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/********************************************************************************************
* SIDH: an efficient supersingular isogeny cryptography library
*
* Abstract: portable modular arithmetic for P503
*********************************************************************************************/
#include <openssl/base.h>
#if defined(OPENSSL_NO_ASM) || \
(!defined(OPENSSL_X86_64) && !defined(OPENSSL_AARCH64))
#include "../utils.h"
#include "../fpx.h"
// Global constants
extern const struct params_t sike_params;
static void digit_x_digit(const crypto_word_t a, const crypto_word_t b, crypto_word_t* c)
{ // Digit multiplication, digit * digit -> 2-digit result
crypto_word_t al, ah, bl, bh, temp;
crypto_word_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
crypto_word_t mask_low = (crypto_word_t)(-1) >> (sizeof(crypto_word_t)*4);
crypto_word_t mask_high = (crypto_word_t)(-1) << (sizeof(crypto_word_t)*4);
al = a & mask_low; // Low part
ah = a >> (sizeof(crypto_word_t) * 4); // High part
bl = b & mask_low;
bh = b >> (sizeof(crypto_word_t) * 4);
albl = al*bl;
albh = al*bh;
ahbl = ah*bl;
ahbh = ah*bh;
c[0] = albl & mask_low; // C00
res1 = albl >> (sizeof(crypto_word_t) * 4);
res2 = ahbl & mask_low;
res3 = albh & mask_low;
temp = res1 + res2 + res3;
carry = temp >> (sizeof(crypto_word_t) * 4);
c[0] ^= temp << (sizeof(crypto_word_t) * 4); // C01
res1 = ahbl >> (sizeof(crypto_word_t) * 4);
res2 = albh >> (sizeof(crypto_word_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
}
void sike_fpadd(const felm_t a, const felm_t b, felm_t c)
{ // Modular addition, c = a+b mod p434.
// Inputs: a, b in [0, 2*p434-1]
// Output: c in [0, 2*p434-1]
unsigned int i, carry = 0;
crypto_word_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], sike_params.prime_x2[i], carry, c[i]);
}
mask = 0 - (crypto_word_t)carry;
carry = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(carry, c[i], sike_params.prime_x2[i] & mask, carry, c[i]);
}
}
void sike_fpsub(const felm_t a, const felm_t b, felm_t c)
{ // Modular subtraction, c = a-b mod p434.
// Inputs: a, b in [0, 2*p434-1]
// Output: c in [0, 2*p434-1]
unsigned int i, borrow = 0;
crypto_word_t mask;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, a[i], b[i], borrow, c[i]);
}
mask = 0 - (crypto_word_t)borrow;
borrow = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(borrow, c[i], sike_params.prime_x2[i] & mask, borrow, c[i]);
}
}
void sike_mpmul(const felm_t a, const felm_t b, dfelm_t c)
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = NWORDS_FIELD.
unsigned int i, j;
crypto_word_t t = 0, u = 0, v = 0, UV[2];
unsigned int carry = 0;
for (i = 0; i < NWORDS_FIELD; 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_FIELD; i < 2*NWORDS_FIELD-1; i++) {
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; 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_FIELD-1] = v;
}
void sike_fprdc(felm_t ma, felm_t mc)
{ // 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.
unsigned int i, j, carry, count = ZERO_WORDS;
crypto_word_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-ZERO_WORDS+1)) {
MUL(mc[j], sike_params.prime_p1[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], sike_params.prime_p1[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;
}
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
mc[NWORDS_FIELD-1] = v;
}
#endif // NO_ASM || (!X86_64 && !AARCH64)
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