diff options
Diffstat (limited to 'plugins/CryptoPP/crypto/src/integer.cpp')
| -rw-r--r-- | plugins/CryptoPP/crypto/src/integer.cpp | 4237 |
1 files changed, 4237 insertions, 0 deletions
diff --git a/plugins/CryptoPP/crypto/src/integer.cpp b/plugins/CryptoPP/crypto/src/integer.cpp new file mode 100644 index 0000000000..fe87a957e8 --- /dev/null +++ b/plugins/CryptoPP/crypto/src/integer.cpp @@ -0,0 +1,4237 @@ +// 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 "cpu.h"
+
+#include <iostream>
+
+#if _MSC_VER >= 1400
+ #include <intrin.h>
+#endif
+
+#ifdef __DECCXX
+ #include <c_asm.h>
+#endif
+
+#ifdef CRYPTOPP_MSVC6_NO_PP
+ #pragma message("You do not seem to have the Visual C++ Processor Pack installed, so use of SSE2 instructions will be disabled.")
+#endif
+
+#define CRYPTOPP_INTEGER_SSE2 (CRYPTOPP_BOOL_SSE2_ASM_AVAILABLE && CRYPTOPP_BOOL_X86)
+
+NAMESPACE_BEGIN(CryptoPP)
+
+bool AssignIntToInteger(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;
+}
+
+inline static int Compare(const word *A, const word *B, size_t N)
+{
+ while (N--)
+ if (A[N] > B[N])
+ return 1;
+ else if (A[N] < B[N])
+ return -1;
+
+ return 0;
+}
+
+inline static int Increment(word *A, size_t 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;
+}
+
+inline static int Decrement(word *A, size_t 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, size_t 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;
+}
+
+// ********************************************************
+
+#if !defined(CRYPTOPP_NATIVE_DWORD_AVAILABLE) || defined(__x86_64__)
+ #define Declare2Words(x) word x##0, x##1;
+ #define AssignWord(a, b) a##0 = b; a##1 = 0;
+ #define Add2WordsBy1(a, b, c) a##0 = b##0 + c; a##1 = b##1 + (a##0 < c);
+ #define LowWord(a) a##0
+ #define HighWord(a) a##1
+ #ifdef _MSC_VER
+ #define MultiplyWords(p, a, b) p##0 = _umul128(a, b, &p##1);
+ #ifndef __INTEL_COMPILER
+ #define Double3Words(c, d) d##1 = __shiftleft128(d##0, d##1, 1); d##0 = __shiftleft128(c, d##0, 1); c *= 2;
+ #endif
+ #elif defined(__DECCXX)
+ #define MultiplyWords(p, a, b) p##0 = a*b; p##1 = asm("umulh %a0, %a1, %v0", a, b);
+ #elif defined(__x86_64__)
+ #define MultiplyWords(p, a, b) asm ("mulq %3" : "=a"(p##0), "=d"(p##1) : "a"(a), "g"(b) : "cc");
+ #define MulAcc(c, d, a, b) asm ("mulq %6; addq %3, %0; adcq %4, %1; adcq $0, %2;" : "+r"(c), "+r"(d##0), "+r"(d##1), "=a"(p0), "=d"(p1) : "a"(a), "g"(b) : "cc");
+ #define Double3Words(c, d) asm ("addq %0, %0; adcq %1, %1; adcq %2, %2;" : "+r"(c), "+r"(d##0), "+r"(d##1) : : "cc");
+ #define Acc2WordsBy1(a, b) asm ("addq %2, %0; adcq $0, %1;" : "+r"(a##0), "+r"(a##1) : "r"(b) : "cc");
+ #define Acc2WordsBy2(a, b) asm ("addq %2, %0; adcq %3, %1;" : "+r"(a##0), "+r"(a##1) : "r"(b##0), "r"(b##1) : "cc");
+ #define Acc3WordsBy2(c, d, e) asm ("addq %5, %0; adcq %6, %1; adcq $0, %2;" : "+r"(c), "=r"(e##0), "=r"(e##1) : "1"(d##0), "2"(d##1), "r"(e##0), "r"(e##1) : "cc");
+ #endif
+ #ifndef Double3Words
+ #define Double3Words(c, d) d##1 = 2*d##1 + (d##0>>(WORD_BITS-1)); d##0 = 2*d##0 + (c>>(WORD_BITS-1)); c *= 2;
+ #endif
+ #ifndef Acc2WordsBy2
+ #define Acc2WordsBy2(a, b) a##0 += b##0; a##1 += a##0 < b##0; a##1 += b##1;
+ #endif
+ #define AddWithCarry(u, a, b) {word t = a+b; u##0 = t + u##1; u##1 = (t<a) + (u##0<t);}
+ #define SubtractWithBorrow(u, a, b) {word t = a-b; u##0 = t - u##1; u##1 = (t>a) + (u##0>t);}
+ #define GetCarry(u) u##1
+ #define GetBorrow(u) u##1
+#else
+ #define Declare2Words(x) dword x;
+ #if _MSC_VER >= 1400 && !defined(__INTEL_COMPILER)
+ #define MultiplyWords(p, a, b) p = __emulu(a, b);
+ #else
+ #define MultiplyWords(p, a, b) p = (dword)a*b;
+ #endif
+ #define AssignWord(a, b) a = b;
+ #define Add2WordsBy1(a, b, c) a = b + c;
+ #define Acc2WordsBy2(a, b) a += b;
+ #define LowWord(a) word(a)
+ #define HighWord(a) word(a>>WORD_BITS)
+ #define Double3Words(c, d) d = 2*d + (c>>(WORD_BITS-1)); c *= 2;
+ #define AddWithCarry(u, a, b) u = dword(a) + b + GetCarry(u);
+ #define SubtractWithBorrow(u, a, b) u = dword(a) - b - GetBorrow(u);
+ #define GetCarry(u) HighWord(u)
+ #define GetBorrow(u) word(u>>(WORD_BITS*2-1))
+#endif
+#ifndef MulAcc
+ #define MulAcc(c, d, a, b) MultiplyWords(p, a, b); Acc2WordsBy1(p, c); c = LowWord(p); Acc2WordsBy1(d, HighWord(p));
+#endif
+#ifndef Acc2WordsBy1
+ #define Acc2WordsBy1(a, b) Add2WordsBy1(a, a, b)
+#endif
+#ifndef Acc3WordsBy2
+ #define Acc3WordsBy2(c, d, e) Acc2WordsBy1(e, c); c = LowWord(e); Add2WordsBy1(e, d, HighWord(e));
+#endif
+
+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(__x86_64__)
+ asm ("mulq %3" : "=a"(r.m_halfs.low), "=d"(r.m_halfs.high) : "a"(a), "g"(b) : "cc");
+ #else
+ r.m_halfs.low = _umul128(a, b, &r.m_halfs.high);
+ #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
+}
+
+// ********************************************************
+
+// use some tricks to share assembly code between MSVC and GCC
+#if defined(__GNUC__)
+ #define AddPrologue \
+ int result; \
+ __asm__ __volatile__ \
+ ( \
+ ".intel_syntax noprefix;"
+ #define AddEpilogue \
+ ".att_syntax prefix;" \
+ : "=a" (result)\
+ : "d" (C), "a" (A), "D" (B), "c" (N) \
+ : "%esi", "memory", "cc" \
+ );\
+ return result;
+ #define MulPrologue \
+ __asm__ __volatile__ \
+ ( \
+ ".intel_syntax noprefix;" \
+ AS1( push ebx) \
+ AS2( mov ebx, edx)
+ #define MulEpilogue \
+ AS1( pop ebx) \
+ ".att_syntax prefix;" \
+ : \
+ : "d" (s_maskLow16), "c" (C), "a" (A), "D" (B) \
+ : "%esi", "memory", "cc" \
+ );
+ #define SquPrologue MulPrologue
+ #define SquEpilogue \
+ AS1( pop ebx) \
+ ".att_syntax prefix;" \
+ : \
+ : "d" (s_maskLow16), "c" (C), "a" (A) \
+ : "%esi", "%edi", "memory", "cc" \
+ );
+ #define TopPrologue MulPrologue
+ #define TopEpilogue \
+ AS1( pop ebx) \
+ ".att_syntax prefix;" \
+ : \
+ : "d" (s_maskLow16), "c" (C), "a" (A), "D" (B), "S" (L) \
+ : "memory", "cc" \
+ );
+#else
+ #define AddPrologue \
+ __asm push edi \
+ __asm push esi \
+ __asm mov eax, [esp+12] \
+ __asm mov edi, [esp+16]
+ #define AddEpilogue \
+ __asm pop esi \
+ __asm pop edi \
+ __asm ret 8
+#if _MSC_VER < 1300
+ #define SaveEBX __asm push ebx
+ #define RestoreEBX __asm pop ebx
+#else
+ #define SaveEBX
+ #define RestoreEBX
+#endif
+ #define SquPrologue \
+ AS2( mov eax, A) \
+ AS2( mov ecx, C) \
+ SaveEBX \
+ AS2( lea ebx, s_maskLow16)
+ #define MulPrologue \
+ AS2( mov eax, A) \
+ AS2( mov edi, B) \
+ AS2( mov ecx, C) \
+ SaveEBX \
+ AS2( lea ebx, s_maskLow16)
+ #define TopPrologue \
+ AS2( mov eax, A) \
+ AS2( mov edi, B) \
+ AS2( mov ecx, C) \
+ AS2( mov esi, L) \
+ SaveEBX \
+ AS2( lea ebx, s_maskLow16)
+ #define SquEpilogue RestoreEBX
+ #define MulEpilogue RestoreEBX
+ #define TopEpilogue RestoreEBX
+#endif
+
+#ifdef CRYPTOPP_X64_MASM_AVAILABLE
+extern "C" {
+int Baseline_Add(size_t N, word *C, const word *A, const word *B);
+int Baseline_Sub(size_t N, word *C, const word *A, const word *B);
+}
+#elif defined(CRYPTOPP_X64_ASM_AVAILABLE) && defined(__GNUC__)
+int Baseline_Add(size_t N, word *C, const word *A, const word *B)
+{
+ word result;
+ __asm__ __volatile__
+ (
+ ".intel_syntax;"
+ AS1( neg %1)
+ ASJ( jz, 1, f)
+ AS2( mov %0,[%3+8*%1])
+ AS2( add %0,[%4+8*%1])
+ AS2( mov [%2+8*%1],%0)
+ ASL(0)
+ AS2( mov %0,[%3+8*%1+8])
+ AS2( adc %0,[%4+8*%1+8])
+ AS2( mov [%2+8*%1+8],%0)
+ AS2( lea %1,[%1+2])
+ ASJ( jrcxz, 1, f)
+ AS2( mov %0,[%3+8*%1])
+ AS2( adc %0,[%4+8*%1])
+ AS2( mov [%2+8*%1],%0)
+ ASJ( jmp, 0, b)
+ ASL(1)
+ AS2( mov %0, 0)
+ AS2( adc %0, %0)
+ ".att_syntax;"
+ : "=&r" (result)
+ : "c" (N), "r" (C+N), "r" (A+N), "r" (B+N)
+ : "memory", "cc"
+ );
+ return (int)result;
+}
+
+int Baseline_Sub(size_t N, word *C, const word *A, const word *B)
+{
+ word result;
+ __asm__ __volatile__
+ (
+ ".intel_syntax;"
+ AS1( neg %1)
+ ASJ( jz, 1, f)
+ AS2( mov %0,[%3+8*%1])
+ AS2( sub %0,[%4+8*%1])
+ AS2( mov [%2+8*%1],%0)
+ ASL(0)
+ AS2( mov %0,[%3+8*%1+8])
+ AS2( sbb %0,[%4+8*%1+8])
+ AS2( mov [%2+8*%1+8],%0)
+ AS2( lea %1,[%1+2])
+ ASJ( jrcxz, 1, f)
+ AS2( mov %0,[%3+8*%1])
+ AS2( sbb %0,[%4+8*%1])
+ AS2( mov [%2+8*%1],%0)
+ ASJ( jmp, 0, b)
+ ASL(1)
+ AS2( mov %0, 0)
+ AS2( adc %0, %0)
+ ".att_syntax;"
+ : "=&r" (result)
+ : "c" (N), "r" (C+N), "r" (A+N), "r" (B+N)
+ : "memory", "cc"
+ );
+ return (int)result;
+}
+#elif defined(CRYPTOPP_X86_ASM_AVAILABLE) && CRYPTOPP_BOOL_X86
+CRYPTOPP_NAKED int CRYPTOPP_FASTCALL Baseline_Add(size_t N, word *C, const word *A, const word *B)
+{
+ AddPrologue
+
+ // now: eax = A, edi = B, edx = C, ecx = N
+ AS2( lea eax, [eax+4*ecx])
+ AS2( lea edi, [edi+4*ecx])
+ AS2( lea edx, [edx+4*ecx])
+
+ AS1( neg ecx) // ecx is negative index
+ AS2( test ecx, 2) // this clears carry flag
+ ASJ( jz, 0, f)
+ AS2( sub ecx, 2)
+ ASJ( jmp, 1, f)
+
+ ASL(0)
+ ASJ( jecxz, 2, f) // loop until ecx overflows and becomes zero
+ AS2( mov esi,[eax+4*ecx])
+ AS2( adc esi,[edi+4*ecx])
+ AS2( mov [edx+4*ecx],esi)
+ AS2( mov esi,[eax+4*ecx+4])
+ AS2( adc esi,[edi+4*ecx+4])
+ AS2( mov [edx+4*ecx+4],esi)
+ ASL(1)
+ AS2( mov esi,[eax+4*ecx+8])
+ AS2( adc esi,[edi+4*ecx+8])
+ AS2( mov [edx+4*ecx+8],esi)
+ AS2( mov esi,[eax+4*ecx+12])
+ AS2( adc esi,[edi+4*ecx+12])
+ AS2( mov [edx+4*ecx+12],esi)
+
+ AS2( lea ecx,[ecx+4]) // advance index, avoid inc which causes slowdown on Intel Core 2
+ ASJ( jmp, 0, b)
+
+ ASL(2)
+ AS2( mov eax, 0)
+ AS1( setc al) // store carry into eax (return result register)
+
+ AddEpilogue
+}
+
+CRYPTOPP_NAKED int CRYPTOPP_FASTCALL Baseline_Sub(size_t N, word *C, const word *A, const word *B)
+{
+ AddPrologue
+
+ // now: eax = A, edi = B, edx = C, ecx = N
+ AS2( lea eax, [eax+4*ecx])
+ AS2( lea edi, [edi+4*ecx])
+ AS2( lea edx, [edx+4*ecx])
+
+ AS1( neg ecx) // ecx is negative index
+ AS2( test ecx, 2) // this clears carry flag
+ ASJ( jz, 0, f)
+ AS2( sub ecx, 2)
+ ASJ( jmp, 1, f)
+
+ ASL(0)
+ ASJ( jecxz, 2, f) // loop until ecx overflows and becomes zero
+ AS2( mov esi,[eax+4*ecx])
+ AS2( sbb esi,[edi+4*ecx])
+ AS2( mov [edx+4*ecx],esi)
+ AS2( mov esi,[eax+4*ecx+4])
+ AS2( sbb esi,[edi+4*ecx+4])
+ AS2( mov [edx+4*ecx+4],esi)
+ ASL(1)
+ AS2( mov esi,[eax+4*ecx+8])
+ AS2( sbb esi,[edi+4*ecx+8])
+ AS2( mov [edx+4*ecx+8],esi)
+ AS2( mov esi,[eax+4*ecx+12])
+ AS2( sbb esi,[edi+4*ecx+12])
+ AS2( mov [edx+4*ecx+12],esi)
+
+ AS2( lea ecx,[ecx+4]) // advance index, avoid inc which causes slowdown on Intel Core 2
+ ASJ( jmp, 0, b)
+
+ ASL(2)
+ AS2( mov eax, 0)
+ AS1( setc al) // store carry into eax (return result register)
+
+ AddEpilogue
+}
+
+#if CRYPTOPP_INTEGER_SSE2
+CRYPTOPP_NAKED int CRYPTOPP_FASTCALL SSE2_Add(size_t N, word *C, const word *A, const word *B)
+{
+ AddPrologue
+
+ // now: eax = A, edi = B, edx = C, ecx = N
+ AS2( lea eax, [eax+4*ecx])
+ AS2( lea edi, [edi+4*ecx])
+ AS2( lea edx, [edx+4*ecx])
+
+ AS1( neg ecx) // ecx is negative index
+ AS2( pxor mm2, mm2)
+ ASJ( jz, 2, f)
+ AS2( test ecx, 2) // this clears carry flag
+ ASJ( jz, 0, f)
+ AS2( sub ecx, 2)
+ ASJ( jmp, 1, f)
+
+ ASL(0)
+ AS2( movd mm0, DWORD PTR [eax+4*ecx])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx])
+ AS2( paddq mm0, mm1)
+ AS2( paddq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx], mm2)
+ AS2( psrlq mm2, 32)
+
+ AS2( movd mm0, DWORD PTR [eax+4*ecx+4])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+4])
+ AS2( paddq mm0, mm1)
+ AS2( paddq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx+4], mm2)
+ AS2( psrlq mm2, 32)
+
+ ASL(1)
+ AS2( movd mm0, DWORD PTR [eax+4*ecx+8])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+8])
+ AS2( paddq mm0, mm1)
+ AS2( paddq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx+8], mm2)
+ AS2( psrlq mm2, 32)
+
+ AS2( movd mm0, DWORD PTR [eax+4*ecx+12])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+12])
+ AS2( paddq mm0, mm1)
+ AS2( paddq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx+12], mm2)
+ AS2( psrlq mm2, 32)
+
+ AS2( add ecx, 4)
+ ASJ( jnz, 0, b)
+
+ ASL(2)
+ AS2( movd eax, mm2)
+ AS1( emms)
+
+ AddEpilogue
+}
+CRYPTOPP_NAKED int CRYPTOPP_FASTCALL SSE2_Sub(size_t N, word *C, const word *A, const word *B)
+{
+ AddPrologue
+
+ // now: eax = A, edi = B, edx = C, ecx = N
+ AS2( lea eax, [eax+4*ecx])
+ AS2( lea edi, [edi+4*ecx])
+ AS2( lea edx, [edx+4*ecx])
+
+ AS1( neg ecx) // ecx is negative index
+ AS2( pxor mm2, mm2)
+ ASJ( jz, 2, f)
+ AS2( test ecx, 2) // this clears carry flag
+ ASJ( jz, 0, f)
+ AS2( sub ecx, 2)
+ ASJ( jmp, 1, f)
+
+ ASL(0)
+ AS2( movd mm0, DWORD PTR [eax+4*ecx])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx])
+ AS2( psubq mm0, mm1)
+ AS2( psubq mm0, mm2)
+ AS2( movd DWORD PTR [edx+4*ecx], mm0)
+ AS2( psrlq mm0, 63)
+
+ AS2( movd mm2, DWORD PTR [eax+4*ecx+4])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+4])
+ AS2( psubq mm2, mm1)
+ AS2( psubq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx+4], mm2)
+ AS2( psrlq mm2, 63)
+
+ ASL(1)
+ AS2( movd mm0, DWORD PTR [eax+4*ecx+8])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+8])
+ AS2( psubq mm0, mm1)
+ AS2( psubq mm0, mm2)
+ AS2( movd DWORD PTR [edx+4*ecx+8], mm0)
+ AS2( psrlq mm0, 63)
+
+ AS2( movd mm2, DWORD PTR [eax+4*ecx+12])
+ AS2( movd mm1, DWORD PTR [edi+4*ecx+12])
+ AS2( psubq mm2, mm1)
+ AS2( psubq mm2, mm0)
+ AS2( movd DWORD PTR [edx+4*ecx+12], mm2)
+ AS2( psrlq mm2, 63)
+
+ AS2( add ecx, 4)
+ ASJ( jnz, 0, b)
+
+ ASL(2)
+ AS2( movd eax, mm2)
+ AS1( emms)
+
+ AddEpilogue
+}
+#endif // #if CRYPTOPP_BOOL_SSE2_ASM_AVAILABLE
+#else
+int CRYPTOPP_FASTCALL Baseline_Add(size_t N, word *C, const word *A, const word *B)
+{
+ assert (N%2 == 0);
+
+ Declare2Words(u);
+ AssignWord(u, 0);
+ for (size_t i=0; i<N; i+=2)
+ {
+ AddWithCarry(u, A[i], B[i]);
+ C[i] = LowWord(u);
+ AddWithCarry(u, A[i+1], B[i+1]);
+ C[i+1] = LowWord(u);
+ }
+ return int(GetCarry(u));
+}
+
+int CRYPTOPP_FASTCALL Baseline_Sub(size_t N, word *C, const word *A, const word *B)
+{
+ assert (N%2 == 0);
+
+ Declare2Words(u);
+ AssignWord(u, 0);
+ for (size_t i=0; i<N; i+=2)
+ {
+ SubtractWithBorrow(u, A[i], B[i]);
+ C[i] = LowWord(u);
+ SubtractWithBorrow(u, A[i+1], B[i+1]);
+ C[i+1] = LowWord(u);
+ }
+ return int(GetBorrow(u));
+}
+#endif
+
+static word LinearMultiply(word *C, const word *A, word B, size_t N)
+{
+ word carry=0;
+ for(unsigned i=0; i<N; i++)
+ {
+ Declare2Words(p);
+ MultiplyWords(p, A[i], B);
+ Acc2WordsBy1(p, carry);
+ C[i] = LowWord(p);
+ carry = HighWord(p);
+ }
+ return carry;
+}
+
+#ifndef CRYPTOPP_DOXYGEN_PROCESSING
+
+#define Mul_2 \
+ Mul_Begin(2) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_End(1, 1)
+
+#define Mul_4 \
+ Mul_Begin(4) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
+ Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Mul_SaveAcc(3, 1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) \
+ Mul_SaveAcc(4, 2, 3) Mul_Acc(3, 2) \
+ Mul_End(5, 3)
+
+#define Mul_8 \
+ Mul_Begin(8) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
+ Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
+ Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
+ Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
+ Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
+ Mul_SaveAcc(7, 1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) \
+ Mul_SaveAcc(8, 2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) \
+ Mul_SaveAcc(9, 3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) \
+ Mul_SaveAcc(10, 4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) \
+ Mul_SaveAcc(11, 5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) \
+ Mul_SaveAcc(12, 6, 7) Mul_Acc(7, 6) \
+ Mul_End(13, 7)
+
+#define Mul_16 \
+ Mul_Begin(16) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
+ Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
+ Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
+ Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
+ Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
+ Mul_SaveAcc(7, 0, 8) Mul_Acc(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) Mul_Acc(8, 0) \
+ Mul_SaveAcc(8, 0, 9) Mul_Acc(1, 8) Mul_Acc(2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) Mul_Acc(8, 1) Mul_Acc(9, 0) \
+ Mul_SaveAcc(9, 0, 10) Mul_Acc(1, 9) Mul_Acc(2, 8) Mul_Acc(3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) Mul_Acc(8, 2) Mul_Acc(9, 1) Mul_Acc(10, 0) \
+ Mul_SaveAcc(10, 0, 11) Mul_Acc(1, 10) Mul_Acc(2, 9) Mul_Acc(3, 8) Mul_Acc(4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) Mul_Acc(8, 3) Mul_Acc(9, 2) Mul_Acc(10, 1) Mul_Acc(11, 0) \
+ Mul_SaveAcc(11, 0, 12) Mul_Acc(1, 11) Mul_Acc(2, 10) Mul_Acc(3, 9) Mul_Acc(4, 8) Mul_Acc(5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) Mul_Acc(8, 4) Mul_Acc(9, 3) Mul_Acc(10, 2) Mul_Acc(11, 1) Mul_Acc(12, 0) \
+ Mul_SaveAcc(12, 0, 13) Mul_Acc(1, 12) Mul_Acc(2, 11) Mul_Acc(3, 10) Mul_Acc(4, 9) Mul_Acc(5, 8) Mul_Acc(6, 7) Mul_Acc(7, 6) Mul_Acc(8, 5) Mul_Acc(9, 4) Mul_Acc(10, 3) Mul_Acc(11, 2) Mul_Acc(12, 1) Mul_Acc(13, 0) \
+ Mul_SaveAcc(13, 0, 14) Mul_Acc(1, 13) Mul_Acc(2, 12) Mul_Acc(3, 11) Mul_Acc(4, 10) Mul_Acc(5, 9) Mul_Acc(6, 8) Mul_Acc(7, 7) Mul_Acc(8, 6) Mul_Acc(9, 5) Mul_Acc(10, 4) Mul_Acc(11, 3) Mul_Acc(12, 2) Mul_Acc(13, 1) Mul_Acc(14, 0) \
+ Mul_SaveAcc(14, 0, 15) Mul_Acc(1, 14) Mul_Acc(2, 13) Mul_Acc(3, 12) Mul_Acc(4, 11) Mul_Acc(5, 10) Mul_Acc(6, 9) Mul_Acc(7, 8) Mul_Acc(8, 7) Mul_Acc(9, 6) Mul_Acc(10, 5) Mul_Acc(11, 4) Mul_Acc(12, 3) Mul_Acc(13, 2) Mul_Acc(14, 1) Mul_Acc(15, 0) \
+ Mul_SaveAcc(15, 1, 15) Mul_Acc(2, 14) Mul_Acc(3, 13) Mul_Acc(4, 12) Mul_Acc(5, 11) Mul_Acc(6, 10) Mul_Acc(7, 9) Mul_Acc(8, 8) Mul_Acc(9, 7) Mul_Acc(10, 6) Mul_Acc(11, 5) Mul_Acc(12, 4) Mul_Acc(13, 3) Mul_Acc(14, 2) Mul_Acc(15, 1) \
+ Mul_SaveAcc(16, 2, 15) Mul_Acc(3, 14) Mul_Acc(4, 13) Mul_Acc(5, 12) Mul_Acc(6, 11) Mul_Acc(7, 10) Mul_Acc(8, 9) Mul_Acc(9, 8) Mul_Acc(10, 7) Mul_Acc(11, 6) Mul_Acc(12, 5) Mul_Acc(13, 4) Mul_Acc(14, 3) Mul_Acc(15, 2) \
+ Mul_SaveAcc(17, 3, 15) Mul_Acc(4, 14) Mul_Acc(5, 13) Mul_Acc(6, 12) Mul_Acc(7, 11) Mul_Acc(8, 10) Mul_Acc(9, 9) Mul_Acc(10, 8) Mul_Acc(11, 7) Mul_Acc(12, 6) Mul_Acc(13, 5) Mul_Acc(14, 4) Mul_Acc(15, 3) \
+ Mul_SaveAcc(18, 4, 15) Mul_Acc(5, 14) Mul_Acc(6, 13) Mul_Acc(7, 12) Mul_Acc(8, 11) Mul_Acc(9, 10) Mul_Acc(10, 9) Mul_Acc(11, 8) Mul_Acc(12, 7) Mul_Acc(13, 6) Mul_Acc(14, 5) Mul_Acc(15, 4) \
+ Mul_SaveAcc(19, 5, 15) Mul_Acc(6, 14) Mul_Acc(7, 13) Mul_Acc(8, 12) Mul_Acc(9, 11) Mul_Acc(10, 10) Mul_Acc(11, 9) Mul_Acc(12, 8) Mul_Acc(13, 7) Mul_Acc(14, 6) Mul_Acc(15, 5) \
+ Mul_SaveAcc(20, 6, 15) Mul_Acc(7, 14) Mul_Acc(8, 13) Mul_Acc(9, 12) Mul_Acc(10, 11) Mul_Acc(11, 10) Mul_Acc(12, 9) Mul_Acc(13, 8) Mul_Acc(14, 7) Mul_Acc(15, 6) \
+ Mul_SaveAcc(21, 7, 15) Mul_Acc(8, 14) Mul_Acc(9, 13) Mul_Acc(10, 12) Mul_Acc(11, 11) Mul_Acc(12, 10) Mul_Acc(13, 9) Mul_Acc(14, 8) Mul_Acc(15, 7) \
+ Mul_SaveAcc(22, 8, 15) Mul_Acc(9, 14) Mul_Acc(10, 13) Mul_Acc(11, 12) Mul_Acc(12, 11) Mul_Acc(13, 10) Mul_Acc(14, 9) Mul_Acc(15, 8) \
+ Mul_SaveAcc(23, 9, 15) Mul_Acc(10, 14) Mul_Acc(11, 13) Mul_Acc(12, 12) Mul_Acc(13, 11) Mul_Acc(14, 10) Mul_Acc(15, 9) \
+ Mul_SaveAcc(24, 10, 15) Mul_Acc(11, 14) Mul_Acc(12, 13) Mul_Acc(13, 12) Mul_Acc(14, 11) Mul_Acc(15, 10) \
+ Mul_SaveAcc(25, 11, 15) Mul_Acc(12, 14) Mul_Acc(13, 13) Mul_Acc(14, 12) Mul_Acc(15, 11) \
+ Mul_SaveAcc(26, 12, 15) Mul_Acc(13, 14) Mul_Acc(14, 13) Mul_Acc(15, 12) \
+ Mul_SaveAcc(27, 13, 15) Mul_Acc(14, 14) Mul_Acc(15, 13) \
+ Mul_SaveAcc(28, 14, 15) Mul_Acc(15, 14) \
+ Mul_End(29, 15)
+
+#define Squ_2 \
+ Squ_Begin(2) \
+ Squ_End(2)
+
+#define Squ_4 \
+ Squ_Begin(4) \
+ Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
+ Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
+ Squ_SaveAcc(3, 1, 3) Squ_Diag(2) \
+ Squ_SaveAcc(4, 2, 3) Squ_NonDiag \
+ Squ_End(4)
+
+#define Squ_8 \
+ Squ_Begin(8) \
+ Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
+ Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
+ Squ_SaveAcc(3, 0, 4) Squ_Acc(1, 3) Squ_Diag(2) \
+ Squ_SaveAcc(4, 0, 5) Squ_Acc(1, 4) Squ_Acc(2, 3) Squ_NonDiag \
+ Squ_SaveAcc(5, 0, 6) Squ_Acc(1, 5) Squ_Acc(2, 4) Squ_Diag(3) \
+ Squ_SaveAcc(6, 0, 7) Squ_Acc(1, 6) Squ_Acc(2, 5) Squ_Acc(3, 4) Squ_NonDiag \
+ Squ_SaveAcc(7, 1, 7) Squ_Acc(2, 6) Squ_Acc(3, 5) Squ_Diag(4) \
+ Squ_SaveAcc(8, 2, 7) Squ_Acc(3, 6) Squ_Acc(4, 5) Squ_NonDiag \
+ Squ_SaveAcc(9, 3, 7) Squ_Acc(4, 6) Squ_Diag(5) \
+ Squ_SaveAcc(10, 4, 7) Squ_Acc(5, 6) Squ_NonDiag \
+ Squ_SaveAcc(11, 5, 7) Squ_Diag(6) \
+ Squ_SaveAcc(12, 6, 7) Squ_NonDiag \
+ Squ_End(8)
+
+#define Squ_16 \
+ Squ_Begin(16) \
+ Squ_SaveAcc(1, 0, 2) Squ_Diag(1) \
+ Squ_SaveAcc(2, 0, 3) Squ_Acc(1, 2) Squ_NonDiag \
+ Squ_SaveAcc(3, 0, 4) Squ_Acc(1, 3) Squ_Diag(2) \
+ Squ_SaveAcc(4, 0, 5) Squ_Acc(1, 4) Squ_Acc(2, 3) Squ_NonDiag \
+ Squ_SaveAcc(5, 0, 6) Squ_Acc(1, 5) Squ_Acc(2, 4) Squ_Diag(3) \
+ Squ_SaveAcc(6, 0, 7) Squ_Acc(1, 6) Squ_Acc(2, 5) Squ_Acc(3, 4) Squ_NonDiag \
+ Squ_SaveAcc(7, 0, 8) Squ_Acc(1, 7) Squ_Acc(2, 6) Squ_Acc(3, 5) Squ_Diag(4) \
+ Squ_SaveAcc(8, 0, 9) Squ_Acc(1, 8) Squ_Acc(2, 7) Squ_Acc(3, 6) Squ_Acc(4, 5) Squ_NonDiag \
+ Squ_SaveAcc(9, 0, 10) Squ_Acc(1, 9) Squ_Acc(2, 8) Squ_Acc(3, 7) Squ_Acc(4, 6) Squ_Diag(5) \
+ Squ_SaveAcc(10, 0, 11) Squ_Acc(1, 10) Squ_Acc(2, 9) Squ_Acc(3, 8) Squ_Acc(4, 7) Squ_Acc(5, 6) Squ_NonDiag \
+ Squ_SaveAcc(11, 0, 12) Squ_Acc(1, 11) Squ_Acc(2, 10) Squ_Acc(3, 9) Squ_Acc(4, 8) Squ_Acc(5, 7) Squ_Diag(6) \
+ Squ_SaveAcc(12, 0, 13) Squ_Acc(1, 12) Squ_Acc(2, 11) Squ_Acc(3, 10) Squ_Acc(4, 9) Squ_Acc(5, 8) Squ_Acc(6, 7) Squ_NonDiag \
+ Squ_SaveAcc(13, 0, 14) Squ_Acc(1, 13) Squ_Acc(2, 12) Squ_Acc(3, 11) Squ_Acc(4, 10) Squ_Acc(5, 9) Squ_Acc(6, 8) Squ_Diag(7) \
+ Squ_SaveAcc(14, 0, 15) Squ_Acc(1, 14) Squ_Acc(2, 13) Squ_Acc(3, 12) Squ_Acc(4, 11) Squ_Acc(5, 10) Squ_Acc(6, 9) Squ_Acc(7, 8) Squ_NonDiag \
+ Squ_SaveAcc(15, 1, 15) Squ_Acc(2, 14) Squ_Acc(3, 13) Squ_Acc(4, 12) Squ_Acc(5, 11) Squ_Acc(6, 10) Squ_Acc(7, 9) Squ_Diag(8) \
+ Squ_SaveAcc(16, 2, 15) Squ_Acc(3, 14) Squ_Acc(4, 13) Squ_Acc(5, 12) Squ_Acc(6, 11) Squ_Acc(7, 10) Squ_Acc(8, 9) Squ_NonDiag \
+ Squ_SaveAcc(17, 3, 15) Squ_Acc(4, 14) Squ_Acc(5, 13) Squ_Acc(6, 12) Squ_Acc(7, 11) Squ_Acc(8, 10) Squ_Diag(9) \
+ Squ_SaveAcc(18, 4, 15) Squ_Acc(5, 14) Squ_Acc(6, 13) Squ_Acc(7, 12) Squ_Acc(8, 11) Squ_Acc(9, 10) Squ_NonDiag \
+ Squ_SaveAcc(19, 5, 15) Squ_Acc(6, 14) Squ_Acc(7, 13) Squ_Acc(8, 12) Squ_Acc(9, 11) Squ_Diag(10) \
+ Squ_SaveAcc(20, 6, 15) Squ_Acc(7, 14) Squ_Acc(8, 13) Squ_Acc(9, 12) Squ_Acc(10, 11) Squ_NonDiag \
+ Squ_SaveAcc(21, 7, 15) Squ_Acc(8, 14) Squ_Acc(9, 13) Squ_Acc(10, 12) Squ_Diag(11) \
+ Squ_SaveAcc(22, 8, 15) Squ_Acc(9, 14) Squ_Acc(10, 13) Squ_Acc(11, 12) Squ_NonDiag \
+ Squ_SaveAcc(23, 9, 15) Squ_Acc(10, 14) Squ_Acc(11, 13) Squ_Diag(12) \
+ Squ_SaveAcc(24, 10, 15) Squ_Acc(11, 14) Squ_Acc(12, 13) Squ_NonDiag \
+ Squ_SaveAcc(25, 11, 15) Squ_Acc(12, 14) Squ_Diag(13) \
+ Squ_SaveAcc(26, 12, 15) Squ_Acc(13, 14) Squ_NonDiag \
+ Squ_SaveAcc(27, 13, 15) Squ_Diag(14) \
+ Squ_SaveAcc(28, 14, 15) Squ_NonDiag \
+ Squ_End(16)
+
+#define Bot_2 \
+ Mul_Begin(2) \
+ Bot_SaveAcc(0, 0, 1) Bot_Acc(1, 0) \
+ Bot_End(2)
+
+#define Bot_4 \
+ Mul_Begin(4) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 2, 0) Mul_Acc(1, 1) Mul_Acc(0, 2) \
+ Bot_SaveAcc(2, 0, 3) Bot_Acc(1, 2) Bot_Acc(2, 1) Bot_Acc(3, 0) \
+ Bot_End(4)
+
+#define Bot_8 \
+ Mul_Begin(8) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
+ Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
+ Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
+ Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
+ Bot_SaveAcc(6, 0, 7) Bot_Acc(1, 6) Bot_Acc(2, 5) Bot_Acc(3, 4) Bot_Acc(4, 3) Bot_Acc(5, 2) Bot_Acc(6, 1) Bot_Acc(7, 0) \
+ Bot_End(8)
+
+#define Bot_16 \
+ Mul_Begin(16) \
+ Mul_SaveAcc(0, 0, 1) Mul_Acc(1, 0) \
+ Mul_SaveAcc(1, 0, 2) Mul_Acc(1, 1) Mul_Acc(2, 0) \
+ Mul_SaveAcc(2, 0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Mul_SaveAcc(3, 0, 4) Mul_Acc(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) Mul_Acc(4, 0) \
+ Mul_SaveAcc(4, 0, 5) Mul_Acc(1, 4) Mul_Acc(2, 3) Mul_Acc(3, 2) Mul_Acc(4, 1) Mul_Acc(5, 0) \
+ Mul_SaveAcc(5, 0, 6) Mul_Acc(1, 5) Mul_Acc(2, 4) Mul_Acc(3, 3) Mul_Acc(4, 2) Mul_Acc(5, 1) Mul_Acc(6, 0) \
+ Mul_SaveAcc(6, 0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
+ Mul_SaveAcc(7, 0, 8) Mul_Acc(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) Mul_Acc(8, 0) \
+ Mul_SaveAcc(8, 0, 9) Mul_Acc(1, 8) Mul_Acc(2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) Mul_Acc(8, 1) Mul_Acc(9, 0) \
+ Mul_SaveAcc(9, 0, 10) Mul_Acc(1, 9) Mul_Acc(2, 8) Mul_Acc(3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) Mul_Acc(8, 2) Mul_Acc(9, 1) Mul_Acc(10, 0) \
+ Mul_SaveAcc(10, 0, 11) Mul_Acc(1, 10) Mul_Acc(2, 9) Mul_Acc(3, 8) Mul_Acc(4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) Mul_Acc(8, 3) Mul_Acc(9, 2) Mul_Acc(10, 1) Mul_Acc(11, 0) \
+ Mul_SaveAcc(11, 0, 12) Mul_Acc(1, 11) Mul_Acc(2, 10) Mul_Acc(3, 9) Mul_Acc(4, 8) Mul_Acc(5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) Mul_Acc(8, 4) Mul_Acc(9, 3) Mul_Acc(10, 2) Mul_Acc(11, 1) Mul_Acc(12, 0) \
+ Mul_SaveAcc(12, 0, 13) Mul_Acc(1, 12) Mul_Acc(2, 11) Mul_Acc(3, 10) Mul_Acc(4, 9) Mul_Acc(5, 8) Mul_Acc(6, 7) Mul_Acc(7, 6) Mul_Acc(8, 5) Mul_Acc(9, 4) Mul_Acc(10, 3) Mul_Acc(11, 2) Mul_Acc(12, 1) Mul_Acc(13, 0) \
+ Mul_SaveAcc(13, 0, 14) Mul_Acc(1, 13) Mul_Acc(2, 12) Mul_Acc(3, 11) Mul_Acc(4, 10) Mul_Acc(5, 9) Mul_Acc(6, 8) Mul_Acc(7, 7) Mul_Acc(8, 6) Mul_Acc(9, 5) Mul_Acc(10, 4) Mul_Acc(11, 3) Mul_Acc(12, 2) Mul_Acc(13, 1) Mul_Acc(14, 0) \
+ Bot_SaveAcc(14, 0, 15) Bot_Acc(1, 14) Bot_Acc(2, 13) Bot_Acc(3, 12) Bot_Acc(4, 11) Bot_Acc(5, 10) Bot_Acc(6, 9) Bot_Acc(7, 8) Bot_Acc(8, 7) Bot_Acc(9, 6) Bot_Acc(10, 5) Bot_Acc(11, 4) Bot_Acc(12, 3) Bot_Acc(13, 2) Bot_Acc(14, 1) Bot_Acc(15, 0) \
+ Bot_End(16)
+
+#endif
+
+#if 0
+#define Mul_Begin(n) \
+ Declare2Words(p) \
+ Declare2Words(c) \
+ Declare2Words(d) \
+ MultiplyWords(p, A[0], B[0]) \
+ AssignWord(c, LowWord(p)) \
+ AssignWord(d, HighWord(p))
+
+#define Mul_Acc(i, j) \
+ MultiplyWords(p, A[i], B[j]) \
+ Acc2WordsBy1(c, LowWord(p)) \
+ Acc2WordsBy1(d, HighWord(p))
+
+#define Mul_SaveAcc(k, i, j) \
+ R[k] = LowWord(c); \
+ Add2WordsBy1(c, d, HighWord(c)) \
+ MultiplyWords(p, A[i], B[j]) \
+ AssignWord(d, HighWord(p)) \
+ Acc2WordsBy1(c, LowWord(p))
+
+#define Mul_End(n) \
+ R[2*n-3] = LowWord(c); \
+ Acc2WordsBy1(d, HighWord(c)) \
+ MultiplyWords(p, A[n-1], B[n-1])\
+ Acc2WordsBy2(d, p) \
+ R[2*n-2] = LowWord(d); \
+ R[2*n-1] = HighWord(d);
+
+#define Bot_SaveAcc(k, i, j) \
+ R[k] = LowWord(c); \
+ word e = LowWord(d) + HighWord(c); \
+ e += A[i] * B[j];
+
+#define Bot_Acc(i, j) \
+ e += A[i] * B[j];
+
+#define Bot_End(n) \
+ R[n-1] = e;
+#else
+#define Mul_Begin(n) \
+ Declare2Words(p) \
+ word c; \
+ Declare2Words(d) \
+ MultiplyWords(p, A[0], B[0]) \
+ c = LowWord(p); \
+ AssignWord(d, HighWord(p))
+
+#define Mul_Acc(i, j) \
+ MulAcc(c, d, A[i], B[j])
+
+#define Mul_SaveAcc(k, i, j) \
+ R[k] = c; \
+ c = LowWord(d); \
+ AssignWord(d, HighWord(d)) \
+ MulAcc(c, d, A[i], B[j])
+
+#define Mul_End(k, i) \
+ R[k] = c; \
+ MultiplyWords(p, A[i], B[i]) \
+ Acc2WordsBy2(p, d) \
+ R[k+1] = LowWord(p); \
+ R[k+2] = HighWord(p);
+
+#define Bot_SaveAcc(k, i, j) \
+ R[k] = c; \
+ c = LowWord(d); \
+ c += A[i] * B[j];
+
+#define Bot_Acc(i, j) \
+ c += A[i] * B[j];
+
+#define Bot_End(n) \
+ R[n-1] = c;
+#endif
+
+#define Squ_Begin(n) \
+ Declare2Words(p) \
+ word c; \
+ Declare2Words(d) \
+ Declare2Words(e) \
+ MultiplyWords(p, A[0], A[0]) \
+ R[0] = LowWord(p); \
+ AssignWord(e, HighWord(p)) \
+ MultiplyWords(p, A[0], A[1]) \
+ c = LowWord(p); \
+ AssignWord(d, HighWord(p)) \
+ Squ_NonDiag \
+
+#define Squ_NonDiag \
+ Double3Words(c, d)
+
+#define Squ_SaveAcc(k, i, j) \
+ Acc3WordsBy2(c, d, e) \
+ R[k] = c; \
+ MultiplyWords(p, A[i], A[j]) \
+ c = LowWord(p); \
+ AssignWord(d, HighWord(p)) \
+
+#define Squ_Acc(i, j) \
+ MulAcc(c, d, A[i], A[j])
+
+#define Squ_Diag(i) \
+ Squ_NonDiag \
+ MulAcc(c, d, A[i], A[i])
+
+#define Squ_End(n) \
+ Acc3WordsBy2(c, d, e) \
+ R[2*n-3] = c; \
+ MultiplyWords(p, A[n-1], A[n-1])\
+ Acc2WordsBy2(p, e) \
+ R[2*n-2] = LowWord(p); \
+ R[2*n-1] = HighWord(p);
+
+void Baseline_Multiply2(word *R, const word *A, const word *B)
+{
+ Mul_2
+}
+
+void Baseline_Multiply4(word *R, const word *A, const word *B)
+{
+ Mul_4
+}
+
+void Baseline_Multiply8(word *R, const word *A, const word *B)
+{
+ Mul_8
+}
+
+void Baseline_Square2(word *R, const word *A)
+{
+ Squ_2
+}
+
+void Baseline_Square4(word *R, const word *A)
+{
+ Squ_4
+}
+
+void Baseline_Square8(word *R, const word *A)
+{
+ Squ_8
+}
+
+void Baseline_MultiplyBottom2(word *R, const word *A, const word *B)
+{
+ Bot_2
+}
+
+void Baseline_MultiplyBottom4(word *R, const word *A, const word *B)
+{
+ Bot_4
+}
+
+void Baseline_MultiplyBottom8(word *R, const word *A, const word *B)
+{
+ Bot_8
+}
+
+#define Top_Begin(n) \
+ Declare2Words(p) \
+ word c; \
+ Declare2Words(d) \
+ MultiplyWords(p, A[0], B[n-2]);\
+ AssignWord(d, HighWord(p));
+
+#define Top_Acc(i, j) \
+ MultiplyWords(p, A[i], B[j]);\
+ Acc2WordsBy1(d, HighWord(p));
+
+#define Top_SaveAcc0(i, j) \
+ c = LowWord(d); \
+ AssignWord(d, HighWord(d)) \
+ MulAcc(c, d, A[i], B[j])
+
+#define Top_SaveAcc1(i, j) \
+ c = L<c; \
+ Acc2WordsBy1(d, c); \
+ c = LowWord(d); \
+ AssignWord(d, HighWord(d)) \
+ MulAcc(c, d, A[i], B[j])
+
+void Baseline_MultiplyTop2(word *R, const word *A, const word *B, word L)
+{
+ word T[4];
+ Baseline_Multiply2(T, A, B);
+ R[0] = T[2];
+ R[1] = T[3];
+}
+
+void Baseline_MultiplyTop4(word *R, const word *A, const word *B, word L)
+{
+ Top_Begin(4)
+ Top_Acc(1, 1) Top_Acc(2, 0) \
+ Top_SaveAcc0(0, 3) Mul_Acc(1, 2) Mul_Acc(2, 1) Mul_Acc(3, 0) \
+ Top_SaveAcc1(1, 3) Mul_Acc(2, 2) Mul_Acc(3, 1) \
+ Mul_SaveAcc(0, 2, 3) Mul_Acc(3, 2) \
+ Mul_End(1, 3)
+}
+
+void Baseline_MultiplyTop8(word *R, const word *A, const word *B, word L)
+{
+ Top_Begin(8)
+ Top_Acc(1, 5) Top_Acc(2, 4) Top_Acc(3, 3) Top_Acc(4, 2) Top_Acc(5, 1) Top_Acc(6, 0) \
+ Top_SaveAcc0(0, 7) Mul_Acc(1, 6) Mul_Acc(2, 5) Mul_Acc(3, 4) Mul_Acc(4, 3) Mul_Acc(5, 2) Mul_Acc(6, 1) Mul_Acc(7, 0) \
+ Top_SaveAcc1(1, 7) Mul_Acc(2, 6) Mul_Acc(3, 5) Mul_Acc(4, 4) Mul_Acc(5, 3) Mul_Acc(6, 2) Mul_Acc(7, 1) \
+ Mul_SaveAcc(0, 2, 7) Mul_Acc(3, 6) Mul_Acc(4, 5) Mul_Acc(5, 4) Mul_Acc(6, 3) Mul_Acc(7, 2) \
+ Mul_SaveAcc(1, 3, 7) Mul_Acc(4, 6) Mul_Acc(5, 5) Mul_Acc(6, 4) Mul_Acc(7, 3) \
+ Mul_SaveAcc(2, 4, 7) Mul_Acc(5, 6) Mul_Acc(6, 5) Mul_Acc(7, 4) \
+ Mul_SaveAcc(3, 5, 7) Mul_Acc(6, 6) Mul_Acc(7, 5) \
+ Mul_SaveAcc(4, 6, 7) Mul_Acc(7, 6) \
+ Mul_End(5, 7)
+}
+
+#if !CRYPTOPP_INTEGER_SSE2 // save memory by not compiling these functions when SSE2 is available
+void Baseline_Multiply16(word *R, const word *A, const word *B)
+{
+ Mul_16
+}
+
+void Baseline_Square16(word *R, const word *A)
+{
+ Squ_16
+}
+
+void Baseline_MultiplyBottom16(word *R, const word *A, const word *B)
+{
+ Bot_16
+}
+
+void Baseline_MultiplyTop16(word *R, const word *A, const word *B, word L)
+{
+ Top_Begin(16)
+ Top_Acc(1, 13) Top_Acc(2, 12) Top_Acc(3, 11) Top_Acc(4, 10) Top_Acc(5, 9) Top_Acc(6, 8) Top_Acc(7, 7) Top_Acc(8, 6) Top_Acc(9, 5) Top_Acc(10, 4) Top_Acc(11, 3) Top_Acc(12, 2) Top_Acc(13, 1) Top_Acc(14, 0) \
+ Top_SaveAcc0(0, 15) Mul_Acc(1, 14) Mul_Acc(2, 13) Mul_Acc(3, 12) Mul_Acc(4, 11) Mul_Acc(5, 10) Mul_Acc(6, 9) Mul_Acc(7, 8) Mul_Acc(8, 7) Mul_Acc(9, 6) Mul_Acc(10, 5) Mul_Acc(11, 4) Mul_Acc(12, 3) Mul_Acc(13, 2) Mul_Acc(14, 1) Mul_Acc(15, 0) \
+ Top_SaveAcc1(1, 15) Mul_Acc(2, 14) Mul_Acc(3, 13) Mul_Acc(4, 12) Mul_Acc(5, 11) Mul_Acc(6, 10) Mul_Acc(7, 9) Mul_Acc(8, 8) Mul_Acc(9, 7) Mul_Acc(10, 6) Mul_Acc(11, 5) Mul_Acc(12, 4) Mul_Acc(13, 3) Mul_Acc(14, 2) Mul_Acc(15, 1) \
+ Mul_SaveAcc(0, 2, 15) Mul_Acc(3, 14) Mul_Acc(4, 13) Mul_Acc(5, 12) Mul_Acc(6, 11) Mul_Acc(7, 10) Mul_Acc(8, 9) Mul_Acc(9, 8) Mul_Acc(10, 7) Mul_Acc(11, 6) Mul_Acc(12, 5) Mul_Acc(13, 4) Mul_Acc(14, 3) Mul_Acc(15, 2) \
+ Mul_SaveAcc(1, 3, 15) Mul_Acc(4, 14) Mul_Acc(5, 13) Mul_Acc(6, 12) Mul_Acc(7, 11) Mul_Acc(8, 10) Mul_Acc(9, 9) Mul_Acc(10, 8) Mul_Acc(11, 7) Mul_Acc(12, 6) Mul_Acc(13, 5) Mul_Acc(14, 4) Mul_Acc(15, 3) \
+ Mul_SaveAcc(2, 4, 15) Mul_Acc(5, 14) Mul_Acc(6, 13) Mul_Acc(7, 12) Mul_Acc(8, 11) Mul_Acc(9, 10) Mul_Acc(10, 9) Mul_Acc(11, 8) Mul_Acc(12, 7) Mul_Acc(13, 6) Mul_Acc(14, 5) Mul_Acc(15, 4) \
+ Mul_SaveAcc(3, 5, 15) Mul_Acc(6, 14) Mul_Acc(7, 13) Mul_Acc(8, 12) Mul_Acc(9, 11) Mul_Acc(10, 10) Mul_Acc(11, 9) Mul_Acc(12, 8) Mul_Acc(13, 7) Mul_Acc(14, 6) Mul_Acc(15, 5) \
+ Mul_SaveAcc(4, 6, 15) Mul_Acc(7, 14) Mul_Acc(8, 13) Mul_Acc(9, 12) Mul_Acc(10, 11) Mul_Acc(11, 10) Mul_Acc(12, 9) Mul_Acc(13, 8) Mul_Acc(14, 7) Mul_Acc(15, 6) \
+ Mul_SaveAcc(5, 7, 15) Mul_Acc(8, 14) Mul_Acc(9, 13) Mul_Acc(10, 12) Mul_Acc(11, 11) Mul_Acc(12, 10) Mul_Acc(13, 9) Mul_Acc(14, 8) Mul_Acc(15, 7) \
+ Mul_SaveAcc(6, 8, 15) Mul_Acc(9, 14) Mul_Acc(10, 13) Mul_Acc(11, 12) Mul_Acc(12, 11) Mul_Acc(13, 10) Mul_Acc(14, 9) Mul_Acc(15, 8) \
+ Mul_SaveAcc(7, 9, 15) Mul_Acc(10, 14) Mul_Acc(11, 13) Mul_Acc(12, 12) Mul_Acc(13, 11) Mul_Acc(14, 10) Mul_Acc(15, 9) \
+ Mul_SaveAcc(8, 10, 15) Mul_Acc(11, 14) Mul_Acc(12, 13) Mul_Acc(13, 12) Mul_Acc(14, 11) Mul_Acc(15, 10) \
+ Mul_SaveAcc(9, 11, 15) Mul_Acc(12, 14) Mul_Acc(13, 13) Mul_Acc(14, 12) Mul_Acc(15, 11) \
+ Mul_SaveAcc(10, 12, 15) Mul_Acc(13, 14) Mul_Acc(14, 13) Mul_Acc(15, 12) \
+ Mul_SaveAcc(11, 13, 15) Mul_Acc(14, 14) Mul_Acc(15, 13) \
+ Mul_SaveAcc(12, 14, 15) Mul_Acc(15, 14) \
+ Mul_End(13, 15)
+}
+#endif
+
+// ********************************************************
+
+#if CRYPTOPP_INTEGER_SSE2
+
+CRYPTOPP_ALIGN_DATA(16) static const word32 s_maskLow16[4] CRYPTOPP_SECTION_ALIGN16 = {0xffff,0xffff,0xffff,0xffff};
+
+#undef Mul_Begin
+#undef Mul_Acc
+#undef Top_Begin
+#undef Top_Acc
+#undef Squ_Acc
+#undef Squ_NonDiag
+#undef Squ_Diag
+#undef Squ_SaveAcc
+#undef Squ_Begin
+#undef Mul_SaveAcc
+#undef Bot_Acc
+#undef Bot_SaveAcc
+#undef Bot_End
+#undef Squ_End
+#undef Mul_End
+
+#define SSE2_FinalSave(k) \
+ AS2( psllq xmm5, 16) \
+ AS2( paddq xmm4, xmm5) \
+ AS2( movq QWORD PTR [ecx+8*(k)], xmm4)
+
+#define SSE2_SaveShift(k) \
+ AS2( movq xmm0, xmm6) \
+ AS2( punpckhqdq xmm6, xmm0) \
+ AS2( movq xmm1, xmm7) \
+ AS2( punpckhqdq xmm7, xmm1) \
+ AS2( paddd xmm6, xmm0) \
+ AS2( pslldq xmm6, 4) \
+ AS2( paddd xmm7, xmm1) \
+ AS2( paddd xmm4, xmm6) \
+ AS2( pslldq xmm7, 4) \
+ AS2( movq xmm6, xmm4) \
+ AS2( paddd xmm5, xmm7) \
+ AS2( movq xmm7, xmm5) \
+ AS2( movd DWORD PTR [ecx+8*(k)], xmm4) \
+ AS2( psrlq xmm6, 16) \
+ AS2( paddq xmm6, xmm7) \
+ AS2( punpckhqdq xmm4, xmm0) \
+ AS2( punpckhqdq xmm5, xmm0) \
+ AS2( movq QWORD PTR [ecx+8*(k)+2], xmm6) \
+ AS2( psrlq xmm6, 3*16) \
+ AS2( paddd xmm4, xmm6) \
+
+#define Squ_SSE2_SaveShift(k) \
+ AS2( movq xmm0, xmm6) \
+ AS2( punpckhqdq xmm6, xmm0) \
+ AS2( movq xmm1, xmm7) \
+ AS2( punpckhqdq xmm7, xmm1) \
+ AS2( paddd xmm6, xmm0) \
+ AS2( pslldq xmm6, 4) \
+ AS2( paddd xmm7, xmm1) \
+ AS2( paddd xmm4, xmm6) \
+ AS2( pslldq xmm7, 4) \
+ AS2( movhlps xmm6, xmm4) \
+ AS2( movd DWORD PTR [ecx+8*(k)], xmm4) \
+ AS2( paddd xmm5, xmm7) \
+ AS2( movhps QWORD PTR [esp+12], xmm5)\
+ AS2( psrlq xmm4, 16) \
+ AS2( paddq xmm4, xmm5) \
+ AS2( movq QWORD PTR [ecx+8*(k)+2], xmm4) \
+ AS2( psrlq xmm4, 3*16) \
+ AS2( paddd xmm4, xmm6) \
+ AS2( movq QWORD PTR [esp+4], xmm4)\
+
+#define SSE2_FirstMultiply(i) \
+ AS2( movdqa xmm7, [esi+(i)*16])\
+ AS2( movdqa xmm5, [edi-(i)*16])\
+ AS2( pmuludq xmm5, xmm7) \
+ AS2( movdqa xmm4, [ebx])\
+ AS2( movdqa xmm6, xmm4) \
+ AS2( pand xmm4, xmm5) \
+ AS2( psrld xmm5, 16) \
+ AS2( pmuludq xmm7, [edx-(i)*16])\
+ AS2( pand xmm6, xmm7) \
+ AS2( psrld xmm7, 16)
+
+#define Squ_Begin(n) \
+ SquPrologue \
+ AS2( mov esi, esp)\
+ AS2( and esp, 0xfffffff0)\
+ AS2( lea edi, [esp-32*n])\
+ AS2( sub esp, 32*n+16)\
+ AS1( push esi)\
+ AS2( mov esi, edi) \
+ AS2( xor edx, edx) \
+ ASL(1) \
+ ASS( pshufd xmm0, [eax+edx], 3,1,2,0) \
+ ASS( pshufd xmm1, [eax+edx], 2,0,3,1) \
+ AS2( movdqa [edi+2*edx], xmm0) \
+ AS2( psrlq xmm0, 32) \
+ AS2( movdqa [edi+2*edx+16], xmm0) \
+ AS2( movdqa [edi+16*n+2*edx], xmm1) \
+ AS2( psrlq xmm1, 32) \
+ AS2( movdqa [edi+16*n+2*edx+16], xmm1) \
+ AS2( add edx, 16) \
+ AS2( cmp edx, 8*(n)) \
+ ASJ( jne, 1, b) \
+ AS2( lea edx, [edi+16*n])\
+ SSE2_FirstMultiply(0) \
+
+#define Squ_Acc(i) \
+ ASL(LSqu##i) \
+ AS2( movdqa xmm1, [esi+(i)*16]) \
+ AS2( movdqa xmm0, [edi-(i)*16]) \
+ AS2( movdqa xmm2, [ebx]) \
+ AS2( pmuludq xmm0, xmm1) \
+ AS2( pmuludq xmm1, [edx-(i)*16]) \
+ AS2( movdqa xmm3, xmm2) \
+ AS2( pand xmm2, xmm0) \
+ AS2( psrld xmm0, 16) \
+ AS2( paddd xmm4, xmm2) \
+ AS2( paddd xmm5, xmm0) \
+ AS2( pand xmm3, xmm1) \
+ AS2( psrld xmm1, 16) \
+ AS2( paddd xmm6, xmm3) \
+ AS2( paddd xmm7, xmm1) \
+
+#define Squ_Acc1(i)
+#define Squ_Acc2(i) ASC(call, LSqu##i)
+#define Squ_Acc3(i) Squ_Acc2(i)
+#define Squ_Acc4(i) Squ_Acc2(i)
+#define Squ_Acc5(i) Squ_Acc2(i)
+#define Squ_Acc6(i) Squ_Acc2(i)
+#define Squ_Acc7(i) Squ_Acc2(i)
+#define Squ_Acc8(i) Squ_Acc2(i)
+
+#define SSE2_End(E, n) \
+ SSE2_SaveShift(2*(n)-3) \
+ AS2( movdqa xmm7, [esi+16]) \
+ AS2( movdqa xmm0, [edi]) \
+ AS2( pmuludq xmm0, xmm7) \
+ AS2( movdqa xmm2, [ebx]) \
+ AS2( pmuludq xmm7, [edx]) \
+ AS2( movdqa xmm6, xmm2) \
+ AS2( pand xmm2, xmm0) \
+ AS2( psrld xmm0, 16) \
+ AS2( paddd xmm4, xmm2) \
+ AS2( paddd xmm5, xmm0) \
+ AS2( pand xmm6, xmm7) \
+ AS2( psrld xmm7, 16) \
+ SSE2_SaveShift(2*(n)-2) \
+ SSE2_FinalSave(2*(n)-1) \
+ AS1( pop esp)\
+ E
+
+#define Squ_End(n) SSE2_End(SquEpilogue, n)
+#define Mul_End(n) SSE2_End(MulEpilogue, n)
+#define Top_End(n) SSE2_End(TopEpilogue, n)
+
+#define Squ_Column1(k, i) \
+ Squ_SSE2_SaveShift(k) \
+ AS2( add esi, 16) \
+ SSE2_FirstMultiply(1)\
+ Squ_Acc##i(i) \
+ AS2( paddd xmm4, xmm4) \
+ AS2( paddd xmm5, xmm5) \
+ AS2( movdqa xmm3, [esi]) \
+ AS2( movq xmm1, QWORD PTR [esi+8]) \
+ AS2( pmuludq xmm1, xmm3) \
+ AS2( pmuludq xmm3, xmm3) \
+ AS2( movdqa xmm0, [ebx])\
+ AS2( movdqa xmm2, xmm0) \
+ AS2( pand xmm0, xmm1) \
+ AS2( psrld xmm1, 16) \
+ AS2( paddd xmm6, xmm0) \
+ AS2( paddd xmm7, xmm1) \
+ AS2( pand xmm2, xmm3) \
+ AS2( psrld xmm3, 16) \
+ AS2( paddd xmm6, xmm6) \
+ AS2( paddd xmm7, xmm7) \
+ AS2( paddd xmm4, xmm2) \
+ AS2( paddd xmm5, xmm3) \
+ AS2( movq xmm0, QWORD PTR [esp+4])\
+ AS2( movq xmm1, QWORD PTR [esp+12])\
+ AS2( paddd xmm4, xmm0)\
+ AS2( paddd xmm5, xmm1)\
+
+#define Squ_Column0(k, i) \
+ Squ_SSE2_SaveShift(k) \
+ AS2( add edi, 16) \
+ AS2( add edx, 16) \
+ SSE2_FirstMultiply(1)\
+ Squ_Acc##i(i) \
+ AS2( paddd xmm6, xmm6) \
+ AS2( paddd xmm7, xmm7) \
+ AS2( paddd xmm4, xmm4) \
+ AS2( paddd xmm5, xmm5) \
+ AS2( movq xmm0, QWORD PTR [esp+4])\
+ AS2( movq xmm1, QWORD PTR [esp+12])\
+ AS2( paddd xmm4, xmm0)\
+ AS2( paddd xmm5, xmm1)\
+
+#define SSE2_MulAdd45 \
+ AS2( movdqa xmm7, [esi]) \
+ AS2( movdqa xmm0, [edi]) \
+ AS2( pmuludq xmm0, xmm7) \
+ AS2( movdqa xmm2, [ebx]) \
+ AS2( pmuludq xmm7, [edx]) \
+ AS2( movdqa xmm6, xmm2) \
+ AS2( pand xmm2, xmm0) \
+ AS2( psrld xmm0, 16) \
+ AS2( paddd xmm4, xmm2) \
+ AS2( paddd xmm5, xmm0) \
+ AS2( pand xmm6, xmm7) \
+ AS2( psrld xmm7, 16)
+
+#define Mul_Begin(n) \
+ MulPrologue \
+ AS2( mov esi, esp)\
+ AS2( and esp, 0xfffffff0)\
+ AS2( sub esp, 48*n+16)\
+ AS1( push esi)\
+ AS2( xor edx, edx) \
+ ASL(1) \
+ ASS( pshufd xmm0, [eax+edx], 3,1,2,0) \
+ ASS( pshufd xmm1, [eax+edx], 2,0,3,1) \
+ ASS( pshufd xmm2, [edi+edx], 3,1,2,0) \
+ AS2( movdqa [esp+20+2*edx], xmm0) \
+ AS2( psrlq xmm0, 32) \
+ AS2( movdqa [esp+20+2*edx+16], xmm0) \
+ AS2( movdqa [esp+20+16*n+2*edx], xmm1) \
+ AS2( psrlq xmm1, 32) \
+ AS2( movdqa [esp+20+16*n+2*edx+16], xmm1) \
+ AS2( movdqa [esp+20+32*n+2*edx], xmm2) \
+ AS2( psrlq xmm2, 32) \
+ AS2( movdqa [esp+20+32*n+2*edx+16], xmm2) \
+ AS2( add edx, 16) \
+ AS2( cmp edx, 8*(n)) \
+ ASJ( jne, 1, b) \
+ AS2( lea edi, [esp+20])\
+ AS2( lea edx, [esp+20+16*n])\
+ AS2( lea esi, [esp+20+32*n])\
+ SSE2_FirstMultiply(0) \
+
+#define Mul_Acc(i) \
+ ASL(LMul##i) \
+ AS2( movdqa xmm1, [esi+i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( movdqa xmm0, [edi-i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( movdqa xmm2, [ebx]) \
+ AS2( pmuludq xmm0, xmm1) \
+ AS2( pmuludq xmm1, [edx-i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( movdqa xmm3, xmm2) \
+ AS2( pand xmm2, xmm0) \
+ AS2( psrld xmm0, 16) \
+ AS2( paddd xmm4, xmm2) \
+ AS2( paddd xmm5, xmm0) \
+ AS2( pand xmm3, xmm1) \
+ AS2( psrld xmm1, 16) \
+ AS2( paddd xmm6, xmm3) \
+ AS2( paddd xmm7, xmm1) \
+
+#define Mul_Acc1(i)
+#define Mul_Acc2(i) ASC(call, LMul##i)
+#define Mul_Acc3(i) Mul_Acc2(i)
+#define Mul_Acc4(i) Mul_Acc2(i)
+#define Mul_Acc5(i) Mul_Acc2(i)
+#define Mul_Acc6(i) Mul_Acc2(i)
+#define Mul_Acc7(i) Mul_Acc2(i)
+#define Mul_Acc8(i) Mul_Acc2(i)
+#define Mul_Acc9(i) Mul_Acc2(i)
+#define Mul_Acc10(i) Mul_Acc2(i)
+#define Mul_Acc11(i) Mul_Acc2(i)
+#define Mul_Acc12(i) Mul_Acc2(i)
+#define Mul_Acc13(i) Mul_Acc2(i)
+#define Mul_Acc14(i) Mul_Acc2(i)
+#define Mul_Acc15(i) Mul_Acc2(i)
+#define Mul_Acc16(i) Mul_Acc2(i)
+
+#define Mul_Column1(k, i) \
+ SSE2_SaveShift(k) \
+ AS2( add esi, 16) \
+ SSE2_MulAdd45\
+ Mul_Acc##i(i) \
+
+#define Mul_Column0(k, i) \
+ SSE2_SaveShift(k) \
+ AS2( add edi, 16) \
+ AS2( add edx, 16) \
+ SSE2_MulAdd45\
+ Mul_Acc##i(i) \
+
+#define Bot_Acc(i) \
+ AS2( movdqa xmm1, [esi+i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( movdqa xmm0, [edi-i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( pmuludq xmm0, xmm1) \
+ AS2( pmuludq xmm1, [edx-i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( paddq xmm4, xmm0) \
+ AS2( paddd xmm6, xmm1)
+
+#define Bot_SaveAcc(k) \
+ SSE2_SaveShift(k) \
+ AS2( add edi, 16) \
+ AS2( add edx, 16) \
+ AS2( movdqa xmm6, [esi]) \
+ AS2( movdqa xmm0, [edi]) \
+ AS2( pmuludq xmm0, xmm6) \
+ AS2( paddq xmm4, xmm0) \
+ AS2( psllq xmm5, 16) \
+ AS2( paddq xmm4, xmm5) \
+ AS2( pmuludq xmm6, [edx])
+
+#define Bot_End(n) \
+ AS2( movhlps xmm7, xmm6) \
+ AS2( paddd xmm6, xmm7) \
+ AS2( psllq xmm6, 32) \
+ AS2( paddd xmm4, xmm6) \
+ AS2( movq QWORD PTR [ecx+8*((n)-1)], xmm4) \
+ AS1( pop esp)\
+ MulEpilogue
+
+#define Top_Begin(n) \
+ TopPrologue \
+ AS2( mov edx, esp)\
+ AS2( and esp, 0xfffffff0)\
+ AS2( sub esp, 48*n+16)\
+ AS1( push edx)\
+ AS2( xor edx, edx) \
+ ASL(1) \
+ ASS( pshufd xmm0, [eax+edx], 3,1,2,0) \
+ ASS( pshufd xmm1, [eax+edx], 2,0,3,1) \
+ ASS( pshufd xmm2, [edi+edx], 3,1,2,0) \
+ AS2( movdqa [esp+20+2*edx], xmm0) \
+ AS2( psrlq xmm0, 32) \
+ AS2( movdqa [esp+20+2*edx+16], xmm0) \
+ AS2( movdqa [esp+20+16*n+2*edx], xmm1) \
+ AS2( psrlq xmm1, 32) \
+ AS2( movdqa [esp+20+16*n+2*edx+16], xmm1) \
+ AS2( movdqa [esp+20+32*n+2*edx], xmm2) \
+ AS2( psrlq xmm2, 32) \
+ AS2( movdqa [esp+20+32*n+2*edx+16], xmm2) \
+ AS2( add edx, 16) \
+ AS2( cmp edx, 8*(n)) \
+ ASJ( jne, 1, b) \
+ AS2( mov eax, esi) \
+ AS2( lea edi, [esp+20+00*n+16*(n/2-1)])\
+ AS2( lea edx, [esp+20+16*n+16*(n/2-1)])\
+ AS2( lea esi, [esp+20+32*n+16*(n/2-1)])\
+ AS2( pxor xmm4, xmm4)\
+ AS2( pxor xmm5, xmm5)
+
+#define Top_Acc(i) \
+ AS2( movq xmm0, QWORD PTR [esi+i/2*(1-(i-2*(i/2))*2)*16+8]) \
+ AS2( pmuludq xmm0, [edx-i/2*(1-(i-2*(i/2))*2)*16]) \
+ AS2( psrlq xmm0, 48) \
+ AS2( paddd xmm5, xmm0)\
+
+#define Top_Column0(i) \
+ AS2( psllq xmm5, 32) \
+ AS2( add edi, 16) \
+ AS2( add edx, 16) \
+ SSE2_MulAdd45\
+ Mul_Acc##i(i) \
+
+#define Top_Column1(i) \
+ SSE2_SaveShift(0) \
+ AS2( add esi, 16) \
+ SSE2_MulAdd45\
+ Mul_Acc##i(i) \
+ AS2( shr eax, 16) \
+ AS2( movd xmm0, eax)\
+ AS2( movd xmm1, [ecx+4])\
+ AS2( psrld xmm1, 16)\
+ AS2( pcmpgtd xmm1, xmm0)\
+ AS2( psrld xmm1, 31)\
+ AS2( paddd xmm4, xmm1)\
+
+void SSE2_Square4(word *C, const word *A)
+{
+ Squ_Begin(2)
+ Squ_Column0(0, 1)
+ Squ_End(2)
+}
+
+void SSE2_Square8(word *C, const word *A)
+{
+ Squ_Begin(4)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Squ_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Squ_Column0(0, 1)
+ Squ_Column1(1, 1)
+ Squ_Column0(2, 2)
+ Squ_Column1(3, 1)
+ Squ_Column0(4, 1)
+ Squ_End(4)
+}
+
+void SSE2_Square16(word *C, const word *A)
+{
+ Squ_Begin(8)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Squ_Acc(4) Squ_Acc(3) Squ_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Squ_Column0(0, 1)
+ Squ_Column1(1, 1)
+ Squ_Column0(2, 2)
+ Squ_Column1(3, 2)
+ Squ_Column0(4, 3)
+ Squ_Column1(5, 3)
+ Squ_Column0(6, 4)
+ Squ_Column1(7, 3)
+ Squ_Column0(8, 3)
+ Squ_Column1(9, 2)
+ Squ_Column0(10, 2)
+ Squ_Column1(11, 1)
+ Squ_Column0(12, 1)
+ Squ_End(8)
+}
+
+void SSE2_Square32(word *C, const word *A)
+{
+ Squ_Begin(16)
+ ASJ( jmp, 0, f)
+ Squ_Acc(8) Squ_Acc(7) Squ_Acc(6) Squ_Acc(5) Squ_Acc(4) Squ_Acc(3) Squ_Acc(2)
+ AS1( ret) ASL(0)
+ Squ_Column0(0, 1)
+ Squ_Column1(1, 1)
+ Squ_Column0(2, 2)
+ Squ_Column1(3, 2)
+ Squ_Column0(4, 3)
+ Squ_Column1(5, 3)
+ Squ_Column0(6, 4)
+ Squ_Column1(7, 4)
+ Squ_Column0(8, 5)
+ Squ_Column1(9, 5)
+ Squ_Column0(10, 6)
+ Squ_Column1(11, 6)
+ Squ_Column0(12, 7)
+ Squ_Column1(13, 7)
+ Squ_Column0(14, 8)
+ Squ_Column1(15, 7)
+ Squ_Column0(16, 7)
+ Squ_Column1(17, 6)
+ Squ_Column0(18, 6)
+ Squ_Column1(19, 5)
+ Squ_Column0(20, 5)
+ Squ_Column1(21, 4)
+ Squ_Column0(22, 4)
+ Squ_Column1(23, 3)
+ Squ_Column0(24, 3)
+ Squ_Column1(25, 2)
+ Squ_Column0(26, 2)
+ Squ_Column1(27, 1)
+ Squ_Column0(28, 1)
+ Squ_End(16)
+}
+
+void SSE2_Multiply4(word *C, const word *A, const word *B)
+{
+ Mul_Begin(2)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_End(2)
+}
+
+void SSE2_Multiply8(word *C, const word *A, const word *B)
+{
+ Mul_Begin(4)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 3)
+ Mul_Column0(4, 2)
+ Mul_End(4)
+}
+
+void SSE2_Multiply16(word *C, const word *A, const word *B)
+{
+ Mul_Begin(8)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 5)
+ Mul_Column0(4, 6)
+ Mul_Column1(5, 7)
+ Mul_Column0(6, 8)
+ Mul_Column1(7, 7)
+ Mul_Column0(8, 6)
+ Mul_Column1(9, 5)
+ Mul_Column0(10, 4)
+ Mul_Column1(11, 3)
+ Mul_Column0(12, 2)
+ Mul_End(8)
+}
+
+void SSE2_Multiply32(word *C, const word *A, const word *B)
+{
+ Mul_Begin(16)
+ ASJ( jmp, 0, f)
+ Mul_Acc(16) Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 5)
+ Mul_Column0(4, 6)
+ Mul_Column1(5, 7)
+ Mul_Column0(6, 8)
+ Mul_Column1(7, 9)
+ Mul_Column0(8, 10)
+ Mul_Column1(9, 11)
+ Mul_Column0(10, 12)
+ Mul_Column1(11, 13)
+ Mul_Column0(12, 14)
+ Mul_Column1(13, 15)
+ Mul_Column0(14, 16)
+ Mul_Column1(15, 15)
+ Mul_Column0(16, 14)
+ Mul_Column1(17, 13)
+ Mul_Column0(18, 12)
+ Mul_Column1(19, 11)
+ Mul_Column0(20, 10)
+ Mul_Column1(21, 9)
+ Mul_Column0(22, 8)
+ Mul_Column1(23, 7)
+ Mul_Column0(24, 6)
+ Mul_Column1(25, 5)
+ Mul_Column0(26, 4)
+ Mul_Column1(27, 3)
+ Mul_Column0(28, 2)
+ Mul_End(16)
+}
+
+void SSE2_MultiplyBottom4(word *C, const word *A, const word *B)
+{
+ Mul_Begin(2)
+ Bot_SaveAcc(0) Bot_Acc(2)
+ Bot_End(2)
+}
+
+void SSE2_MultiplyBottom8(word *C, const word *A, const word *B)
+{
+ Mul_Begin(4)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Bot_SaveAcc(2) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
+ Bot_End(4)
+}
+
+void SSE2_MultiplyBottom16(word *C, const word *A, const word *B)
+{
+ Mul_Begin(8)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 5)
+ Mul_Column0(4, 6)
+ Mul_Column1(5, 7)
+ Bot_SaveAcc(6) Bot_Acc(8) Bot_Acc(7) Bot_Acc(6) Bot_Acc(5) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
+ Bot_End(8)
+}
+
+void SSE2_MultiplyBottom32(word *C, const word *A, const word *B)
+{
+ Mul_Begin(16)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Mul_Column0(0, 2)
+ Mul_Column1(1, 3)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 5)
+ Mul_Column0(4, 6)
+ Mul_Column1(5, 7)
+ Mul_Column0(6, 8)
+ Mul_Column1(7, 9)
+ Mul_Column0(8, 10)
+ Mul_Column1(9, 11)
+ Mul_Column0(10, 12)
+ Mul_Column1(11, 13)
+ Mul_Column0(12, 14)
+ Mul_Column1(13, 15)
+ Bot_SaveAcc(14) Bot_Acc(16) Bot_Acc(15) Bot_Acc(14) Bot_Acc(13) Bot_Acc(12) Bot_Acc(11) Bot_Acc(10) Bot_Acc(9) Bot_Acc(8) Bot_Acc(7) Bot_Acc(6) Bot_Acc(5) Bot_Acc(4) Bot_Acc(3) Bot_Acc(2)
+ Bot_End(16)
+}
+
+void SSE2_MultiplyTop8(word *C, const word *A, const word *B, word L)
+{
+ Top_Begin(4)
+ Top_Acc(3) Top_Acc(2) Top_Acc(1)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Top_Column0(4)
+ Top_Column1(3)
+ Mul_Column0(0, 2)
+ Top_End(2)
+}
+
+void SSE2_MultiplyTop16(word *C, const word *A, const word *B, word L)
+{
+ Top_Begin(8)
+ Top_Acc(7) Top_Acc(6) Top_Acc(5) Top_Acc(4) Top_Acc(3) Top_Acc(2) Top_Acc(1)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Top_Column0(8)
+ Top_Column1(7)
+ Mul_Column0(0, 6)
+ Mul_Column1(1, 5)
+ Mul_Column0(2, 4)
+ Mul_Column1(3, 3)
+ Mul_Column0(4, 2)
+ Top_End(4)
+}
+
+void SSE2_MultiplyTop32(word *C, const word *A, const word *B, word L)
+{
+ Top_Begin(16)
+ Top_Acc(15) Top_Acc(14) Top_Acc(13) Top_Acc(12) Top_Acc(11) Top_Acc(10) Top_Acc(9) Top_Acc(8) Top_Acc(7) Top_Acc(6) Top_Acc(5) Top_Acc(4) Top_Acc(3) Top_Acc(2) Top_Acc(1)
+#ifndef __GNUC__
+ ASJ( jmp, 0, f)
+ Mul_Acc(16) Mul_Acc(15) Mul_Acc(14) Mul_Acc(13) Mul_Acc(12) Mul_Acc(11) Mul_Acc(10) Mul_Acc(9) Mul_Acc(8) Mul_Acc(7) Mul_Acc(6) Mul_Acc(5) Mul_Acc(4) Mul_Acc(3) Mul_Acc(2)
+ AS1( ret) ASL(0)
+#endif
+ Top_Column0(16)
+ Top_Column1(15)
+ Mul_Column0(0, 14)
+ Mul_Column1(1, 13)
+ Mul_Column0(2, 12)
+ Mul_Column1(3, 11)
+ Mul_Column0(4, 10)
+ Mul_Column1(5, 9)
+ Mul_Column0(6, 8)
+ Mul_Column1(7, 7)
+ Mul_Column0(8, 6)
+ Mul_Column1(9, 5)
+ Mul_Column0(10, 4)
+ Mul_Column1(11, 3)
+ Mul_Column0(12, 2)
+ Top_End(8)
+}
+
+#endif // #if CRYPTOPP_INTEGER_SSE2
+
+// ********************************************************
+
+typedef int (CRYPTOPP_FASTCALL * PAdd)(size_t N, word *C, const word *A, const word *B);
+typedef void (* PMul)(word *C, const word *A, const word *B);
+typedef void (* PSqu)(word *C, const word *A);
+typedef void (* PMulTop)(word *C, const word *A, const word *B, word L);
+
+#if CRYPTOPP_INTEGER_SSE2
+static PAdd s_pAdd = &Baseline_Add, s_pSub = &Baseline_Sub;
+static size_t s_recursionLimit = 8;
+#else
+static const size_t s_recursionLimit = 16;
+#endif
+
+static PMul s_pMul[9], s_pBot[9];
+static PSqu s_pSqu[9];
+static PMulTop s_pTop[9];
+
+static void SetFunctionPointers()
+{
+ s_pMul[0] = &Baseline_Multiply2;
+ s_pBot[0] = &Baseline_MultiplyBottom2;
+ s_pSqu[0] = &Baseline_Square2;
+ s_pTop[0] = &Baseline_MultiplyTop2;
+ s_pTop[1] = &Baseline_MultiplyTop4;
+
+#if CRYPTOPP_INTEGER_SSE2
+ if (HasSSE2())
+ {
+#if _MSC_VER != 1200 || defined(NDEBUG)
+ if (IsP4())
+ {
+ s_pAdd = &SSE2_Add;
+ s_pSub = &SSE2_Sub;
+ }
+#endif
+
+ s_recursionLimit = 32;
+
+ s_pMul[1] = &SSE2_Multiply4;
+ s_pMul[2] = &SSE2_Multiply8;
+ s_pMul[4] = &SSE2_Multiply16;
+ s_pMul[8] = &SSE2_Multiply32;
+
+ s_pBot[1] = &SSE2_MultiplyBottom4;
+ s_pBot[2] = &SSE2_MultiplyBottom8;
+ s_pBot[4] = &SSE2_MultiplyBottom16;
+ s_pBot[8] = &SSE2_MultiplyBottom32;
+
+ s_pSqu[1] = &SSE2_Square4;
+ s_pSqu[2] = &SSE2_Square8;
+ s_pSqu[4] = &SSE2_Square16;
+ s_pSqu[8] = &SSE2_Square32;
+
+ s_pTop[2] = &SSE2_MultiplyTop8;
+ s_pTop[4] = &SSE2_MultiplyTop16;
+ s_pTop[8] = &SSE2_MultiplyTop32;
+ }
+ else
+#endif
+ {
+ s_pMul[1] = &Baseline_Multiply4;
+ s_pMul[2] = &Baseline_Multiply8;
+
+ s_pBot[1] = &Baseline_MultiplyBottom4;
+ s_pBot[2] = &Baseline_MultiplyBottom8;
+
+ s_pSqu[1] = &Baseline_Square4;
+ s_pSqu[2] = &Baseline_Square8;
+
+ s_pTop[2] = &Baseline_MultiplyTop8;
+
+#if !CRYPTOPP_INTEGER_SSE2
+ s_pMul[4] = &Baseline_Multiply16;
+ s_pBot[4] = &Baseline_MultiplyBottom16;
+ s_pSqu[4] = &Baseline_Square16;
+ s_pTop[4] = &Baseline_MultiplyTop16;
+#endif
+ }
+}
+
+inline int Add(word *C, const word *A, const word *B, size_t N)
+{
+#if CRYPTOPP_INTEGER_SSE2
+ return s_pAdd(N, C, A, B);
+#else
+ return Baseline_Add(N, C, A, B);
+#endif
+}
+
+inline int Subtract(word *C, const word *A, const word *B, size_t N)
+{
+#if CRYPTOPP_INTEGER_SSE2
+ return s_pSub(N, C, A, B);
+#else
+ return Baseline_Sub(N, C, A, B);
+#endif
+}
+
+// ********************************************************
+
+
+#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, size_t N)
+{
+ assert(N>=2 && N%2==0);
+
+ if (N <= s_recursionLimit)
+ s_pMul[N/4](R, A, B);
+ else
+ {
+ const size_t N2 = N/2;
+
+ size_t AN2 = Compare(A0, A1, N2) > 0 ? 0 : N2;
+ Subtract(R0, A + AN2, A + (N2 ^ AN2), N2);
+
+ size_t BN2 = Compare(B0, B1, N2) > 0 ? 0 : N2;
+ Subtract(R1, B + BN2, B + (N2 ^ BN2), N2);
+
+ RecursiveMultiply(R2, T2, A1, B1, N2);
+ RecursiveMultiply(T0, T2, R0, R1, N2);
+ RecursiveMultiply(R0, T2, A0, B0, N2);
+
+ // now T[01] holds (A1-A0)*(B0-B1), R[01] holds A0*B0, R[23] holds A1*B1
+
+ int c2 = Add(R2, R2, R1, N2);
+ int c3 = c2;
+ c2 += Add(R1, R2, R0, N2);
+ c3 += Add(R2, R2, R3, N2);
+
+ if (AN2 == BN2)
+ c3 -= Subtract(R1, R1, T0, N);
+ else
+ c3 += Add(R1, R1, T0, N);
+
+ c3 += Increment(R2, N2, c2);
+ assert (c3 >= 0 && c3 <= 2);
+ Increment(R3, N2, c3);
+ }
+}
+
+// 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, size_t N)
+{
+ assert(N && N%2==0);
+
+ if (N <= s_recursionLimit)
+ s_pSqu[N/4](R, A);
+ else
+ {
+ const size_t N2 = N/2;
+
+ RecursiveSquare(R0, T2, A0, N2);
+ RecursiveSquare(R2, T2, A1, N2);
+ RecursiveMultiply(T0, T2, A0, A1, N2);
+
+ int carry = Add(R1, R1, T0, N);
+ carry += Add(R1, R1, T0, N);
+ Increment(R3, N2, carry);
+ }
+}
+
+// R[N] - bottom half of A*B
+// T[3*N/2] - temporary work space
+// A[N] - multiplier
+// B[N] - multiplicant
+
+void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, size_t N)
+{
+ assert(N>=2 && N%2==0);
+
+ if (N <= s_recursionLimit)
+ s_pBot[N/4](R, A, B);
+ else
+ {
+ const size_t N2 = N/2;
+
+ RecursiveMultiply(R, T, A0, B0, N2);
+ RecursiveMultiplyBottom(T0, T1, A1, B0, N2);
+ Add(R1, R1, T0, N2);
+ RecursiveMultiplyBottom(T0, T1, A0, B1, N2);
+ 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 MultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, size_t N)
+{
+ assert(N>=2 && N%2==0);
+
+ if (N <= s_recursionLimit)
+ s_pTop[N/4](R, A, B, L[N-1]);
+ else
+ {
+ const size_t N2 = N/2;
+
+ size_t AN2 = Compare(A0, A1, N2) > 0 ? 0 : N2;
+ Subtract(R0, A + AN2, A + (N2 ^ AN2), N2);
+
+ size_t BN2 = Compare(B0, B1, N2) > 0 ? 0 : N2;
+ Subtract(R1, B + BN2, B + (N2 ^ BN2), N2);
+
+ RecursiveMultiply(T0, T2, R0, R1, N2);
+ RecursiveMultiply(R0, T2, A1, B1, N2);
+
+ // now T[01] holds (A1-A0)*(B0-B1) = A1*B0+A0*B1-A1*B1-A0*B0, R[01] holds A1*B1
+
+ int t, c3;
+ int c2 = Subtract(T2, L+N2, L, N2);
+
+ if (AN2 == BN2)
+ {
+ c2 -= Add(T2, T2, T0, N2);
+ t = (Compare(T2, R0, N2) == -1);
+ c3 = t - Subtract(T2, T2, T1, N2);
+ }
+ else
+ {
+ c2 += Subtract(T2, T2, T0, N2);
+ t = (Compare(T2, R0, N2) == -1);
+ c3 = t + Add(T2, T2, T1, N2);
+ }
+
+ c2 += t;
+ if (c2 >= 0)
+ c3 += Increment(T2, N2, c2);
+ else
+ c3 -= Decrement(T2, N2, -c2);
+ c3 += Add(R0, T2, R1, N2);
+
+ assert (c3 >= 0 && c3 <= 2);
+ Increment(R1, N2, c3);
+ }
+}
+
+inline void Multiply(word *R, word *T, const word *A, const word *B, size_t N)
+{
+ RecursiveMultiply(R, T, A, B, N);
+}
+
+inline void Square(word *R, word *T, const word *A, size_t N)
+{
+ RecursiveSquare(R, T, A, N);
+}
+
+inline void MultiplyBottom(word *R, word *T, const word *A, const word *B, size_t N)
+{
+ RecursiveMultiplyBottom(R, T, A, B, N);
+}
+
+// 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, size_t NA, const word *B, size_t 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);
+
+ 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;
+ }
+ }
+
+ size_t i;
+ if ((NB/NA)%2 == 0)
+ {
+ Multiply(R, T, A, B, NA);
+ CopyWords(T+2*NA, R+NA, NA);
+
+ 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);
+ }
+ else
+ {
+ for (i=0; i<NB; i+=2*NA)
+ Multiply(R+i, T, A, B+i, NA);
+ for (i=NA; i<NB; i+=2*NA)
+ Multiply(T+NA+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, size_t N)
+{
+ if (N==2)
+ {
+ T[0] = AtomicInverseModPower2(A[0]);
+ T[1] = 0;
+ s_pBot[0](T+2, T, A);
+ TwosComplement(T+2, 2);
+ Increment(T+2, 2, 2);
+ s_pBot[0](R, T, T+2);
+ }
+ else
+ {
+ const size_t 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, word *X, const word *M, const word *U, size_t N)
+{
+#if 1
+ 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 + ((0-borrow) & N), N);
+#elif 0
+ const word u = 0-U[0];
+ Declare2Words(p)
+ for (size_t i=0; i<N; i++)
+ {
+ const word t = u * X[i];
+ word c = 0;
+ for (size_t j=0; j<N; j+=2)
+ {
+ MultiplyWords(p, t, M[j]);
+ Acc2WordsBy1(p, X[i+j]);
+ Acc2WordsBy1(p, c);
+ X[i+j] = LowWord(p);
+ c = HighWord(p);
+ MultiplyWords(p, t, M[j+1]);
+ Acc2WordsBy1(p, X[i+j+1]);
+ Acc2WordsBy1(p, c);
+ X[i+j+1] = LowWord(p);
+ c = HighWord(p);
+ }
+
+ if (Increment(X+N+i, N-i, c))
+ while (!Subtract(X+N, X+N, M, N)) {}
+ }
+
+ memcpy(R, X+N, N*WORD_SIZE);
+#else
+ __m64 u = _mm_cvtsi32_si64(0-U[0]), p;
+ for (size_t i=0; i<N; i++)
+ {
+ __m64 t = _mm_cvtsi32_si64(X[i]);
+ t = _mm_mul_su32(t, u);
+ __m64 c = _mm_setzero_si64();
+ for (size_t j=0; j<N; j+=2)
+ {
+ p = _mm_mul_su32(t, _mm_cvtsi32_si64(M[j]));
+ p = _mm_add_si64(p, _mm_cvtsi32_si64(X[i+j]));
+ c = _mm_add_si64(c, p);
+ X[i+j] = _mm_cvtsi64_si32(c);
+ c = _mm_srli_si64(c, 32);
+ p = _mm_mul_su32(t, _mm_cvtsi32_si64(M[j+1]));
+ p = _mm_add_si64(p, _mm_cvtsi32_si64(X[i+j+1]));
+ c = _mm_add_si64(c, p);
+ X[i+j+1] = _mm_cvtsi64_si32(c);
+ c = _mm_srli_si64(c, 32);
+ }
+
+ if (Increment(X+N+i, N-i, _mm_cvtsi64_si32(c)))
+ while (!Subtract(X+N, X+N, M, N)) {}
+ }
+
+ memcpy(R, X+N, N*WORD_SIZE);
+ _mm_empty();
+#endif
+}
+
+// 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, size_t 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 size_t 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];
+ s_pMul[0](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, size_t N)
+{
+ assert(N && N%2==0);
+
+ AsymmetricMultiply(T, T+N+2, Q, 2, B, N);
+
+ 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+3*(NB+2)] - temp work space
+// A[NA] -------- dividend
+// B[NB] -------- divisor
+
+void Divide(word *R, word *Q, word *T, const word *A, size_t NA, const word *B, size_t 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 (size_t 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 size_t EvenWordCount(const word *X, size_t 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, size_t NA, const word *M, size_t 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;
+ size_t 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, size_t k, const word *M, size_t 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, size_t k, const word *M, size_t N)
+{
+ CopyWords(R, A, N);
+
+ while (k--)
+ if (ShiftWordsLeftByBits(R, N, 1) || Compare(R, M, N)>=0)
+ Subtract(R, R, M, N);
+}
+
+// ******************************************************************
+
+InitializeInteger::InitializeInteger()
+{
+ if (!g_pAssignIntToInteger)
+ {
+ SetFunctionPointers();
+ g_pAssignIntToInteger = AssignIntToInteger;
+ }
+}
+
+static const unsigned int RoundupSizeTable[] = {2, 2, 2, 4, 4, 8, 8, 8, 8};
+
+static inline size_t RoundupSize(size_t 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 size_t(1) << 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 = (unsigned long)reg[0];
+ value += SafeLeftShift<WORD_BITS, unsigned long>((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 = (unsigned long)reg[0];
+ value += SafeLeftShift<WORD_BITS, unsigned long>((unsigned long)reg[1]);
+ return sign==POSITIVE ? value : -(signed long)value;
+}
+
+Integer::Integer(BufferedTransformation &encodedInteger, size_t byteCount, Signedness s)
+{
+ Decode(encodedInteger, byteCount, s);
+}
+
+Integer::Integer(const byte *encodedInteger, size_t byteCount, Signedness s)
+{
+ Decode(encodedInteger, byteCount, s);
+}
+
+Integer::Integer(BufferedTransformation &bt)
+{
+ BERDecode(bt);
+}
+
+Integer::Integer(RandomNumberGenerator &rng, size_t 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(size_t 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)
+ {
+ if (reg.size() != t.reg.size() || t.reg[t.reg.size()/2] == 0)
+ reg.New(RoundupSize(t.WordCount()));
+ CopyWords(reg, t.reg, reg.size());
+ sign = t.sign;
+ }
+ return *this;
+}
+
+bool Integer::GetBit(size_t n) const
+{
+ if (n/WORD_BITS >= reg.size())
+ return 0;
+ else
+ return bool((reg[n/WORD_BITS] >> (n % WORD_BITS)) & 1);
+}
+
+void Integer::SetBit(size_t 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(size_t n) const
+{
+ if (n/WORD_SIZE >= reg.size())
+ return 0;
+ else
+ return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
+}
+
+void Integer::SetByte(size_t 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));
+}
+
+lword Integer::GetBits(size_t i, size_t n) const
+{
+ lword v = 0;
+ assert(n <= sizeof(v)*8);
+ for (unsigned int j=0; j<n; j++)
+ v |= lword(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, size_t 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)
+{
+ int radix;
+ // GCC workaround
+ // 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++)
+ {
+ int 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 (unsigned int)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, size_t inputLen, Signedness s)
+{
+ StringStore store(input, inputLen);
+ Decode(store, inputLen, s);
+}
+
+void Integer::Decode(BufferedTransformation &bt, size_t 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 (size_t i=inputLen; i > 0; i--)
+ {
+ bt.Get(b);
+ reg[(i-1)/WORD_SIZE] |= word(b) << ((i-1)%WORD_SIZE)*8;
+ }
+
+ if (sign == NEGATIVE)
+ {
+ for (size_t i=inputLen; i<reg.size()*WORD_SIZE; i++)
+ reg[i/WORD_SIZE] |= word(0xff) << (i%WORD_SIZE)*8;
+ TwosComplement(reg, reg.size());
+ }
+}
+
+size_t 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;
+}
+
+void Integer::Encode(byte *output, size_t outputLen, Signedness signedness) const
+{
+ ArraySink sink(output, outputLen);
+ Encode(sink, outputLen, signedness);
+}
+
+void Integer::Encode(BufferedTransformation &bt, size_t outputLen, Signedness signedness) const
+{
+ if (signedness == UNSIGNED || NotNegative())
+ {
+ for (size_t i=outputLen; i > 0; i--)
+ bt.Put(GetByte(i-1));
+ }
+ else
+ {
+ // take two's complement of *this
+ Integer temp = Integer::Power2(8*STDMAX((size_t)ByteCount(), outputLen)) + *this;
+ temp.Encode(bt, outputLen, UNSIGNED);
+ }
+}
+
+void Integer::DEREncode(BufferedTransformation &bt) const
+{
+ DERGeneralEncoder enc(bt, INTEGER);
+ Encode(enc, MinEncodedSize(SIGNED), SIGNED);
+ enc.MessageEnd();
+}
+
+void Integer::BERDecode(const byte *input, size_t 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, (size_t)dec.RemainingLength(), SIGNED);
+ dec.MessageEnd();
+}
+
+void Integer::DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const
+{
+ DERGeneralEncoder enc(bt, OCTET_STRING);
+ Encode(enc, length);
+ enc.MessageEnd();
+}
+
+void Integer::BERDecodeAsOctetString(BufferedTransformation &bt, size_t length)
+{
+ BERGeneralDecoder dec(bt, OCTET_STRING);
+ if (!dec.IsDefiniteLength() || dec.RemainingLength() != length)
+ BERDecodeError();
+ Decode(dec, length);
+ dec.MessageEnd();
+}
+
+size_t Integer::OpenPGPEncode(byte *output, size_t len) const
+{
+ ArraySink sink(output, len);
+ return OpenPGPEncode(sink);
+}
+
+size_t Integer::OpenPGPEncode(BufferedTransformation &bt) const
+{
+ word16 bitCount = BitCount();
+ bt.PutWord16(bitCount);
+ size_t byteCount = BitsToBytes(bitCount);
+ Encode(bt, byteCount);
+ return 2 + byteCount;
+}
+
+void Integer::OpenPGPDecode(const byte *input, size_t 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, size_t nbits)
+{
+ const size_t 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, size_t seedSize)
+ : m_counter(0), m_counterAndSeed(seedSize + 4)
+ {
+ memcpy(m_counterAndSeed + 4, seed, seedSize);
+ }
+
+ void GenerateBlock(byte *output, size_t size)
+ {
+ PutWord(false, 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 ¶ms)
+{
+ 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((size_t)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)
+{
+ int 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;
+ }
+}
+
+// MSVC .NET 2003 workaround
+template <class T> inline const T& STDMAX2(const T& a, const T& b)
+{
+ return a < b ? b : a;
+}
+
+Integer Integer::Plus(const Integer& b) const
+{
+ Integer sum((word)0, STDMAX2(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, STDMAX2(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<<=(size_t n)
+{
+ const size_t wordCount = WordCount();
+ const size_t shiftWords = n / WORD_BITS;
+ const unsigned int shiftBits = (unsigned int)(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>>=(size_t n)
+{
+ const size_t wordCount = WordCount();
+ const size_t shiftWords = n / WORD_BITS;
+ const unsigned int shiftBits = (unsigned int)(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)
+{
+ size_t aSize = RoundupSize(a.WordCount());
+ size_t bSize = RoundupSize(b.WordCount());
+
+ product.reg.CleanNew(RoundupSize(aSize+bSize));
+ product.sign = Integer::POSITIVE;
+
+ IntegerSecBlock 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 "ient,
+ const Integer ÷nd, 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 "ient,
+ 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;
+
+ IntegerSecBlock T(aSize+3*(bSize+2));
+ Divide(remainder.reg, quotient.reg, T, a.reg, aSize, b.reg, bSize);
+}
+
+void Integer::Divide(Integer &remainder, Integer "ient, const Integer ÷nd, 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 size_t 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] %= (word(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 "ient, const Integer ÷nd, 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(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();
+ m_modulus.BERDecode(seq);
+ seq.MessageEnd();
+ m_result.reg.resize(m_modulus.reg.size());
+}
+
+void ModularArithmetic::DEREncode(BufferedTransformation &bt) const
+{
+ DERSequenceEncoder seq(bt);
+ ASN1::prime_field().DEREncode(seq);
+ m_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()==m_modulus.reg.size())
+ {
+ CryptoPP::DivideByPower2Mod(m_result.reg.begin(), a.reg, 1, m_modulus.reg, a.reg.size());
+ return m_result;
+ }
+ else
+ return m_result1 = (a.IsEven() ? (a >> 1) : ((a+m_modulus) >> 1));
+}
+
+const Integer& ModularArithmetic::Add(const Integer &a, const Integer &b) const
+{
+ if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
+ {
+ if (CryptoPP::Add(m_result.reg.begin(), a.reg, b.reg, a.reg.size())
+ || Compare(m_result.reg, m_modulus.reg, a.reg.size()) >= 0)
+ {
+ CryptoPP::Subtract(m_result.reg.begin(), m_result.reg, m_modulus.reg, a.reg.size());
+ }
+ return m_result;
+ }
+ else
+ {
+ m_result1 = a+b;
+ if (m_result1 >= m_modulus)
+ m_result1 -= m_modulus;
+ return m_result1;
+ }
+}
+
+Integer& ModularArithmetic::Accumulate(Integer &a, const Integer &b) const
+{
+ if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
+ {
+ if (CryptoPP::Add(a.reg, a.reg, b.reg, a.reg.size())
+ || Compare(a.reg, m_modulus.reg, a.reg.size()) >= 0)
+ {
+ CryptoPP::Subtract(a.reg, a.reg, m_modulus.reg, a.reg.size());
+ }
+ }
+ else
+ {
+ a+=b;
+ if (a>=m_modulus)
+ a-=m_modulus;
+ }
+
+ return a;
+}
+
+const Integer& ModularArithmetic::Subtract(const Integer &a, const Integer &b) const
+{
+ if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
+ {
+ if (CryptoPP::Subtract(m_result.reg.begin(), a.reg, b.reg, a.reg.size()))
+ CryptoPP::Add(m_result.reg.begin(), m_result.reg, m_modulus.reg, a.reg.size());
+ return m_result;
+ }
+ else
+ {
+ m_result1 = a-b;
+ if (m_result1.IsNegative())
+ m_result1 += m_modulus;
+ return m_result1;
+ }
+}
+
+Integer& ModularArithmetic::Reduce(Integer &a, const Integer &b) const
+{
+ if (a.reg.size()==m_modulus.reg.size() && b.reg.size()==m_modulus.reg.size())
+ {
+ if (CryptoPP::Subtract(a.reg, a.reg, b.reg, a.reg.size()))
+ CryptoPP::Add(a.reg, a.reg, m_modulus.reg, a.reg.size());
+ }
+ else
+ {
+ a-=b;
+ if (a.IsNegative())
+ a+=m_modulus;
+ }
+
+ return a;
+}
+
+const Integer& ModularArithmetic::Inverse(const Integer &a) const
+{
+ if (!a)
+ return a;
+
+ CopyWords(m_result.reg.begin(), m_modulus.reg, m_modulus.reg.size());
+ if (CryptoPP::Subtract(m_result.reg.begin(), m_result.reg, a.reg, a.reg.size()))
+ Decrement(m_result.reg.begin()+a.reg.size(), m_modulus.reg.size()-a.reg.size());
+
+ return m_result;
+}
+
+Integer ModularArithmetic::CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
+{
+ if (m_modulus.IsOdd())
+ {
+ MontgomeryRepresentation dr(m_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 (m_modulus.IsOdd())
+ {
+ MontgomeryRepresentation dr(m_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),
+ m_u((word)0, m_modulus.reg.size()),
+ m_workspace(5*m_modulus.reg.size())
+{
+ if (!m_modulus.IsOdd())
+ throw InvalidArgument("MontgomeryRepresentation: Montgomery representation requires an odd modulus");
+
+ RecursiveInverseModPower2(m_u.reg, m_workspace, m_modulus.reg, m_modulus.reg.size());
+}
+
+const Integer& MontgomeryRepresentation::Multiply(const Integer &a, const Integer &b) const
+{
+ word *const T = m_workspace.begin();
+ word *const R = m_result.reg.begin();
+ const size_t N = m_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, m_modulus.reg, m_u.reg, N);
+ return m_result;
+}
+
+const Integer& MontgomeryRepresentation::Square(const Integer &a) const
+{
+ word *const T = m_workspace.begin();
+ word *const R = m_result.reg.begin();
+ const size_t N = m_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, m_modulus.reg, m_u.reg, N);
+ return m_result;
+}
+
+Integer MontgomeryRepresentation::ConvertOut(const Integer &a) const
+{
+ word *const T = m_workspace.begin();
+ word *const R = m_result.reg.begin();
+ const size_t N = m_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, m_modulus.reg, m_u.reg, N);
+ return m_result;
+}
+
+const Integer& MontgomeryRepresentation::MultiplicativeInverse(const Integer &a) const
+{
+// return (EuclideanMultiplicativeInverse(a, modulus)<<(2*WORD_BITS*modulus.reg.size()))%modulus;
+ word *const T = m_workspace.begin();
+ word *const R = m_result.reg.begin();
+ const size_t N = m_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, m_modulus.reg, m_u.reg, N);
+ unsigned k = AlmostInverse(R, T, R, N, m_modulus.reg, N);
+
+// cout << "k=" << k << " N*32=" << 32*N << endl;
+
+ if (k>N*WORD_BITS)
+ DivideByPower2Mod(R, R, k-N*WORD_BITS, m_modulus.reg, N);
+ else
+ MultiplyByPower2Mod(R, R, N*WORD_BITS-k, m_modulus.reg, N);
+
+ return m_result;
+}
+
+NAMESPACE_END
+
+#endif
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