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/********************************************************************************************
* SIDH: an efficient supersingular isogeny cryptography library
*
* Abstract: Portable C and x86_64 ASM functions for modular arithmetic for P434
*********************************************************************************************/
#include "P434_internal.h"
// Modular addition, c = a+b mod p434.
// Inputs: a, b in [0, 2*p434-1]
// Output: c in [0, 2*p434-1]
void fpadd434(const digit_t *a, const digit_t *b, digit_t *c) {
#if defined(S2N_SIKEP434R2_ASM)
if (s2n_sikep434r2_asm_is_enabled()) {
fpadd434_asm(a, b, c);
return;
}
#endif
unsigned int i, carry = 0;
digit_t mask;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(carry, a[i], b[i], carry, c[i]);
}
carry = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(carry, c[i], ((const digit_t *) p434x2)[i], carry, c[i]);
}
mask = 0 - (digit_t) carry;
carry = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(carry, c[i], ((const digit_t *) p434x2)[i] & mask, carry, c[i]);
}
}
// Modular subtraction, c = a-b mod p434.
// Inputs: a, b in [0, 2*p434-1]
// Output: c in [0, 2*p434-1]
void fpsub434(const digit_t *a, const digit_t *b, digit_t *c) {
#if defined(S2N_SIKEP434R2_ASM)
if (s2n_sikep434r2_asm_is_enabled()) {
fpsub434_asm(a, b, c);
return;
}
#endif
unsigned int i, borrow = 0;
digit_t mask;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, a[i], b[i], borrow, c[i]);
}
mask = 0 - (digit_t) borrow;
borrow = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(borrow, c[i], ((const digit_t *) p434x2)[i] & mask, borrow, c[i]);
}
}
// Modular negation, a = -a mod p434.
// Input/output: a in [0, 2*p434-1]
void fpneg434(digit_t *a) {
unsigned int i, borrow = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, ((const digit_t *) p434x2)[i], a[i], borrow, a[i]);
}
}
// Modular division by two, c = a/2 mod p434.
// Input : a in [0, 2*p434-1]
// Output: c in [0, 2*p434-1]
void fpdiv2_434(const digit_t *a, digit_t *c) {
unsigned int i, carry = 0;
digit_t mask;
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p434
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(carry, a[i], ((const digit_t *) p434)[i] & mask, carry, c[i]);
}
mp_shiftr1(c, NWORDS_FIELD);
}
// Modular correction to reduce field element a in [0, 2*p434-1] to [0, p434-1].
void fpcorrection434(digit_t *a) {
unsigned int i, borrow = 0;
digit_t mask;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, a[i], ((const digit_t *) p434)[i], borrow, a[i]);
}
mask = 0 - (digit_t) borrow;
borrow = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(borrow, a[i], ((const digit_t *) p434)[i] & mask, borrow, a[i]);
}
}
// Digit multiplication, digit * digit -> 2-digit result
void digit_x_digit(const digit_t a, const digit_t b, digit_t *c) {
register digit_t al, ah, bl, bh, temp;
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t) * 4), mask_high = (digit_t)(-1) << (sizeof(digit_t) * 4);
al = a & mask_low; // Low part
ah = a >> (sizeof(digit_t) * 4); // High part
bl = b & mask_low;
bh = b >> (sizeof(digit_t) * 4);
albl = al * bl;
albh = al * bh;
ahbl = ah * bl;
ahbh = ah * bh;
c[0] = albl & mask_low; // C00
res1 = albl >> (sizeof(digit_t) * 4);
res2 = ahbl & mask_low;
res3 = albh & mask_low;
temp = res1 + res2 + res3;
carry = temp >> (sizeof(digit_t) * 4);
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
res1 = ahbl >> (sizeof(digit_t) * 4);
res2 = albh >> (sizeof(digit_t) * 4);
res3 = ahbh & mask_low;
temp = res1 + res2 + res3 + carry;
c[1] = temp & mask_low; // C10
carry = temp & mask_high;
c[1] ^= (ahbh & mask_high) + carry; // C11
}
// Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
void mp_mul(const digit_t *a, const digit_t *b, digit_t *c, const unsigned int nwords) {
#if defined(S2N_SIKEP434R2_ASM)
if (s2n_sikep434r2_asm_is_enabled()) {
UNREFERENCED_PARAMETER(nwords);
mul434_asm(a, b, c);
return;
}
#endif
unsigned int i, j, carry;
digit_t t = 0, u = 0, v = 0, UV[2];
for (i = 0; i < nwords; i++) {
for (j = 0; j <= i; j++) {
MUL(a[j], b[i - j], UV + 1, UV[0]);
ADDC(0, UV[0], v, carry, v);
ADDC(carry, UV[1], u, carry, u);
t += carry;
}
c[i] = v;
v = u;
u = t;
t = 0;
}
for (i = nwords; i < 2 * nwords - 1; i++) {
for (j = i - nwords + 1; j < nwords; j++) {
MUL(a[j], b[i - j], UV + 1, UV[0]);
ADDC(0, UV[0], v, carry, v);
ADDC(carry, UV[1], u, carry, u);
t += carry;
}
c[i] = v;
v = u;
u = t;
t = 0;
}
c[2 * nwords - 1] = v;
}
// Efficient Montgomery reduction using comba and exploiting the special form of the prime p434.
// mc = ma*R^-1 mod p434x2, where R = 2^448.
// If ma < 2^448*p434, the output mc is in the range [0, 2*p434-1].
// ma is assumed to be in Montgomery representation.
void rdc_mont(const digit_t *ma, digit_t *mc) {
#if defined(S2N_SIKEP434R2_ASM)
if (s2n_sikep434r2_asm_is_enabled()) {
rdc434_asm(ma, mc);
return;
}
#endif
unsigned int i, j, carry, count = p434_ZERO_WORDS;
digit_t UV[2], t = 0, u = 0, v = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
mc[i] = 0;
}
for (i = 0; i < NWORDS_FIELD; i++) {
for (j = 0; j < i; j++) {
if (j < (i - p434_ZERO_WORDS + 1)) {
MUL(mc[j], ((const digit_t *) p434p1)[i - j], UV + 1, UV[0]);
ADDC(0, UV[0], v, carry, v);
ADDC(carry, UV[1], u, carry, u);
t += carry;
}
}
ADDC(0, v, ma[i], carry, v);
ADDC(carry, u, 0, carry, u);
t += carry;
mc[i] = v;
v = u;
u = t;
t = 0;
}
for (i = NWORDS_FIELD; i < 2 * NWORDS_FIELD - 1; i++) {
if (count > 0) {
count -= 1;
}
for (j = i - NWORDS_FIELD + 1; j < NWORDS_FIELD; j++) {
if (j < (NWORDS_FIELD - count)) {
MUL(mc[j], ((const digit_t *) p434p1)[i - j], UV + 1, UV[0]);
ADDC(0, UV[0], v, carry, v);
ADDC(carry, UV[1], u, carry, u);
t += carry;
}
}
ADDC(0, v, ma[i], carry, v);
ADDC(carry, u, 0, carry, u);
t += carry;
mc[i - NWORDS_FIELD] = v;
v = u;
u = t;
t = 0;
}
/* `carry` isn't read after this, but it's still a necessary argument to the macro */
/* cppcheck-suppress unreadVariable */
ADDC(0, v, ma[2 * NWORDS_FIELD - 1], carry, v);
mc[NWORDS_FIELD - 1] = v;
}
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