static enum eExprErr ComputeExpr(char *expr, BigInteger *ExpressionResult)
{
int i, shLeft;
int retcode;
limb carry;
boolean leftNumberFlag = FALSE;
int exprIndexAux, offset;
enum eExprErr SubExprResult;
int len;
limb largeLen;
limb *ptrLimb;
BigInteger *pBigInt;
int c;
int startStackIndex = stackIndex;
exprLength = (int)strlen(expr);
while (exprIndex < exprLength)
{
char charValue;
charValue = *(expr+exprIndex);
if (charValue == ' ' || charValue == 9)
{ // Ignore spaces and horizontal tabs.
exprIndex++;
continue;
}
if (charValue == '^')
{ // Caret is exponentiation operation.
charValue = OPER_POWER;
exprIndex++;
}
else if (charValue == '*' && *(expr + exprIndex + 1) == '*')
{ // Double asterisk is exponentiation operation too.
charValue = OPER_POWER;
exprIndex += 2;
}
else if (charValue == '*')
{
charValue = OPER_MULTIPLY;
exprIndex++;
}
else if (charValue == '/')
{
charValue = OPER_DIVIDE;
exprIndex++;
}
else if (charValue == '%')
{
charValue = OPER_REMAINDER;
exprIndex++;
}
else if (charValue == '+')
{
charValue = OPER_PLUS;
exprIndex++;
}
else if (charValue == '-')
{
charValue = OPER_MINUS;
exprIndex++;
}
else if (charValue == '<' && *(expr + exprIndex + 1) == '=')
{
charValue = OPER_NOT_GREATER;
exprIndex += 2;
}
else if (charValue == '>' && *(expr + exprIndex + 1) == '=')
{
charValue = OPER_NOT_LESS;
exprIndex += 2;
}
else if (charValue == '!' && *(expr + exprIndex + 1) == '=')
{
charValue = OPER_NOT_EQUAL;
exprIndex += 2;
}
else if (charValue == '=' && *(expr + exprIndex + 1) == '=')
{
charValue = OPER_EQUAL;
exprIndex += 2;
}
else if (charValue == '>')
{
charValue = OPER_GREATER;
exprIndex++;
}
else if (charValue == '<')
{
charValue = OPER_LESS;
exprIndex++;
}
else if ((charValue & 0xDF) == 'N' && (*(expr + exprIndex + 1) & 0xDF) == 'O' &&
(*(expr + exprIndex + 2) & 0xDF) == 'T')
{
charValue = OPER_NOT;
exprIndex += 3;
}
else if ((charValue & 0xDF) == 'A' && (*(expr + exprIndex + 1) & 0xDF) == 'N' &&
(*(expr + exprIndex + 2) & 0xDF) == 'D')
{
charValue = OPER_AND;
exprIndex += 3;
}
else if ((charValue & 0xDF) == 'O' && (*(expr + exprIndex + 1) & 0xDF) == 'R')
{
charValue = OPER_OR;
exprIndex += 2;
}
else if ((charValue & 0xDF) == 'X' && (*(expr + exprIndex + 1) & 0xDF) == 'O' &&
(*(expr + exprIndex + 2) & 0xDF) == 'R')
{
charValue = OPER_XOR;
exprIndex += 3;
}
else if ((charValue & 0xDF) == 'S' && (*(expr + exprIndex + 1) & 0xDF) == 'H' &&
(*(expr + exprIndex + 2) & 0xDF) == 'L')
{
charValue = OPER_SHL;
exprIndex += 3;
}
else if ((charValue & 0xDF) == 'S' && (*(expr + exprIndex + 1) & 0xDF) == 'H' &&
(*(expr + exprIndex + 2) & 0xDF) == 'R')
{
charValue = OPER_SHR;
exprIndex += 3;
}
else if (charValue == '!')
{ // Calculating factorial.
if (leftNumberFlag == FALSE)
{
return EXPR_SYNTAX_ERROR;
}
if (stackValues[stackIndex].nbrLimbs > 1)
{
return EXPR_INTERM_TOO_HIGH;
}
#ifdef FACTORIZATION_APP
if (stackValues[stackIndex].limbs[0].x < 0 || stackValues[stackIndex].limbs[0].x >= 47177)
#else
if (stackValues[stackIndex].limbs[0].x < 0 || stackValues[stackIndex].limbs[0].x >= 5984)
#endif
{
return EXPR_INTERM_TOO_HIGH;
}
factorial(&stackValues[stackIndex], (int)stackValues[stackIndex].limbs[0].x);
exprIndex++;
continue;
}
else if (charValue == '#')
{ // Calculating primorial.
if (leftNumberFlag == FALSE)
{
return EXPR_SYNTAX_ERROR;
}
if (stackValues[stackIndex].nbrLimbs > 2)
{
return EXPR_INTERM_TOO_HIGH;
}
if (stackValues[stackIndex].nbrLimbs == 2)
{
largeLen.x = stackValues[stackIndex].limbs[0].x +
(stackValues[stackIndex].limbs[1].x << BITS_PER_GROUP);
}
else
{
largeLen.x = stackValues[stackIndex].limbs[0].x;
}
len = (int)largeLen.x;
#ifdef FACTORIZATION_APP
if (len < 0 || len > 460490)
#else
if (len < 0 || len > 46049)
#endif
{
return EXPR_INTERM_TOO_HIGH;
}
primorial(&stackValues[stackIndex], (int)stackValues[stackIndex].limbs[0].x);
exprIndex++;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"GCD", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
BigIntGcd(&stackValues[stackIndex], &stackValues[stackIndex + 1], &stackValues[stackIndex]);
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"MODPOW", 3, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = BigIntGeneralModularPower(&stackValues[stackIndex], &stackValues[stackIndex + 1],
&stackValues[stackIndex + 2], &stackValues[stackIndex]);
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"MODINV", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeModInv();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
#ifdef FACTORIZATION_FUNCTIONS
else if ((retcode = func(expr, ExpressionResult,
"TOTIENT", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeTotient();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"NUMDIVS", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeNumDivs();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"SUMDIVS", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeSumDivs();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"CONCATFACT", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeConcatFact();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
#endif
else if ((retcode = func(expr, ExpressionResult,
"SUMDIGITS", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeSumDigits();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"NUMDIGITS", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeNumDigits();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"REVDIGITS", 2, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeRevDigits();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"ISPRIME", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
#ifdef FACTORIZATION_APP
if (BpswPrimalityTest(&stackValues[stackIndex], NULL) == 0)
#else
if (BpswPrimalityTest(&stackValues[stackIndex]) == 0)
#endif
{ // Argument is a probable prime.
intToBigInteger(&stackValues[stackIndex], -1);
}
else
{ // Argument is not a probable prime.
intToBigInteger(&stackValues[stackIndex], 0);
}
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"F", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeFibLucas(0);
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"L", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeFibLucas(2);
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"P", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputePartition();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"N", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeNext();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((retcode = func(expr, ExpressionResult,
"B", 1, leftNumberFlag)) <= 0)
{
if (retcode != 0) { return retcode; }
retcode = ComputeBack();
if (retcode != 0) { return retcode; }
leftNumberFlag = 1;
continue;
}
else if ((charValue & 0xDF) == 'X')
{
if (leftNumberFlag || valueX.nbrLimbs == 0)
{
return EXPR_SYNTAX_ERROR;
}
CopyBigInt(&stackValues[stackIndex], &valueX);
valueXused = TRUE;
exprIndex++;
leftNumberFlag = TRUE;
continue;
}
else if ((charValue & 0xDF) == 'C')
{
if (leftNumberFlag || valueX.nbrLimbs == 0)
{
return EXPR_SYNTAX_ERROR;
}
intToBigInteger(&stackValues[stackIndex], counterC);
valueXused = TRUE;
exprIndex++;
leftNumberFlag = TRUE;
continue;
}
else if (charValue == '(')
{
if (leftNumberFlag == TRUE)
{
return EXPR_SYNTAX_ERROR;
}
if (stackIndex >= PAREN_STACK_SIZE)
{
return EXPR_TOO_MANY_PAREN;
}
stackOperators[stackIndex++] = charValue;
exprIndex++;
continue;
}
else if (charValue == ')' || charValue == ',')
{
if (leftNumberFlag == 0)
{
return EXPR_SYNTAX_ERROR;
}
while (stackIndex > startStackIndex &&
stackOperators[stackIndex - 1] != '(')
{
if ((SubExprResult = ComputeSubExpr()) != 0)
{
return SubExprResult;
}
}
if (stackIndex == startStackIndex)
{
break;
}
if (charValue == ',')
{
return EXPR_PAREN_MISMATCH;
}
stackIndex--; /* Discard ')' */
stackValues[stackIndex] = stackValues[stackIndex + 1];
leftNumberFlag = 1;
exprIndex++;
continue;
}
else if (charValue >= '0' && charValue <= '9')
{
exprIndexAux = exprIndex;
if (charValue == '0' && exprIndexAux < exprLength - 2 &&
*(expr+exprIndexAux + 1) == 'x')
{ // hexadecimal
exprIndexAux++;
while (exprIndexAux < exprLength - 1)
{
charValue = *(expr+exprIndexAux + 1);
if ((charValue >= '0' && charValue <= '9') ||
(charValue >= 'A' && charValue <= 'F') ||
(charValue >= 'a' && charValue <= 'f'))
{
exprIndexAux++;
}
else
{
break;
}
}
// Generate big integer from hexadecimal number from right to left.
carry.x = 0;
i = 0; // limb number.
shLeft = 0;
offset = exprIndexAux;
ptrLimb = &stackValues[stackIndex].limbs[0];
for (; exprIndexAux >= exprIndex + 2; exprIndexAux--)
{
c = *(expr + exprIndexAux);
if (c >= '0' && c <= '9')
{
c -= '0';
}
else if (c >= 'A' && c <= 'F')
{
c -= 'A' - 10;
}
else
{
c -= 'a' - 10;
}
carry.x += c << shLeft;
shLeft += 4; // 4 bits per hex digit.
if (shLeft >= BITS_PER_GROUP)
{
shLeft -= BITS_PER_GROUP;
(ptrLimb++)->x = carry.x & MAX_VALUE_LIMB;
carry.x = c >> (4-shLeft);
}
}
if (carry.x != 0 || ptrLimb == &stackValues[stackIndex].limbs[0])
{
(ptrLimb++)->x = carry.x;
}
exprIndex = offset+1;
stackValues[stackIndex].nbrLimbs = (int)(ptrLimb - &stackValues[stackIndex].limbs[0]);
stackValues[stackIndex].sign = SIGN_POSITIVE;
}
void DiscreteLogarithm(void)
{
BigInteger groupOrder, subGroupOrder, powSubGroupOrder, powSubGroupOrderBak;
BigInteger Exponent, runningExp, baseExp, mod;
BigInteger logar, logarMult, runningExpBase;
BigInteger currentExp;
int indexBase, indexExp;
int index, expon;
limb addA, addB, addA2, addB2;
limb mult1, mult2;
double magnitude, firstLimit, secondLimit;
long long brentK, brentR;
unsigned char EndPollardBrentRho;
int nbrLimbs;
struct sFactors *pstFactors;
enum eLogMachineState logMachineState;
char *ptr;
#ifdef __EMSCRIPTEN__
lModularMult = 0;
#endif
NumberLength = modulus.nbrLimbs;
if (!TestBigNbrEqual(&LastModulus, &modulus))
{
CompressBigInteger(nbrToFactor, &modulus);
Bin2Dec(modulus.limbs, tofactorDec, modulus.nbrLimbs, groupLen);
factor(&modulus, nbrToFactor, factorsMod, astFactorsMod, NULL);
NbrFactorsMod = astFactorsMod[0].multiplicity;
}
intToBigInteger(&DiscreteLog, 0); // DiscreteLog <- 0
intToBigInteger(&DiscreteLogPeriod, 1); // DiscreteLogPeriod <- 1
for (index = 1; index <= NbrFactorsMod; index++)
{
int mostSignificantDword, leastSignificantDword;
int NbrFactors;
int *ptrPrime;
int multiplicity;
ptrPrime = astFactorsMod[index].ptrFactor;
NumberLength = *ptrPrime;
UncompressBigInteger(ptrPrime, &groupOrder);
groupOrder.sign = SIGN_POSITIVE;
BigIntRemainder(&base, &groupOrder, &tmpBase);
if (tmpBase.nbrLimbs == 1 && tmpBase.limbs[0].x == 0)
{ // modulus and base are not relatively prime.
int ctr;
multiplicity = astFactorsMod[index].multiplicity;
CopyBigInt(&bigNbrA, &power);
for (ctr = multiplicity; ctr > 0; ctr--)
{
BigIntRemainder(&bigNbrA, &groupOrder, &bigNbrB);
if (bigNbrB.nbrLimbs != 1 || bigNbrB.limbs[0].x != 0)
{ // Exit loop if integer division cannot be performed
break;
}
BigIntDivide(&bigNbrA, &groupOrder, &bigNbrB);
CopyBigInt(&bigNbrA, &bigNbrB);
}
if (ctr == 0)
{ // Power is multiple of prime^exp.
continue;
}
// Compute prime^mutliplicity.
BigIntPowerIntExp(&groupOrder, multiplicity, &tmp2);
BigIntRemainder(&base, &tmp2, &tmpBase);
// Get tentative exponent.
ctr = multiplicity - ctr;
intToBigInteger(&bigNbrB, ctr); // Convert exponent to big integer.
NumberLength = tmp2.nbrLimbs;
memcpy(TestNbr, tmp2.limbs, (NumberLength + 1) * sizeof(limb));
GetMontgomeryParms(NumberLength);
BigIntModularPower(&tmpBase, &bigNbrB, &bigNbrA);
BigIntRemainder(&power, &tmp2, &bigNbrB);
BigIntSubt(&bigNbrA, &bigNbrB, &bigNbrA);
if (bigNbrA.nbrLimbs == 1 && bigNbrA.limbs[0].x == 0)
{
intToBigInteger(&DiscreteLog, ctr); // DiscreteLog <- exponent
intToBigInteger(&DiscreteLogPeriod, 0); // DiscreteLogPeriod <- 0
break;
}
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
else
{ // modulus and base are relatively prime.
BigIntRemainder(&power, &groupOrder, &bigNbrB);
if (bigNbrB.nbrLimbs == 1 && bigNbrB.limbs[0].x == 0)
{ // power is multiple of prime. Error.
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
}
CompressLimbsBigInteger(baseMontg, &tmpBase);
BigIntRemainder(&power, &groupOrder, &tmpBase);
CompressLimbsBigInteger(powerMontg, &tmpBase);
// Compute group order as the prime minus 1.
groupOrder.limbs[0].x--;
showText("Computing discrete logarithm...");
CompressBigInteger(nbrToFactor, &groupOrder);
factor(&groupOrder, nbrToFactor, factorsGO, astFactorsGO, NULL); // factor groupOrder.
NbrFactors = astFactorsGO[0].multiplicity;
NumberLength = *ptrPrime;
UncompressBigInteger(ptrPrime, &mod);
intToBigInteger(&logar, 0); // logar <- 0
intToBigInteger(&logarMult, 1); // logarMult <- 1
NumberLength = mod.nbrLimbs;
memcpy(TestNbr, mod.limbs, NumberLength * sizeof(limb));
TestNbr[NumberLength].x = 0;
// yieldFreq = 1000000 / (NumberLength*NumberLength);
GetMontgomeryParms(NumberLength);
#if 0
char *ptrText = textExp;
strcpy(ptrText, "<p>NumberLength (2) = ");
ptrText = ptrText + strlen(ptrText);
int2dec(&ptrText, NumberLength);
strcpy(ptrText, "</p>");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
#endif
// Convert base and power to Montgomery notation.
modmult(baseMontg, MontgomeryMultR2, baseMontg);
modmult(powerMontg, MontgomeryMultR2, powerMontg);
mostSignificantDword = NumberLength - 1;
if (NumberLength == 1)
{
leastSignificantDword = NumberLength - 1;
firstLimit = (double)TestNbr[leastSignificantDword].x / 3;
}
else
{
leastSignificantDword = NumberLength - 2;
firstLimit = ((double)TestNbr[mostSignificantDword].x * LIMB_RANGE +
TestNbr[leastSignificantDword].x) / 3;
}
secondLimit = firstLimit * 2;
for (indexBase = 0; indexBase < NbrFactors; indexBase++)
{
NumberLength = *astFactorsGO[indexBase + 1].ptrFactor;
UncompressBigInteger(astFactorsGO[indexBase + 1].ptrFactor, &subGroupOrder);
subGroupOrder.sign = SIGN_POSITIVE;
strcpy(textExp, "Computing discrete logarithm in subgroup of ");
Bin2Dec(subGroupOrder.limbs, textExp + strlen(textExp), subGroupOrder.nbrLimbs, groupLen);
ptr = textExp + strlen(textExp);
if (astFactorsGO[indexBase + 1].multiplicity > 1)
{
*ptr++ = '<';
*ptr++ = 's';
*ptr++ = 'u';
*ptr++ = 'p';
*ptr++ = '>';
int2dec(&ptr, astFactorsGO[indexBase + 1].multiplicity);
*ptr++ = '<';
*ptr++ = '/';
*ptr++ = 's';
*ptr++ = 'u';
*ptr++ = 'p';
*ptr++ = '>';
}
strcpy(ptr, " elements.");
showText(textExp);
NumberLength = mod.nbrLimbs;
memcpy(TestNbr, mod.limbs, NumberLength * sizeof(limb));
NumberLengthOther = subGroupOrder.nbrLimbs;
memcpy(TestNbrOther, subGroupOrder.limbs, NumberLengthOther * sizeof(limb));
TestNbr[NumberLength].x = 0;
GetMontgomeryParms(NumberLength);
nbrLimbs = subGroupOrder.nbrLimbs;
dN = (double)subGroupOrder.limbs[nbrLimbs - 1].x;
if (nbrLimbs > 1)
{
dN += (double)subGroupOrder.limbs[nbrLimbs - 2].x / LIMB_RANGE;
if (nbrLimbs > 2)
{
dN += (double)subGroupOrder.limbs[nbrLimbs - 3].x / LIMB_RANGE / LIMB_RANGE;
}
}
CopyBigInt(&baseExp, &groupOrder);
// Check whether base is primitive root.
BigIntDivide(&groupOrder, &subGroupOrder, &tmpBase);
modPow(baseMontg, tmpBase.limbs, tmpBase.nbrLimbs, primRootPwr);
if (!memcmp(primRootPwr, MontgomeryMultR1, NumberLength * sizeof(limb)))
{ // Power is one, so it is not a primitive root.
logMachineState = CALC_LOG_BASE;
// Find primitive root
primRoot[0].x = 1;
if (NumberLength > 1)
{
memset(&primRoot[1], 0, (NumberLength - 1) * sizeof(limb));
}
do
{
primRoot[0].x++;
modPow(primRoot, tmpBase.limbs, tmpBase.nbrLimbs, primRootPwr);
} while (!memcmp(primRootPwr, MontgomeryMultR1, NumberLength * sizeof(limb)));
}
else
{ // Power is not 1, so the base is a primitive root.
logMachineState = BASE_PRIMITIVE_ROOT;
memcpy(primRoot, baseMontg, NumberLength * sizeof(limb));
}
for (;;)
{ // Calculate discrete logarithm in subgroup.
runningExp.nbrLimbs = 1; // runningExp <- 0
runningExp.limbs[0].x = 0;
runningExp.sign = SIGN_POSITIVE;
powSubGroupOrder.nbrLimbs = 1; // powSubGroupOrder <- 1
powSubGroupOrder.limbs[0].x = 1;
powSubGroupOrder.sign = SIGN_POSITIVE;
CopyBigInt(¤tExp, &groupOrder);
if (logMachineState == BASE_PRIMITIVE_ROOT)
{
memcpy(basePHMontg, baseMontg, NumberLength * sizeof(limb));
memcpy(currPowerMontg, powerMontg, NumberLength * sizeof(limb));
}
else if (logMachineState == CALC_LOG_BASE)
{
memcpy(basePHMontg, primRoot, NumberLength * sizeof(limb));
memcpy(currPowerMontg, baseMontg, NumberLength * sizeof(limb));
}
else
{ // logMachineState == CALC_LOG_POWER
memcpy(primRoot, basePHMontg, NumberLength * sizeof(limb));
memcpy(currPowerMontg, powerMontg, NumberLength * sizeof(limb));
}
for (indexExp = 0; indexExp < astFactorsGO[indexBase + 1].multiplicity; indexExp++)
{
/* PH below comes from Pohlig-Hellman algorithm */
BigIntDivide(¤tExp, &subGroupOrder, ¤tExp);
modPow(currPowerMontg, currentExp.limbs, currentExp.nbrLimbs, powerPHMontg);
BigIntDivide(&baseExp, &subGroupOrder, &baseExp);
if (subGroupOrder.nbrLimbs == 1 && subGroupOrder.limbs[0].x < 20)
{ // subGroupOrder less than 20.
if (!ComputeDLogModSubGroupOrder(indexBase, indexExp, &Exponent, &subGroupOrder))
{
return;
}
}
else
{ // Use Pollard's rho method with Brent's modification
memcpy(nbrPower, powerPHMontg, NumberLength * sizeof(limb));
memcpy(nbrBase, primRootPwr, NumberLength * sizeof(limb));
memcpy(nbrR2, nbrBase, NumberLength * sizeof(limb));
memset(nbrA2, 0, NumberLength * sizeof(limb));
memset(nbrB2, 0, NumberLength * sizeof(limb));
nbrB2[0].x = 1;
addA2.x = addB2.x = 0;
mult2.x = 1;
brentR = 1;
brentK = 0;
EndPollardBrentRho = FALSE;
do
{
memcpy(nbrR, nbrR2, NumberLength * sizeof(limb));
memcpy(nbrA, nbrA2, NumberLength * sizeof(limb));
memcpy(nbrB, nbrB2, NumberLength * sizeof(limb));
addA = addA2;
addB = addB2;
mult1 = mult2;
brentR *= 2;
do
{
brentK++;
if (NumberLength == 1)
{
magnitude = (double)nbrR2[leastSignificantDword].x;
}
else
{
magnitude = (double)nbrR2[mostSignificantDword].x * LIMB_RANGE +
nbrR2[leastSignificantDword].x;
}
if (magnitude < firstLimit)
{
modmult(nbrR2, nbrPower, nbrROther);
addA2.x++;
}
else if (magnitude < secondLimit)
{
modmult(nbrR2, nbrR2, nbrROther);
mult2.x *= 2;
addA2.x *= 2;
addB2.x *= 2;
}
else
{
modmult(nbrR2, nbrBase, nbrROther);
addB2.x++;
}
// Exchange nbrR2 and nbrROther
memcpy(nbrTemp, nbrR2, NumberLength * sizeof(limb));
memcpy(nbrR2, nbrROther, NumberLength * sizeof(limb));
memcpy(nbrROther, nbrTemp, NumberLength * sizeof(limb));
if (addA2.x >= (int)(LIMB_RANGE / 2) || addB2.x >= (int)(LIMB_RANGE / 2) ||
mult2.x >= (int)(LIMB_RANGE / 2))
{
// nbrA2 <- (nbrA2 * mult2 + addA2) % subGroupOrder
AdjustExponent(nbrA2, mult2, addA2, &subGroupOrder);
// nbrB2 <- (nbrB2 * mult2 + addB2) % subGroupOrder
AdjustExponent(nbrB2, mult2, addB2, &subGroupOrder);
mult2.x = 1;
addA2.x = addB2.x = 0;
}
if (!memcmp(nbrR, nbrR2, NumberLength * sizeof(limb)))
{
EndPollardBrentRho = TRUE;
break;
}
} while (brentK < brentR);
} while (EndPollardBrentRho == FALSE);
ExchangeMods(); // TestNbr <- subGroupOrder
// nbrA <- (nbrA * mult1 + addA) % subGroupOrder
AdjustExponent(nbrA, mult1, addA, &subGroupOrder);
// nbrB <- (nbrB * mult1 + addB) % subGroupOrder
AdjustExponent(nbrB, mult1, addB, &subGroupOrder);
// nbrA2 <- (nbrA * mult2 + addA2) % subGroupOrder
AdjustExponent(nbrA2, mult2, addA2, &subGroupOrder);
// nbrB2 <- (nbrA * mult2 + addB2) % subGroupOrder
AdjustExponent(nbrB2, mult2, addB2, &subGroupOrder);
// nbrB <- (nbrB2 - nbrB) % subGroupOrder
SubtBigNbrMod(nbrB2, nbrB, nbrB);
SubtBigNbrMod(nbrA, nbrA2, nbrA);
if (BigNbrIsZero(nbrA))
{ // Denominator is zero, so rho does not work.
ExchangeMods(); // TestNbr <- modulus
if (!ComputeDLogModSubGroupOrder(indexBase, indexExp, &Exponent, &subGroupOrder))
{
return; // Cannot compute discrete logarithm.
}
}
else
{
// Exponent <- (nbrB / nbrA) (mod subGroupOrder)
UncompressLimbsBigInteger(nbrA, &bigNbrA);
UncompressLimbsBigInteger(nbrB, &bigNbrB);
BigIntModularDivisionSaveTestNbr(&bigNbrB, &bigNbrA, &subGroupOrder, &Exponent);
Exponent.sign = SIGN_POSITIVE;
ExchangeMods(); // TestNbr <- modulus
}
}
modPow(primRoot, Exponent.limbs, Exponent.nbrLimbs, tmpBase.limbs);
ModInvBigNbr(tmpBase.limbs, tmpBase.limbs, TestNbr, NumberLength);
modmult(tmpBase.limbs, currPowerMontg, currPowerMontg);
BigIntMultiply(&Exponent, &powSubGroupOrder, &tmpBase);
BigIntAdd(&runningExp, &tmpBase, &runningExp);
BigIntMultiply(&powSubGroupOrder, &subGroupOrder, &powSubGroupOrder);
modPow(primRoot, subGroupOrder.limbs, subGroupOrder.nbrLimbs, tmpBase.limbs);
memcpy(primRoot, tmpBase.limbs, NumberLength * sizeof(limb));
}
if (logMachineState == BASE_PRIMITIVE_ROOT)
{ // Discrete logarithm was determined for this subgroup.
ExponentsGOComputed[indexBase] = astFactorsGO[indexBase + 1].multiplicity;
break;
}
if (logMachineState == CALC_LOG_BASE)
{
CopyBigInt(&runningExpBase, &runningExp);
logMachineState = CALC_LOG_POWER;
}
else
{ // Set powSubGroupOrderBak to powSubGroupOrder.
// if runningExpBase is not multiple of subGroupOrder,
// discrete logarithm is runningExp/runningExpBase mod powSubGroupOrderBak.
// Otherwise if runningExp is multiple of subGroupOrder, there is no logarithm.
// Otherwise, divide runningExp, runnignExpBase and powSubGroupOrderBak by subGroupOrder and repeat.
ExponentsGOComputed[indexBase] = astFactorsGO[indexBase + 1].multiplicity;
CopyBigInt(&powSubGroupOrderBak, &powSubGroupOrder);
do
{
BigIntRemainder(&runningExpBase, &subGroupOrder, &tmpBase);
if (tmpBase.nbrLimbs > 1 || tmpBase.limbs[0].x != 0)
{ // runningExpBase is not multiple of subGroupOrder
BigIntModularDivisionSaveTestNbr(&runningExp, &runningExpBase, &powSubGroupOrderBak, &tmpBase);
CopyBigInt(&runningExp, &tmpBase);
break;
}
BigIntRemainder(&runningExp, &subGroupOrder, &tmpBase);
if (tmpBase.nbrLimbs > 1 || tmpBase.limbs[0].x != 0)
{ // runningExpBase is not multiple of subGroupOrder
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
BigIntDivide(&runningExp, &subGroupOrder, &tmpBase);
CopyBigInt(&runningExp, &tmpBase);
BigIntDivide(&runningExpBase, &subGroupOrder, &tmpBase);
CopyBigInt(&runningExpBase, &tmpBase);
BigIntDivide(&powSubGroupOrderBak, &subGroupOrder, &tmpBase);
CopyBigInt(&powSubGroupOrderBak, &tmpBase);
ExponentsGOComputed[indexBase]--;
if (tmpBase.nbrLimbs == 1 && tmpBase.limbs[0].x == 1)
{
break;
}
BigIntRemainder(&runningExpBase, &subGroupOrder, &tmpBase);
} while (tmpBase.nbrLimbs == 1 && tmpBase.limbs[0].x == 0);
CopyBigInt(&powSubGroupOrder, &powSubGroupOrderBak);
// The logarithm is runningExp / runningExpBase mod powSubGroupOrder
// When powSubGroupOrder is even, we cannot use Montgomery.
if (powSubGroupOrder.limbs[0].x & 1)
{ // powSubGroupOrder is odd.
BigIntModularDivisionSaveTestNbr(&runningExp, &runningExpBase, &powSubGroupOrder, &tmpBase);
CopyBigInt(&runningExp, &tmpBase);
}
else
{ // powSubGroupOrder is even (power of 2).
NumberLength = powSubGroupOrder.nbrLimbs;
CompressLimbsBigInteger(nbrB, &runningExpBase);
ComputeInversePower2(nbrB, nbrA, nbrB2); // nbrB2 is auxiliary var.
CompressLimbsBigInteger(nbrB, &runningExp);
multiply(nbrA, nbrB, nbrA, NumberLength, NULL); // nbrA <- quotient.
UncompressLimbsBigInteger(nbrA, &runningExp);
}
break;
}
}
CopyBigInt(&nbrV[indexBase], &runningExp);
NumberLength = powSubGroupOrder.nbrLimbs;
memcpy(TestNbr, powSubGroupOrder.limbs, NumberLength * sizeof(limb));
TestNbr[NumberLength].x = 0;
GetMontgomeryParms(NumberLength);
for (indexExp = 0; indexExp < indexBase; indexExp++)
{
// nbrV[indexBase] <- (nbrV[indexBase] - nbrV[indexExp])*
// modinv(PrimesGO[indexExp]^(ExponentsGO[indexExp]),
// powSubGroupOrder)
NumberLength = mod.nbrLimbs;
BigIntSubt(&nbrV[indexBase], &nbrV[indexExp], &nbrV[indexBase]);
BigIntRemainder(&nbrV[indexBase], &powSubGroupOrder, &nbrV[indexBase]);
if (nbrV[indexBase].sign == SIGN_NEGATIVE)
{
BigIntAdd(&nbrV[indexBase], &powSubGroupOrder, &nbrV[indexBase]);
}
pstFactors = &astFactorsGO[indexExp + 1];
UncompressBigInteger(pstFactors->ptrFactor, &tmpBase);
BigIntPowerIntExp(&tmpBase, ExponentsGOComputed[indexExp], &tmpBase);
BigIntRemainder(&tmpBase, &powSubGroupOrder, &tmpBase);
NumberLength = powSubGroupOrder.nbrLimbs;
CompressLimbsBigInteger(tmp2.limbs, &tmpBase);
modmult(tmp2.limbs, MontgomeryMultR2, tmp2.limbs);
if (NumberLength > 1 || TestNbr[0].x != 1)
{ // If TestNbr != 1 ...
ModInvBigNbr(tmp2.limbs, tmp2.limbs, TestNbr, NumberLength);
}
tmpBase.limbs[0].x = 1;
memset(&tmpBase.limbs[1], 0, (NumberLength - 1) * sizeof(limb));
modmult(tmpBase.limbs, tmp2.limbs, tmp2.limbs);
UncompressLimbsBigInteger(tmp2.limbs, &tmpBase);
BigIntMultiply(&tmpBase, &nbrV[indexBase], &nbrV[indexBase]);
}
BigIntRemainder(&nbrV[indexBase], &powSubGroupOrder, &nbrV[indexBase]);
BigIntMultiply(&nbrV[indexBase], &logarMult, &tmpBase);
BigIntAdd(&logar, &tmpBase, &logar);
BigIntMultiply(&logarMult, &powSubGroupOrder, &logarMult);
}
multiplicity = astFactorsMod[index].multiplicity;
UncompressBigInteger(ptrPrime, &bigNbrB);
expon = 1;
if (bigNbrB.nbrLimbs == 1 && bigNbrB.limbs[0].x == 2)
{ // Prime factor is 2. Base and power are odd at this moment.
int lsbBase = base.limbs[0].x;
int lsbPower = power.limbs[0].x;
if (multiplicity > 1)
{
int mask = (multiplicity == 2? 3 : 7);
expon = (multiplicity == 2 ? 2 : 3);
if ((lsbPower & mask) == 1)
{
intToBigInteger(&logar, 0);
intToBigInteger(&logarMult, (lsbBase == 1 ? 1 : 2));
}
else if (((lsbPower - lsbBase) & mask) == 0)
{
intToBigInteger(&logar, 1);
intToBigInteger(&logarMult, 2);
}
else
{
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
}
}
for (; expon < multiplicity; expon++)
{ // Repeated factor.
// L = logar, LM = logarMult
// B = base, P = power, p = prime
// B^n = P (mod p^(k+1)) -> n = L + m*LM m = ?
// B^(L + m*LM) = P
// (B^LM) ^ m = P*B^(-L)
// B^LM = r*p^k + 1, P*B^(-L) = s*p^k + 1
// (r*p^k + 1)^m = s*p^k + 1
// From binomial theorem: m = s / r (mod p)
// If r = 0 and s != 0 there is no solution.
// If r = 0 and s = 0 do not change LM.
BigIntPowerIntExp(&bigNbrB, expon + 1, &bigNbrA);
NumberLength = bigNbrA.nbrLimbs;
memcpy(TestNbr, bigNbrA.limbs, NumberLength * sizeof(limb));
GetMontgomeryParms(NumberLength);
BigIntRemainder(&base, &bigNbrA, &tmpBase);
CompressLimbsBigInteger(baseMontg, &tmpBase);
modmult(baseMontg, MontgomeryMultR2, baseMontg);
modPow(baseMontg, logarMult.limbs, logarMult.nbrLimbs, primRootPwr); // B^LM
tmpBase.limbs[0].x = 1; // Convert from Montgomery to standard notation.
memset(&tmpBase.limbs[1], 0, (NumberLength - 1) * sizeof(limb));
modmult(primRootPwr, tmpBase.limbs, primRootPwr); // B^LM
ModInvBigNbr(baseMontg, tmpBase.limbs, TestNbr, NumberLength); // B^(-1)
modPow(tmpBase.limbs, logar.limbs, logar.nbrLimbs, primRoot); // B^(-L)
BigIntRemainder(&power, &bigNbrA, &tmpBase);
CompressLimbsBigInteger(tmp2.limbs, &tmpBase);
modmult(primRoot, tmp2.limbs, primRoot); // P*B^(-L)
BigIntDivide(&bigNbrA, &bigNbrB, &tmpBase);
UncompressLimbsBigInteger(primRootPwr, &tmp2);
BigIntDivide(&tmp2, &tmpBase, &bigNbrA); // s
UncompressLimbsBigInteger(primRoot, &baseModGO); // Use baseMontGO as temp var.
BigIntDivide(&baseModGO, &tmpBase, &tmp2); // r
if (bigNbrA.nbrLimbs == 1 && bigNbrA.limbs[0].x == 0)
{ // r equals zero.
if (tmp2.nbrLimbs != 1 || tmp2.limbs[0].x != 0)
{ // s does not equal zero.
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
}
else
{ // r does not equal zero.
BigIntModularDivisionSaveTestNbr(&tmp2, &bigNbrA, &bigNbrB, &tmpBase); // m
BigIntMultiply(&tmpBase, &logarMult, &tmp2);
BigIntAdd(&logar, &tmp2, &logar);
BigIntMultiply(&logarMult, &bigNbrB, &logarMult);
}
}
// Based on logar and logarMult, compute DiscreteLog and DiscreteLogPeriod
// using the following formulas, that can be deduced from the Chinese
// Remainder Theorem:
// L = logar, LM = logarMult, DL = DiscreteLog, DLP = DiscreteLogPeriod.
// The modular implementation does not allow operating with even moduli.
//
// g <- gcd(LM, DLP)
// if (L%g != DL%g) there is no discrete logarithm, so go out.
// h <- LM / g
// if h is odd:
// t <- (L - DL) / DLP (mod h)
// t <- DLP * t + DL
// else
// i <- DLP / g
// t <- (DL - L) / LM (mod i)
// t <- LM * t + L
// endif
// DLP <- DLP * h
// DL <- t % DLP
BigIntGcd(&logarMult, &DiscreteLogPeriod, &tmpBase);
BigIntRemainder(&logar, &tmpBase, &bigNbrA);
BigIntRemainder(&DiscreteLog, &tmpBase, &bigNbrB);
if (!TestBigNbrEqual(&bigNbrA, &bigNbrB))
{
showText("There is no discrete logarithm");
DiscreteLogPeriod.sign = SIGN_NEGATIVE;
return;
}
BigIntDivide(&logarMult, &tmpBase, &tmp2);
if (tmp2.limbs[0].x & 1)
{ // h is odd.
BigIntSubt(&logar, &DiscreteLog, &tmpBase);
BigIntModularDivisionSaveTestNbr(&tmpBase, &DiscreteLogPeriod, &tmp2, &bigNbrA);
BigIntMultiply(&DiscreteLogPeriod, &bigNbrA, &tmpBase);
BigIntAdd(&tmpBase, &DiscreteLog, &tmpBase);
}
else
{ // h is even.
BigIntDivide(&DiscreteLogPeriod, &tmpBase, &bigNbrB);
BigIntSubt(&DiscreteLog, &logar, &tmpBase);
BigIntModularDivisionSaveTestNbr(&tmpBase, &logarMult, &bigNbrB, &bigNbrA);
BigIntMultiply(&logarMult, &bigNbrA, &tmpBase);
BigIntAdd(&tmpBase, &logar, &tmpBase);
}
BigIntMultiply(&DiscreteLogPeriod, &tmp2, &DiscreteLogPeriod);
BigIntRemainder(&tmpBase, &DiscreteLogPeriod, &DiscreteLog);
}
#if 0
textExp.setText(DiscreteLog.toString());
textPeriod.setText(DiscreteLogPeriod.toString());
long t = OldTimeElapsed / 1000;
labelStatus.setText("Time elapsed: " +
t / 86400 + "d " + (t % 86400) / 3600 + "h " + ((t % 3600) / 60) + "m " + (t % 60) +
"s mod mult: " + lModularMult);
#endif
}
