integer.cpp

此文件是实现加解密算法的函数库

// 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"
#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
#include <emmintrin.h>
#endif

#include "algebra.cpp"
#include "eprecomp.cpp"

NAMESPACE_BEGIN(CryptoPP)

#ifdef SSE2_INTRINSICS_AVAILABLE
template <class T>
AllocatorBase<T>::pointer AlignedAllocator<T>::allocate(size_type n, const void *)
{
	if (n < 4)
		return new T[n];
	else
		return (T *)_mm_malloc(sizeof(T)*n, 16);

}

template <class T>
void AlignedAllocator<T>::deallocate(void *p, size_type n)
{
	memset(p, 0, n*sizeof(T));
	if (n < 4)
		delete [] p;
	else
		_mm_free(p);
}

template class AlignedAllocator<word>;
#endif

#define MAKE_DWORD(lowWord, highWord) ((dword(highWord)<<WORD_BITS) | (lowWord))

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 LinearMultiply(word *C, const word *A, word B, unsigned int N)
{
	word carry=0;
	for(unsigned i=0; i<N; i++)
	{
		dword p = (dword)A[i] * B + carry;
		C[i] = LOW_WORD(p);
		carry = HIGH_WORD(p);
	}
	return carry;
}

static void AtomicInverseModPower2(word *C, word A0, word A1)
{
	assert(A0%2==1);

	dword A=MAKE_DWORD(A0, A1), R=A0%8;

	for (unsigned i=3; i<2*WORD_BITS; i*=2)
		R = R*(2-R*A);

	assert(R*A==1);

	C[0] = LOW_WORD(R);
	C[1] = HIGH_WORD(R);
}

// ********************************************************

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);

#ifdef IS_LITTLE_ENDIAN
	if (sizeof(dword) == sizeof(size_t))	// dword is only register size
	{
		dword carry = 0;
		N >>= 1;
		for (unsigned int i = 0; i < N; i++)
		{
			dword a = ((const dword *)A)[i] + carry;
			dword c = a + ((const dword *)B)[i];
			((dword *)C)[i] = c;
			carry = (a < carry) | (c < a);
		}
		return (word)carry;
	}
	else
#endif
	{
		word carry = 0;
		for (unsigned int i = 0; i < N; i+=2)
		{
			dword u = (dword) carry + A[i] + B[i];
			C[i] = LOW_WORD(u);
			u = (dword) HIGH_WORD(u) + A[i+1] + B[i+1];
			C[i+1] = LOW_WORD(u);
			carry = HIGH_WORD(u);
		}
		return carry;
	}
}

word Portable::Subtract(word *C, const word *A, const word *B, unsigned int N)
{
	assert (N%2 == 0);

#ifdef IS_LITTLE_ENDIAN
	if (sizeof(dword) == sizeof(size_t))	// dword is only register size
	{
		dword borrow = 0;
		N >>= 1;
		for (unsigned int i = 0; i < N; i++)
		{
			dword a = ((const dword *)A)[i];
			dword b = a - borrow;
			dword c = b - ((const dword *)B)[i];
			((dword *)C)[i] = c;
			borrow = (b > a) | (c > b);
		}
		return (word)borrow;
	}
	else
#endif
	{
		word borrow=0;
		for (unsigned i = 0; i < N; i+=2)
		{
			dword u = (dword) A[i] - B[i] - borrow;
			C[i] = LOW_WORD(u);
			u = (dword) A[i+1] - B[i+1] - (word)(0-HIGH_WORD(u));
			C[i+1] = LOW_WORD(u);
			borrow = 0-HIGH_WORD(u);
		}
		return borrow;
	}
}

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)D[di]*D[di+2];
	D[1] = D[3] = 0;
	unsigned int si = ai + !bi;
	word s = D[si];

	dword A0B0 = (dword)A[0]*B[0];
	C[0] = LOW_WORD(A0B0);

	dword A1B1 = (dword)A[1]*B[1];
	dword t = (dword) HIGH_WORD(A0B0) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1);
	C[1] = LOW_WORD(t);

	t = A1B1 + HIGH_WORD(t) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s;
	C[2] = LOW_WORD(t);
	C[3] = HIGH_WORD(t);
}

inline void Portable::Multiply2Bottom(word *C, const word *A, const word *B)
{
#ifdef IS_LITTLE_ENDIAN
	if (sizeof(dword) == sizeof(size_t))
	{
		dword a = *(const dword *)A, b = *(const dword *)B;
		((dword *)C)[0] = a*b;
	}
	else
#endif
	{
		dword t = (dword)A[0]*B[0];
		C[0] = LOW_WORD(t);
		C[1] = HIGH_WORD(t) + 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)D[di]*D[di+2];
	D[1] = D[3] = 0;
	unsigned int si = ai + !bi;
	word s = D[si];

	dword A0B0 = (dword)A[0]*B[0];
	dword t = A0B0 + C[0];
	C[0] = LOW_WORD(t);

	dword A1B1 = (dword)A[1]*B[1];
	t = (dword) HIGH_WORD(t) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1) + C[1];
	C[1] = LOW_WORD(t);

	t = (dword) HIGH_WORD(t) + LOW_WORD(A1B1) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s + C[2];
	C[2] = LOW_WORD(t);

	t = (dword) HIGH_WORD(t) + HIGH_WORD(A1B1) + C[3];
	C[3] = LOW_WORD(t);
	return HIGH_WORD(t);
}

#define MulAcc(x, y)								\
	p = (dword)A[x] * B[y] + c; 					\
	c = LOW_WORD(p);								\
	p = (dword)d + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e += HIGH_WORD(p);

#define SaveMulAcc(s, x, y) 						\
	R[s] = c;										\
	p = (dword)A[x] * B[y] + d; 					\
	c = LOW_WORD(p);								\
	p = (dword)e + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e = HIGH_WORD(p);

#define SquAcc(x, y)								\
	q = (dword)A[x] * A[y];	\
	p = q + c; 					\
	c = LOW_WORD(p);								\
	p = (dword)d + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e += HIGH_WORD(p);			\
	p = q + c; 					\
	c = LOW_WORD(p);								\
	p = (dword)d + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e += HIGH_WORD(p);

#define SaveSquAcc(s, x, y) 						\
	R[s] = c;										\
	q = (dword)A[x] * A[y];	\
	p = q + d; 					\
	c = LOW_WORD(p);								\
	p = (dword)e + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e = HIGH_WORD(p);			\
	p = q + c; 					\
	c = LOW_WORD(p);								\
	p = (dword)d + HIGH_WORD(p);					\
	d = LOW_WORD(p);								\
	e += HIGH_WORD(p);

void Portable::Multiply4(word *R, const word *A, const word *B)
{
	dword p;
	word c, d, e;

	p = (dword)A[0] * B[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	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)A[3] * B[3] + d;
	R[6] = LOW_WORD(p);
	R[7] = e + HIGH_WORD(p);
}

void Portable::Square2(word *R, const word *A)
{
	dword p, q;
	word c, d, e;

	p = (dword)A[0] * A[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	d = e = 0;

	SquAcc(0, 1);

	R[1] = c;
	p = (dword)A[1] * A[1] + d;
	R[2] = LOW_WORD(p);
	R[3] = e + HIGH_WORD(p);
}

void Portable::Square4(word *R, const word *A)
{
	const word *B = A;
	dword p, q;
	word c, d, e;

	p = (dword)A[0] * A[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	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)A[3] * A[3] + d;
	R[6] = LOW_WORD(p);
	R[7] = e + HIGH_WORD(p);
}

void Portable::Multiply8(word *R, const word *A, const word *B)
{
	dword p;
	word c, d, e;

	p = (dword)A[0] * B[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	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)A[7] * B[7] + d;
	R[14] = LOW_WORD(p);
	R[15] = e + HIGH_WORD(p);
}

void Portable::Multiply4Bottom(word *R, const word *A, const word *B)
{
	dword p;
	word c, d, e;

	p = (dword)A[0] * B[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	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)A[0] * B[0];
	R[0] = LOW_WORD(p);
	c = HIGH_WORD(p);
	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];
}