmetic::DEREncodeElement(BufferedTransformation &out, const Element &a) const
{
a.DEREncodeAsOctetString(out, MaxElementByteLength());
}
void ModularArithmetic::BERDecodeElement(BufferedTransformation &in, Element &a) const
{
a.BERDecodeAsOctetString(in, MaxElementByteLength());
}
const Integer& ModularArithmetic::Half(const Integer &a) const
{
if (a.reg.size()==modulus.reg.size())
{
CryptoPP::DivideByPower2Mod(result.reg.begin(), a.reg, 1, modulus.reg, a.reg.size());
return result;
}
else
return result1 = (a.IsEven() ? (a >> 1) : ((a+modulus) >> 1));
}
const Integer& ModularArithmetic::Add(const Integer &a, const Integer &b) const
{
if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
{
if (CryptoPP::Add(result.reg.begin(), a.reg, b.reg, a.reg.size())
|| Compare(result.reg, modulus.reg, a.reg.size()) >= 0)
{
CryptoPP::Subtract(result.reg.begin(), result.reg, modulus.reg, a.reg.size());
}
return result;
}
else
{
result1 = a+b;
if (result1 >= modulus)
result1 -= modulus;
return result1;
}
}
Integer& ModularArithmetic::Accumulate(Integer &a, const Integer &b) const
{
if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
{
if (CryptoPP::Add(a.reg, a.reg, b.reg, a.reg.size())
|| Compare(a.reg, modulus.reg, a.reg.size()) >= 0)
{
CryptoPP::Subtract(a.reg, a.reg, modulus.reg, a.reg.size());
}
}
else
{
a+=b;
if (a>=modulus)
a-=modulus;
}
return a;
}
const Integer& ModularArithmetic::Subtract(const Integer &a, const Integer &b) const
{
if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
{
if (CryptoPP::Subtract(result.reg.begin(), a.reg, b.reg, a.reg.size()))
CryptoPP::Add(result.reg.begin(), result.reg, modulus.reg, a.reg.size());
return result;
}
else
{
result1 = a-b;
if (result1.IsNegative())
result1 += modulus;
return result1;
}
}
Integer& ModularArithmetic::Reduce(Integer &a, const Integer &b) const
{
if (a.reg.size()==modulus.reg.size() && b.reg.size()==modulus.reg.size())
{
if (CryptoPP::Subtract(a.reg, a.reg, b.reg, a.reg.size()))
CryptoPP::Add(a.reg, a.reg, modulus.reg, a.reg.size());
}
else
{
a-=b;
if (a.IsNegative())
a+=modulus;
}
return a;
}
const Integer& ModularArithmetic::Inverse(const Integer &a) const
{
if (!a)
return a;
CopyWords(result.reg.begin(), modulus.reg, modulus.reg.size());
if (CryptoPP::Subtract(result.reg.begin(), result.reg, a.reg, a.reg.size()))
Decrement(result.reg.begin()+a.reg.size(), 1, modulus.reg.size()-a.reg.size());
return result;
}
Integer ModularArithmetic::CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
{
if (modulus.IsOdd())
{
MontgomeryRepresentation dr(modulus);
return dr.ConvertOut(dr.CascadeExponentiate(dr.ConvertIn(x), e1, dr.ConvertIn(y), e2));
}
else
return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);
}
void ModularArithmetic::SimultaneousExponentiate(Integer *results, const Integer &base, const Integer *exponents, unsigned int exponentsCount) const
{
if (modulus.IsOdd())
{
MontgomeryRepresentation dr(modulus);
dr.SimultaneousExponentiate(results, dr.ConvertIn(base), exponents, exponentsCount);
for (unsigned int i=0; i<exponentsCount; i++)
results[i] = dr.ConvertOut(results[i]);
}
else
AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);
}
MontgomeryRepresentation::MontgomeryRepresentation(const Integer &m) // modulus must be odd
: ModularArithmetic(m),
u((word)0, modulus.reg.size()),
workspace(5*modulus.reg.size())
{
if (!modulus.IsOdd())
throw InvalidArgument("MontgomeryRepresentation: Montgomery representation requires an odd modulus");
RecursiveInverseModPower2(u.reg, workspace, modulus.reg, modulus.reg.size());
}
const Integer& MontgomeryRepresentation::Multiply(const Integer &a, const Integer &b) const
{
word *const T = workspace.begin();
word *const R = result.reg.begin();
const unsigned int N = modulus.reg.size();
assert(a.reg.size()<=N && b.reg.size()<=N);
AsymmetricMultiply(T, T+2*N, a.reg, a.reg.size(), b.reg, b.reg.size());
SetWords(T+a.reg.size()+b.reg.size(), 0, 2*N-a.reg.size()-b.reg.size());
MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
return result;
}
const Integer& MontgomeryRepresentation::Square(const Integer &a) const
{
word *const T = workspace.begin();
word *const R = result.reg.begin();
const unsigned int N = modulus.reg.size();
assert(a.reg.size()<=N);
CryptoPP::Square(T, T+2*N, a.reg, a.reg.size());
SetWords(T+2*a.reg.size(), 0, 2*N-2*a.reg.size());
MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
return result;
}
Integer MontgomeryRepresentation::ConvertOut(const Integer &a) const
{
word *const T = workspace.begin();
word *const R = result.reg.begin();
const unsigned int N = modulus.reg.size();
assert(a.reg.size()<=N);
CopyWords(T, a.reg, a.reg.size());
SetWords(T+a.reg.size(), 0, 2*N-a.reg.size());
MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
return result;
}
const Integer& MontgomeryRepresentation::MultiplicativeInverse(const Integer &a) const
{
// return (EuclideanMultiplicativeInverse(a, modulus)<<(2*WORD_BITS*modulus.reg.size()))%modulus;
word *const T = workspace.begin();
word *const R = result.reg.begin();
const unsigned int N = modulus.reg.size();
assert(a.reg.size()<=N);
CopyWords(T, a.reg, a.reg.size());
SetWords(T+a.reg.size(), 0, 2*N-a.reg.size());
MontgomeryReduce(R, T+2*N, T, modulus.reg, u.reg, N);
unsigned k = AlmostInverse(R, T, R, N, modulus.reg, N);
// cout << "k=" << k << " N*32=" << 32*N << endl;
if (k>N*WORD_BITS)
DivideByPower2Mod(R, R, k-N*WORD_BITS, modulus.reg, N);
else
MultiplyByPower2Mod(R, R, N*WORD_BITS-k, modulus.reg, N);
return result;
}
NAMESPACE_END
#endif
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