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/********************************************************************************************
* Supersingular Isogeny Key Encapsulation Library
*
* Abstract: portable modular arithmetic for P503
*********************************************************************************************/
#include "sike_r1_namespace.h"
#include "P503_internal_r1.h"
// Global constants
extern const uint64_t p503[NWORDS_FIELD];
extern const uint64_t p503p1[NWORDS_FIELD];
extern const uint64_t p503x2[NWORDS_FIELD];
void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
{ // Modular addition, c = a+b mod p503.
// Inputs: a, b in [0, 2*p503-1]
// Output: c in [0, 2*p503-1]
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*)p503x2)[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*)p503x2)[i] & mask, carry, c[i]);
}
}
void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
{ // Modular subtraction, c = a-b mod p503.
// Inputs: a, b in [0, 2*p503-1]
// Output: c in [0, 2*p503-1]
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*)p503x2)[i] & mask, borrow, c[i]);
}
}
void fpneg503(digit_t* a)
{ // Modular negation, a = -a mod p503.
// Input/output: a in [0, 2*p503-1]
unsigned int i, borrow = 0;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, ((const digit_t*)p503x2)[i], a[i], borrow, a[i]);
}
}
void fpdiv2_503(const digit_t* a, digit_t* c)
{ // Modular division by two, c = a/2 mod p503.
// Input : a in [0, 2*p503-1]
// Output: c in [0, 2*p503-1]
unsigned int i, carry = 0;
digit_t mask;
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p503
for (i = 0; i < NWORDS_FIELD; i++) {
ADDC(carry, a[i], ((const digit_t*)p503)[i] & mask, carry, c[i]);
}
mp_shiftr1(c, NWORDS_FIELD);
}
void fpcorrection503(digit_t* a)
{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
unsigned int i, borrow = 0;
digit_t mask;
for (i = 0; i < NWORDS_FIELD; i++) {
SUBC(borrow, a[i], ((const digit_t*)p503)[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*)p503)[i] & mask, borrow, a[i]);
}
}
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
{ // Digit multiplication, digit * digit -> 2-digit result
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
}
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
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;
}
void rdc_mont(const dfelm_t ma, felm_t mc)
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p503.
// mc = ma*R^-1 mod p503x2, where R = 2^512.
// If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
// ma is assumed to be in Montgomery representation.
unsigned int i, j, carry, count = p503_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-p503_ZERO_WORDS+1)) {
MUL(mc[j], ((const digit_t*)p503p1)[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*)p503p1)[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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