diff -r f18401adf8e1 -r 641f389e9157 crypto/weakcrypto/source/bigint/algorithms.cpp
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/crypto/weakcrypto/source/bigint/algorithms.cpp	Tue Aug 31 17:00:08 2010 +0300
@@ -0,0 +1,1160 @@
+/*
+* Copyright (c) 2003-2009 Nokia Corporation and/or its subsidiary(-ies).
+* All rights reserved.
+* This component and the accompanying materials are made available
+* under the terms of the License "Eclipse Public License v1.0"
+* which accompanies this distribution, and is available
+* at the URL "http://www.eclipse.org/legal/epl-v10.html".
+*
+* Initial Contributors:
+* Nokia Corporation - initial contribution.
+*
+* Contributors:
+*
+* Description: 
+*
+*/
+
+
+#include "words.h"
+#include "algorithms.h"
+
+word Add(word *C, const word *A, const word *B, unsigned int N)
+{
+	assert (N%2 == 0);
+	word carry = 0;
+	for (unsigned int i = 0; i < N; i+=2)
+	{
+		dword u = (dword) carry + A[i] + B[i];
+		C[i] = LOW_WORD(u);
+		u = (dword) HIGH_WORD(u) + A[i+1] + B[i+1];
+		C[i+1] = LOW_WORD(u);
+		carry = HIGH_WORD(u);
+	}
+	return carry;
+}
+
+word Subtract(word *C, const word *A, const word *B, unsigned int N)
+{
+	assert (N%2 == 0);
+	word borrow=0;
+	for (unsigned i = 0; i < N; i+=2)
+	{
+		dword u = (dword) A[i] - B[i] - borrow;
+		C[i] = LOW_WORD(u);
+		u = (dword) A[i+1] - B[i+1] - (word)(0-HIGH_WORD(u));
+		C[i+1] = LOW_WORD(u);
+		borrow = 0-HIGH_WORD(u);
+	}
+	return borrow;
+}
+
+int Compare(const word *A, const word *B, unsigned int N)
+{
+	while (N--)
+		if (A[N] > B[N])
+			return 1;
+		else if (A[N] < B[N])
+			return -1;
+
+	return 0;
+}
+
+// It is the job of the calling code to ensure that this won't carry.
+// If you aren't sure, use the next version that will tell you if you need to
+// grow your integer.
+// Having two of these creates ever so slightly more code but avoids having
+// ifdefs all over the rest of the code checking the following type stuff which
+// causes warnings in certain compilers about unused parameters in release
+// builds.  We can't have that can we!
+/*
+Allows avoid this all over bigint.cpp and primes.cpp
+ifdef _DEBUG
+	TUint carry = Increment(Ptr(), Size());
+	assert(!carry);
+else
+	Increment(Ptr(), Size())
+endif
+*/
+void IncrementNoCarry(word *A, unsigned int N, word B)
+{
+	assert(N);
+	word t = A[0];
+	A[0] = t+B;
+	if (A[0] >= t)
+		return;
+	for (unsigned i=1; i<N; i++)
+		if (++A[i])
+			return;
+	assert(0);
+}
+
+word Increment(word *A, unsigned int N, word B)
+{
+	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;
+}
+
+//See commments above about IncrementNoCarry
+void DecrementNoCarry(word *A, unsigned int N, word B)
+{
+	assert(N);
+	word t = A[0];
+	A[0] = t-B;
+	if (A[0] <= t)
+		return;
+	for (unsigned i=1; i<N; i++)
+		if (A[i]--)
+			return;
+	assert(0);
+}
+
+word Decrement(word *A, unsigned int N, word B)
+{
+	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;
+}
+
+void TwosComplement(word *A, unsigned int N)
+{
+	Decrement(A, N);
+	for (unsigned i=0; i<N; i++)
+		A[i] = ~A[i];
+}
+
+static word LinearMultiply(word *C, const word *A, word B, unsigned int N)
+{
+	word carry=0;
+	for(unsigned i=0; i<N; i++)
+	{
+		dword p = (dword)A[i] * B + carry;
+		C[i] = LOW_WORD(p);
+		carry = HIGH_WORD(p);
+	}
+	return carry;
+}
+
+static void AtomicMultiply(word *C, const word *A, const word *B)
+{
+/*
+	word s;
+	dword d;
+
+	if (A1 >= A0)
+		if (B0 >= B1)
+		{
+			s = 0;
+			d = (dword)(A1-A0)*(B0-B1);
+		}
+		else
+		{
+			s = (A1-A0);
+			d = (dword)s*(word)(B0-B1);
+		}
+	else
+		if (B0 > B1)
+		{
+			s = (B0-B1);
+			d = (word)(A1-A0)*(dword)s;
+		}
+		else
+		{
+			s = 0;
+			d = (dword)(A0-A1)*(B1-B0);
+		}
+*/
+	// this segment is the branchless equivalent of above
+	word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
+	unsigned int ai = A[1] < A[0];
+	unsigned int bi = B[0] < B[1];
+	unsigned int di = ai & bi;
+	dword d = (dword)D[di]*D[di+2];
+	D[1] = D[3] = 0;
+	unsigned int si = ai + !bi;
+	word s = D[si];
+
+	dword A0B0 = (dword)A[0]*B[0];
+	C[0] = LOW_WORD(A0B0);
+
+	dword A1B1 = (dword)A[1]*B[1];
+	dword t = (dword) HIGH_WORD(A0B0) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1);
+	C[1] = LOW_WORD(t);
+
+	t = A1B1 + HIGH_WORD(t) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s;
+	C[2] = LOW_WORD(t);
+	C[3] = HIGH_WORD(t);
+}
+
+static word AtomicMultiplyAdd(word *C, const word *A, const word *B)
+{
+	word D[4] = {A[1]-A[0], A[0]-A[1], B[0]-B[1], B[1]-B[0]};
+	unsigned int ai = A[1] < A[0];
+	unsigned int bi = B[0] < B[1];
+	unsigned int di = ai & bi;
+	dword d = (dword)D[di]*D[di+2];
+	D[1] = D[3] = 0;
+	unsigned int si = ai + !bi;
+	word s = D[si];
+
+	dword A0B0 = (dword)A[0]*B[0];
+	dword t = A0B0 + C[0];
+	C[0] = LOW_WORD(t);
+
+	dword A1B1 = (dword)A[1]*B[1];
+	t = (dword) HIGH_WORD(t) + LOW_WORD(A0B0) + LOW_WORD(d) + LOW_WORD(A1B1) + C[1];
+	C[1] = LOW_WORD(t);
+
+	t = (dword) HIGH_WORD(t) + LOW_WORD(A1B1) + HIGH_WORD(A0B0) + HIGH_WORD(d) + HIGH_WORD(A1B1) - s + C[2];
+	C[2] = LOW_WORD(t);
+
+	t = (dword) HIGH_WORD(t) + HIGH_WORD(A1B1) + C[3];
+	C[3] = LOW_WORD(t);
+	return HIGH_WORD(t);
+}
+
+static inline void AtomicMultiplyBottom(word *C, const word *A, const word *B)
+{
+	dword t = (dword)A[0]*B[0];
+	C[0] = LOW_WORD(t);
+	C[1] = HIGH_WORD(t) + A[0]*B[1] + A[1]*B[0];
+}
+
+#define MulAcc(x, y)								\
+	p = (dword)A[x] * B[y] + c; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)d + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e += HIGH_WORD(p);
+
+#define SaveMulAcc(s, x, y) 						\
+	R[s] = c;										\
+	p = (dword)A[x] * B[y] + d; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)e + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e = HIGH_WORD(p);
+
+#define MulAcc1(x, y)								\
+	p = (dword)A[x] * A[y] + c; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)d + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e += HIGH_WORD(p);
+
+#define SaveMulAcc1(s, x, y) 						\
+	R[s] = c;										\
+	p = (dword)A[x] * A[y] + d; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)e + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e = HIGH_WORD(p);
+
+#define SquAcc(x, y)								\
+	p = (dword)A[x] * A[y];	\
+	p = p + p + c; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)d + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e += HIGH_WORD(p);
+
+#define SaveSquAcc(s, x, y) 						\
+	R[s] = c;										\
+	p = (dword)A[x] * A[y];	\
+	p = p + p + d; 					\
+	c = LOW_WORD(p);								\
+	p = (dword)e + HIGH_WORD(p);					\
+	d = LOW_WORD(p);								\
+	e = HIGH_WORD(p);
+
+// VC60 workaround: MSVC 6.0 has an optimization problem that makes
+// (dword)A*B where either A or B has been cast to a dword before
+// very expensive. Revisit a CombaSquare4() function when this
+// problem is fixed.               
+
+// WARNING: KeithR.  05/08/03 This routine doesn't work with gcc on hardware
+// either.  I've completely removed it.  It may be worth looking into sometime
+// in the future.
+/*#ifndef __WINS__
+static void CombaSquare4(word *R, const word *A)
+{
+	dword p;
+	word c, d, e;
+
+	p = (dword)A[0] * A[0];
+	R[0] = LOW_WORD(p);
+	c = HIGH_WORD(p);
+	d = e = 0;
+
+	SquAcc(0, 1);
+
+	SaveSquAcc(1, 2, 0);
+	MulAcc1(1, 1);
+
+	SaveSquAcc(2, 0, 3);
+	SquAcc(1, 2);
+
+	SaveSquAcc(3, 3, 1);
+	MulAcc1(2, 2);
+
+	SaveSquAcc(4, 2, 3);
+
+	R[5] = c;
+	p = (dword)A[3] * A[3] + d;
+	R[6] = LOW_WORD(p);
+	R[7] = e + HIGH_WORD(p);
+}
+#endif */
+
+static void CombaMultiply4(word *R, const word *A, const word *B)
+{
+	dword p;
+	word c, d, e;
+
+	p = (dword)A[0] * B[0];
+	R[0] = LOW_WORD(p);
+	c = HIGH_WORD(p);
+	d = e = 0;
+
+	MulAcc(0, 1);
+	MulAcc(1, 0);
+
+	SaveMulAcc(1, 2, 0);
+	MulAcc(1, 1);
+	MulAcc(0, 2);
+
+	SaveMulAcc(2, 0, 3);
+	MulAcc(1, 2);
+	MulAcc(2, 1);
+	MulAcc(3, 0);
+
+	SaveMulAcc(3, 3, 1);
+	MulAcc(2, 2);
+	MulAcc(1, 3);
+
+	SaveMulAcc(4, 2, 3);
+	MulAcc(3, 2);
+
+	R[5] = c;
+	p = (dword)A[3] * B[3] + d;
+	R[6] = LOW_WORD(p);
+	R[7] = e + HIGH_WORD(p);
+}
+
+static void CombaMultiply8(word *R, const word *A, const word *B)
+{
+	dword p;
+	word c, d, e;
+
+	p = (dword)A[0] * B[0];
+	R[0] = LOW_WORD(p);
+	c = HIGH_WORD(p);
+	d = e = 0;
+
+	MulAcc(0, 1);
+	MulAcc(1, 0);
+
+	SaveMulAcc(1, 2, 0);
+	MulAcc(1, 1);
+	MulAcc(0, 2);
+
+	SaveMulAcc(2, 0, 3);
+	MulAcc(1, 2);
+	MulAcc(2, 1);
+	MulAcc(3, 0);
+
+	SaveMulAcc(3, 0, 4);
+	MulAcc(1, 3);
+	MulAcc(2, 2);
+	MulAcc(3, 1);
+	MulAcc(4, 0);
+
+	SaveMulAcc(4, 0, 5);
+	MulAcc(1, 4);
+	MulAcc(2, 3);
+	MulAcc(3, 2);
+	MulAcc(4, 1);
+	MulAcc(5, 0);
+
+	SaveMulAcc(5, 0, 6);
+	MulAcc(1, 5);
+	MulAcc(2, 4);
+	MulAcc(3, 3);
+	MulAcc(4, 2);
+	MulAcc(5, 1);
+	MulAcc(6, 0);
+
+	SaveMulAcc(6, 0, 7);
+	MulAcc(1, 6);
+	MulAcc(2, 5);
+	MulAcc(3, 4);
+	MulAcc(4, 3);
+	MulAcc(5, 2);
+	MulAcc(6, 1);
+	MulAcc(7, 0);
+
+	SaveMulAcc(7, 1, 7);
+	MulAcc(2, 6);
+	MulAcc(3, 5);
+	MulAcc(4, 4);
+	MulAcc(5, 3);
+	MulAcc(6, 2);
+	MulAcc(7, 1);
+
+	SaveMulAcc(8, 2, 7);
+	MulAcc(3, 6);
+	MulAcc(4, 5);
+	MulAcc(5, 4);
+	MulAcc(6, 3);
+	MulAcc(7, 2);
+
+	SaveMulAcc(9, 3, 7);
+	MulAcc(4, 6);
+	MulAcc(5, 5);
+	MulAcc(6, 4);
+	MulAcc(7, 3);
+
+	SaveMulAcc(10, 4, 7);
+	MulAcc(5, 6);
+	MulAcc(6, 5);
+	MulAcc(7, 4);
+
+	SaveMulAcc(11, 5, 7);
+	MulAcc(6, 6);
+	MulAcc(7, 5);
+
+	SaveMulAcc(12, 6, 7);
+	MulAcc(7, 6);
+
+	R[13] = c;
+	p = (dword)A[7] * B[7] + d;
+	R[14] = LOW_WORD(p);
+	R[15] = e + HIGH_WORD(p);
+}
+
+static void CombaMultiplyBottom4(word *R, const word *A, const word *B)
+{
+	dword p;
+	word c, d, e;
+
+	p = (dword)A[0] * B[0];
+	R[0] = LOW_WORD(p);
+	c = HIGH_WORD(p);
+	d = e = 0;
+
+	MulAcc(0, 1);
+	MulAcc(1, 0);
+
+	SaveMulAcc(1, 2, 0);
+	MulAcc(1, 1);
+	MulAcc(0, 2);
+
+	R[2] = c;
+	R[3] = d + A[0] * B[3] + A[1] * B[2] + A[2] * B[1] + A[3] * B[0];
+}
+
+static void CombaMultiplyBottom8(word *R, const word *A, const word *B)
+{
+	dword p;
+	word c, d, e;
+
+	p = (dword)A[0] * B[0];
+	R[0] = LOW_WORD(p);
+	c = HIGH_WORD(p);
+	d = e = 0;
+
+	MulAcc(0, 1);
+	MulAcc(1, 0);
+
+	SaveMulAcc(1, 2, 0);
+	MulAcc(1, 1);
+	MulAcc(0, 2);
+
+	SaveMulAcc(2, 0, 3);
+	MulAcc(1, 2);
+	MulAcc(2, 1);
+	MulAcc(3, 0);
+
+	SaveMulAcc(3, 0, 4);
+	MulAcc(1, 3);
+	MulAcc(2, 2);
+	MulAcc(3, 1);
+	MulAcc(4, 0);
+
+	SaveMulAcc(4, 0, 5);
+	MulAcc(1, 4);
+	MulAcc(2, 3);
+	MulAcc(3, 2);
+	MulAcc(4, 1);
+	MulAcc(5, 0);
+
+	SaveMulAcc(5, 0, 6);
+	MulAcc(1, 5);
+	MulAcc(2, 4);
+	MulAcc(3, 3);
+	MulAcc(4, 2);
+	MulAcc(5, 1);
+	MulAcc(6, 0);
+
+	R[6] = c;
+	R[7] = d + A[0] * B[7] + A[1] * B[6] + A[2] * B[5] + A[3] * B[4] +
+				A[4] * B[3] + A[5] * B[2] + A[6] * B[1] + A[7] * B[0];
+}
+
+#undef MulAcc
+#undef SaveMulAcc
+static void AtomicInverseModPower2(word *C, word A0, word A1)
+{
+	assert(A0%2==1);
+
+	dword A=MAKE_DWORD(A0, A1), R=A0%8;
+
+	for (unsigned i=3; i<2*WORD_BITS; i*=2)
+		R = R*(2-R*A);
+
+	assert(R*A==1);
+
+	C[0] = LOW_WORD(R);
+	C[1] = HIGH_WORD(R);
+}
+// ********************************************************
+
+#define A0		A
+#define A1		(A+N2)
+#define B0		B
+#define B1		(B+N2)
+
+#define T0		T
+#define T1		(T+N2)
+#define T2		(T+N)
+#define T3		(T+N+N2)
+
+#define R0		R
+#define R1		(R+N2)
+#define R2		(R+N)
+#define R3		(R+N+N2)
+
+// R[2*N] - result = A*B
+// T[2*N] - temporary work space
+// A[N] --- multiplier
+// B[N] --- multiplicant
+
+void RecursiveMultiply(word *R, word *T, const word *A, const word *B, unsigned int N)
+{
+	assert(N>=2 && N%2==0);
+
+	if (N==2)
+		AtomicMultiply(R, A, B);
+	else if (N==4)
+		CombaMultiply4(R, A, B);
+	else if (N==8)
+		CombaMultiply8(R, A, B);
+	else
+	{
+		const unsigned int N2 = N/2;
+		int carry;
+
+		int aComp = Compare(A0, A1, N2);
+		int bComp = Compare(B0, B1, N2);
+
+		switch (2*aComp + aComp + bComp)
+		{
+		case -4:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			Subtract(T1, T1, R0, N2);
+			carry = -1;
+			break;
+		case -2:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			carry = 0;
+			break;
+		case 2:
+			Subtract(R0, A0, A1, N2);
+			Subtract(R1, B1, B0, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			carry = 0;
+			break;
+		case 4:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			Subtract(T1, T1, R1, N2);
+			carry = -1;
+			break;
+		default:
+			SetWords(T0, 0, N);
+			carry = 0;
+		}
+
+		RecursiveMultiply(R0, T2, A0, B0, N2);
+		RecursiveMultiply(R2, T2, A1, B1, N2);
+
+		// now T[01] holds (A1-A0)*(B0-B1), R[01] holds A0*B0, R[23] holds A1*B1
+
+		carry += Add(T0, T0, R0, N);
+		carry += Add(T0, T0, R2, N);
+		carry += Add(R1, R1, T0, N);
+
+		assert (carry >= 0 && carry <= 2);
+		Increment(R3, N2, carry);
+	}
+}
+
+// R[2*N] - result = A*A
+// T[2*N] - temporary work space
+// A[N] --- number to be squared
+
+void RecursiveSquare(word *R, word *T, const word *A, unsigned int N)
+{
+	assert(N && N%2==0);
+
+	if (N==2)
+		AtomicMultiply(R, A, A);
+	else if (N==4)
+	{
+		// VC60 workaround: MSVC 6.0 has an optimization problem that makes
+		// (dword)A*B where either A or B has been cast to a dword before
+		// very expensive. Revisit a CombaSquare4() function when this
+		// problem is fixed.               
+
+// WARNING: KeithR. 05/08/03 This routine doesn't work with gcc on hardware
+// either.  I've completely removed it.  It may be worth looking into sometime
+// in the future.  Therefore, we use the CombaMultiply4 on all targets.
+//#ifdef __WINS__
+		CombaMultiply4(R, A, A);
+/*#else
+		CombaSquare4(R, A);
+#endif*/
+	}
+	else
+	{
+		const unsigned int N2 = N/2;
+
+		RecursiveSquare(R0, T2, A0, N2);
+		RecursiveSquare(R2, T2, A1, N2);
+		RecursiveMultiply(T0, T2, A0, A1, N2);
+
+		word carry = Add(R1, R1, T0, N);
+		carry += Add(R1, R1, T0, N);
+		Increment(R3, N2, carry);
+	}
+}
+// R[N] - bottom half of A*B
+// T[N] - temporary work space
+// A[N] - multiplier
+// B[N] - multiplicant
+
+void RecursiveMultiplyBottom(word *R, word *T, const word *A, const word *B, unsigned int N)
+{
+	assert(N>=2 && N%2==0);
+
+	if (N==2)
+		AtomicMultiplyBottom(R, A, B);
+	else if (N==4)
+		CombaMultiplyBottom4(R, A, B);
+	else if (N==8)
+		CombaMultiplyBottom8(R, A, B);
+	else
+	{
+		const unsigned int 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 RecursiveMultiplyTop(word *R, word *T, const word *L, const word *A, const word *B, unsigned int N)
+{
+	assert(N>=2 && N%2==0);
+
+	if (N==2)
+	{
+		AtomicMultiply(T, A, B);
+		((dword *)R)[0] = ((dword *)T)[1];
+	}
+	else if (N==4)
+	{
+		CombaMultiply4(T, A, B);
+		((dword *)R)[0] = ((dword *)T)[2];
+		((dword *)R)[1] = ((dword *)T)[3];
+	}
+	else
+	{
+		const unsigned int N2 = N/2;
+		int carry;
+
+		int aComp = Compare(A0, A1, N2);
+		int bComp = Compare(B0, B1, N2);
+
+		switch (2*aComp + aComp + bComp)
+		{
+		case -4:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			Subtract(T1, T1, R0, N2);
+			carry = -1;
+			break;
+		case -2:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			carry = 0;
+			break;
+		case 2:
+			Subtract(R0, A0, A1, N2);
+			Subtract(R1, B1, B0, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			carry = 0;
+			break;
+		case 4:
+			Subtract(R0, A1, A0, N2);
+			Subtract(R1, B0, B1, N2);
+			RecursiveMultiply(T0, T2, R0, R1, N2);
+			Subtract(T1, T1, R1, N2);
+			carry = -1;
+			break;
+		default:
+			SetWords(T0, 0, N);
+			carry = 0;
+		}
+
+		RecursiveMultiply(T2, R0, A1, B1, N2);
+
+		// now T[01] holds (A1-A0)*(B0-B1), T[23] holds A1*B1
+
+		CopyWords(R0, L+N2, N2);
+		word c2 = Subtract(R0, R0, L, N2);
+		c2 += Subtract(R0, R0, T0, N2);
+		word t = (Compare(R0, T2, N2) == -1);
+
+		carry += t;
+		carry += Increment(R0, N2, c2+t);
+		carry += Add(R0, R0, T1, N2);
+		carry += Add(R0, R0, T3, N2);
+
+		CopyWords(R1, T3, N2);
+		assert (carry >= 0 && carry <= 2);
+		Increment(R1, N2, carry);
+	}
+}
+
+// R[NA+NB] - result = A*B
+// T[NA+NB] - temporary work space
+// A[NA] ---- multiplier
+// B[NB] ---- multiplicant
+
+void AsymmetricMultiply(word *R, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
+{
+	if (NA == NB)
+	{
+		if (A == B)
+			RecursiveSquare(R, T, A, NA);
+		else
+			RecursiveMultiply(R, T, A, B, NA);
+
+		return;
+	}
+
+	if (NA > NB)
+	{
+		TClassSwap(A, B);
+		TClassSwap(NA, NB);
+		//std::swap(A, B);
+		//std::swap(NA, NB);
+	}
+
+	assert(NB % NA == 0);
+	assert((NB/NA)%2 == 0); 	// NB is an even multiple of NA
+
+	if (NA==2 && !A[1])
+	{
+		switch (A[0])
+		{
+		case 0:
+			SetWords(R, 0, NB+2);
+			return;
+		case 1:
+			CopyWords(R, B, NB);
+			R[NB] = R[NB+1] = 0;
+			return;
+		default:
+			R[NB] = LinearMultiply(R, B, A[0], NB);
+			R[NB+1] = 0;
+			return;
+		}
+	}
+
+	RecursiveMultiply(R, T, A, B, NA);
+	CopyWords(T+2*NA, R+NA, NA);
+
+	unsigned i;
+
+	for (i=2*NA; i<NB; i+=2*NA)
+		RecursiveMultiply(T+NA+i, T, A, B+i, NA);
+	for (i=NA; i<NB; i+=2*NA)
+		RecursiveMultiply(R+i, T, A, B+i, NA);
+
+	if (Add(R+NA, R+NA, T+2*NA, NB-NA))
+		Increment(R+NB, NA);
+}
+// R[N] ----- result = A inverse mod 2**(WORD_BITS*N)
+// T[3*N/2] - temporary work space
+// A[N] ----- an odd number as input
+
+void RecursiveInverseModPower2(word *R, word *T, const word *A, unsigned int N)
+{
+	if (N==2)
+		AtomicInverseModPower2(R, A[0], A[1]);
+	else
+	{
+		const unsigned int N2 = N/2;
+		RecursiveInverseModPower2(R0, T0, A0, N2);
+		T0[0] = 1;
+		SetWords(T0+1, 0, N2-1);
+		RecursiveMultiplyTop(R1, T1, T0, R0, A0, N2);
+		RecursiveMultiplyBottom(T0, T1, R0, A1, N2);
+		Add(T0, R1, T0, N2);
+		TwosComplement(T0, N2);
+		RecursiveMultiplyBottom(R1, T1, R0, T0, N2);
+	}
+}
+#undef A0
+#undef A1
+#undef B0
+#undef B1
+
+#undef T0
+#undef T1
+#undef T2
+#undef T3
+
+#undef R0
+#undef R1
+#undef R2
+#undef R3
+
+// R[N] --- result = X/(2**(WORD_BITS*N)) mod M
+// T[3*N] - temporary work space
+// X[2*N] - number to be reduced
+// M[N] --- modulus
+// U[N] --- multiplicative inverse of M mod 2**(WORD_BITS*N)
+
+void MontgomeryReduce(word *R, word *T, const word *X, const word *M, const word *U, unsigned int N)
+{
+	RecursiveMultiplyBottom(R, T, X, U, N);
+	RecursiveMultiplyTop(T, T+N, X, R, M, N);
+	if (Subtract(R, X+N, T, N))
+	{
+#ifdef _DEBUG
+		word carry = Add(R, R, M, N);
+		assert(carry);
+#else
+		Add(R, R, M, N);
+#endif
+	}
+}
+
+// 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));
+
+	dword p, u;
+	word Q;
+
+	// estimate the quotient: do a 2 word by 1 word divide
+	if (B1+1 == 0)
+		Q = A[2];
+	else
+		Q = word(MAKE_DWORD(A[1], A[2]) / (B1+1));
+
+	// now subtract Q*B from A
+	p = (dword) B0*Q;
+	u = (dword) A[0] - LOW_WORD(p);
+	A[0] = LOW_WORD(u);
+	u = (dword) A[1] - HIGH_WORD(p) - (word)(0-HIGH_WORD(u)) - (dword)B1*Q;
+	A[1] = LOW_WORD(u);
+	A[2] += HIGH_WORD(u);
+
+	// 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] = LOW_WORD(u);
+		u = (dword) A[1] - B1 - (word)(0-HIGH_WORD(u));
+		A[1] = LOW_WORD(u);
+		A[2] += HIGH_WORD(u);
+		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]);
+
+#ifdef _DEBUG
+		// 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];
+		AtomicMultiply(P, Q, B);
+		Add(P, P, T, 4);
+		assert(Mem::Compare((TUint8*)P, 4*WORD_SIZE, (TUint8*)A, 4*WORD_SIZE)==0);
+#endif
+	}
+}
+
+// for use by Divide(), corrects the underestimated quotient {Q1,Q0}
+static void CorrectQuotientEstimate(word *R, word *T, word *Q, const word *B, unsigned int N)
+{
+	assert(N && N%2==0);
+
+	if (Q[1])
+	{
+		T[N] = T[N+1] = 0;
+		unsigned i;
+		for (i=0; i<N; i+=4)
+			AtomicMultiply(T+i, Q, B+i);
+		for (i=2; i<N; i+=4)
+			if (AtomicMultiplyAdd(T+i, Q, B+i))
+				T[i+5] += (++T[i+4]==0);
+	}
+	else
+	{
+		T[N] = LinearMultiply(T, B, Q[0], N);
+		T[N+1] = 0;
+	}
+
+#ifdef _DEBUG
+	word borrow = Subtract(R, R, T, N+2);
+	assert(!borrow && !R[N+1]);
+#else
+	Subtract(R, R, T, N+2);
+#endif
+
+	while (R[N] || Compare(R, B, N) >= 0)
+	{
+		R[N] -= Subtract(R, R, B, N);
+		Q[1] += (++Q[0]==0);
+		assert(Q[0] || Q[1]); // no overflow
+	}
+}
+
+// R[NB] -------- remainder = A%B
+// Q[NA-NB+2] --- quotient	= A/B
+// T[NA+2*NB+4] - temp work space
+// A[NA] -------- dividend
+// B[NB] -------- divisor
+
+void Divide(word *R, word *Q, word *T, const word *A, unsigned int NA, const word *B, unsigned int NB)
+{
+	assert(NA && NB && NA%2==0 && NB%2==0);
+	assert(B[NB-1] || B[NB-2]);
+	assert(NB <= NA);
+
+	// set up temporary work space
+	word *const TA=T;
+	word *const TB=T+NA+2;
+	word *const TP=T+NA+2+NB;
+
+	// copy B into TB and normalize it so that TB has highest bit set to 1
+	unsigned shiftWords = (B[NB-1]==0);
+	TB[0] = TB[NB-1] = 0;
+	CopyWords(TB+shiftWords, B, NB-shiftWords);
+	unsigned shiftBits = WORD_BITS - BitPrecision(TB[NB-1]);
+	assert(shiftBits < WORD_BITS);
+	ShiftWordsLeftByBits(TB, NB, shiftBits);
+
+	// copy A into TA and normalize it
+	TA[0] = TA[NA] = TA[NA+1] = 0;
+	CopyWords(TA+shiftWords, A, NA);
+	ShiftWordsLeftByBits(TA, NA+2, shiftBits);
+
+	if (TA[NA+1]==0 && TA[NA] <= 1)
+	{
+		Q[NA-NB+1] = Q[NA-NB] = 0;
+		while (TA[NA] || Compare(TA+NA-NB, TB, NB) >= 0)
+		{
+			TA[NA] -= Subtract(TA+NA-NB, TA+NA-NB, TB, NB);
+			++Q[NA-NB];
+		}
+	}
+	else
+	{
+		NA+=2;
+		assert(Compare(TA+NA-NB, TB, NB) < 0);
+	}
+
+	word BT[2];
+	BT[0] = TB[NB-2] + 1;
+	BT[1] = TB[NB-1] + (BT[0]==0);
+
+	// start reducing TA mod TB, 2 words at a time
+	for (unsigned i=NA-2; i>=NB; i-=2)
+	{
+		AtomicDivide(Q+i-NB, TA+i-2, BT);
+		CorrectQuotientEstimate(TA+i-NB, TP, Q+i-NB, TB, NB);
+	}
+
+	// copy TA into R, and denormalize it
+	CopyWords(R, TA+shiftWords, NB);
+	ShiftWordsRightByBits(R, NB, shiftBits);
+}
+
+static inline unsigned int EvenWordCount(const word *X, unsigned int N)
+{
+	while (N && X[N-2]==0 && X[N-1]==0)
+		N-=2;
+	return N;
+}
+
+// return k
+// R[N] --- result = A^(-1) * 2^k mod M
+// T[4*N] - temporary work space
+// A[NA] -- number to take inverse of
+// M[N] --- modulus
+
+unsigned int AlmostInverse(word *R, word *T, const word *A, unsigned int NA, const word *M, unsigned int N)
+{
+	assert(NA<=N && N && N%2==0);
+
+	word *b = T;
+	word *c = T+N;
+	word *f = T+2*N;
+	word *g = T+3*N;
+	unsigned int bcLen=2, fgLen=EvenWordCount(M, N);
+	unsigned int k=0, s=0;
+
+	SetWords(T, 0, 3*N);
+	b[0]=1;
+	CopyWords(f, A, NA);
+	CopyWords(g, M, N);
+
+	FOREVER
+	{
+		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)
+		{
+			TClassSwap<word*>(f,g);
+			TClassSwap<word*>(b,c);
+			s++;
+		}
+
+		Subtract(f, f, g, fgLen);
+
+		if (Add(b, b, c, bcLen))
+		{
+			b[bcLen] = 1;
+			bcLen+=2;
+			assert(bcLen <= N);
+		}
+	}
+}
+
+// R[N] - result = A/(2^k) mod M
+// A[N] - input
+// M[N] - modulus
+
+void DivideByPower2Mod(word *R, const word *A, unsigned int k, const word *M, unsigned int N)
+{
+	CopyWords(R, A, N);
+
+	while (k--)
+	{
+		if (R[0]%2==0)
+			ShiftWordsRightByBits(R, N, 1);
+		else
+		{
+			word carry = Add(R, R, M, N);
+			ShiftWordsRightByBits(R, N, 1);
+			R[N-1] += carry<<(WORD_BITS-1);
+		}
+	}
+}
+