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Diffstat (limited to 'src/third_party/sike/fpx.c')
-rw-r--r-- | src/third_party/sike/fpx.c | 283 |
1 files changed, 283 insertions, 0 deletions
diff --git a/src/third_party/sike/fpx.c b/src/third_party/sike/fpx.c new file mode 100644 index 00000000..9917116c --- /dev/null +++ b/src/third_party/sike/fpx.c @@ -0,0 +1,283 @@ +/******************************************************************************************** +* SIDH: an efficient supersingular isogeny cryptography library +* +* Abstract: core functions over GF(p) and GF(p^2) +*********************************************************************************************/ +#include <openssl/base.h> + +#include "utils.h" +#include "fpx.h" + +extern const struct params_t sike_params; + +// Multiprecision squaring, c = a^2 mod p. +static void fpsqr_mont(const felm_t ma, felm_t mc) +{ + dfelm_t temp = {0}; + sike_mpmul(ma, ma, temp); + sike_fprdc(temp, mc); +} + +// Chain to compute a^(p-3)/4 using Montgomery arithmetic. +static void fpinv_chain_mont(felm_t a) +{ + unsigned int i, j; + felm_t t[31], tt; + + // Precomputed table + fpsqr_mont(a, tt); + sike_fpmul_mont(a, tt, t[0]); + for (i = 0; i <= 29; i++) sike_fpmul_mont(t[i], tt, t[i+1]); + + sike_fpcopy(a, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[5], tt, tt); + for (i = 0; i < 10; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[14], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[3], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[23], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[13], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[24], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[7], tt, tt); + for (i = 0; i < 8; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[12], tt, tt); + for (i = 0; i < 8; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[30], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[1], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[30], tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[21], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[2], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[19], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[1], tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[24], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[26], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[16], tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[10], tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[6], tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[0], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[20], tt, tt); + for (i = 0; i < 8; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[9], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[25], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[30], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[26], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(a, tt, tt); + for (i = 0; i < 7; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[28], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[6], tt, tt); + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[10], tt, tt); + for (i = 0; i < 9; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[22], tt, tt); + for (j = 0; j < 35; j++) { + for (i = 0; i < 6; i++) fpsqr_mont(tt, tt); + sike_fpmul_mont(t[30], tt, tt); + } + sike_fpcopy(tt, a); +} + +// Field inversion using Montgomery arithmetic, a = a^(-1)*R mod p. +static void fpinv_mont(felm_t a) +{ + felm_t tt = {0}; + sike_fpcopy(a, tt); + fpinv_chain_mont(tt); + fpsqr_mont(tt, tt); + fpsqr_mont(tt, tt); + sike_fpmul_mont(a, tt, a); +} + +// Multiprecision addition, c = a+b, where lng(a) = lng(b) = nwords. Returns the carry bit. +#if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_X86_64) && !defined(OPENSSL_AARCH64)) +inline static unsigned int mp_add(const felm_t a, const felm_t b, felm_t c, const unsigned int nwords) { + uint8_t carry = 0; + for (size_t i = 0; i < nwords; i++) { + ADDC(carry, a[i], b[i], carry, c[i]); + } + return carry; +} + +// Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit. +inline static unsigned int mp_sub(const felm_t a, const felm_t b, felm_t c, const unsigned int nwords) { + uint32_t borrow = 0; + for (size_t i = 0; i < nwords; i++) { + SUBC(borrow, a[i], b[i], borrow, c[i]); + } + return borrow; +} +#endif + +// Multiprecision addition, c = a+b. +inline static void mp_addfast(const felm_t a, const felm_t b, felm_t c) +{ +#if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_X86_64) && !defined(OPENSSL_AARCH64)) + mp_add(a, b, c, NWORDS_FIELD); +#else + sike_mpadd_asm(a, b, c); +#endif +} + +// Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD. +// If c < 0 then returns mask = 0xFF..F, else mask = 0x00..0 +inline static crypto_word_t mp_subfast(const dfelm_t a, const dfelm_t b, dfelm_t c) { +#if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_X86_64) && !defined(OPENSSL_AARCH64)) + return (0 - (crypto_word_t)mp_sub(a, b, c, 2*NWORDS_FIELD)); +#else + return sike_mpsubx2_asm(a, b, c); +#endif +} + +// Multiprecision subtraction, c = c-a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD. +// Inputs should be s.t. c > a and c > b +inline static void mp_dblsubfast(const dfelm_t a, const dfelm_t b, dfelm_t c) { +#if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_X86_64) && !defined(OPENSSL_AARCH64)) + mp_sub(c, a, c, 2*NWORDS_FIELD); + mp_sub(c, b, c, 2*NWORDS_FIELD); +#else + sike_mpdblsubx2_asm(a, b, c); +#endif +} + +// Copy a field element, c = a. +void sike_fpcopy(const felm_t a, felm_t c) { + for (size_t i = 0; i < NWORDS_FIELD; i++) { + c[i] = a[i]; + } +} + +// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod prime, where R=2^768 +void sike_fpmul_mont(const felm_t ma, const felm_t mb, felm_t mc) +{ + dfelm_t temp = {0}; + sike_mpmul(ma, mb, temp); + sike_fprdc(temp, mc); +} + +// Conversion from Montgomery representation to standard representation, +// c = ma*R^(-1) mod p = a mod p, where ma in [0, p-1]. +void sike_from_mont(const felm_t ma, felm_t c) +{ + felm_t one = {0}; + one[0] = 1; + + sike_fpmul_mont(ma, one, c); + sike_fpcorrection(c); +} + +// GF(p^2) squaring using Montgomery arithmetic, c = a^2 in GF(p^2). +// Inputs: a = a0+a1*i, where a0, a1 are in [0, 2*p-1] +// Output: c = c0+c1*i, where c0, c1 are in [0, 2*p-1] +void sike_fp2sqr_mont(const f2elm_t a, f2elm_t c) { + felm_t t1, t2, t3; + + mp_addfast(a->c0, a->c1, t1); // t1 = a0+a1 + sike_fpsub(a->c0, a->c1, t2); // t2 = a0-a1 + mp_addfast(a->c0, a->c0, t3); // t3 = 2a0 + sike_fpmul_mont(t1, t2, c->c0); // c0 = (a0+a1)(a0-a1) + sike_fpmul_mont(t3, a->c1, c->c1); // c1 = 2a0*a1 +} + +// Modular negation, a = -a mod p503. +// Input/output: a in [0, 2*p503-1] +void sike_fpneg(felm_t a) { + uint32_t borrow = 0; + for (size_t i = 0; i < NWORDS_FIELD; i++) { + SUBC(borrow, sike_params.prime_x2[i], a[i], borrow, a[i]); + } +} + +// Modular division by two, c = a/2 mod p503. +// Input : a in [0, 2*p503-1] +// Output: c in [0, 2*p503-1] +void sike_fpdiv2(const felm_t a, felm_t c) { + uint32_t carry = 0; + crypto_word_t mask; + + mask = 0 - (crypto_word_t)(a[0] & 1); // If a is odd compute a+p503 + for (size_t i = 0; i < NWORDS_FIELD; i++) { + ADDC(carry, a[i], sike_params.prime[i] & mask, carry, c[i]); + } + + // Multiprecision right shift by one. + for (size_t i = 0; i < NWORDS_FIELD-1; i++) { + c[i] = (c[i] >> 1) ^ (c[i+1] << (RADIX - 1)); + } + c[NWORDS_FIELD-1] >>= 1; +} + +// Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1]. +void sike_fpcorrection(felm_t a) { + uint32_t borrow = 0; + crypto_word_t mask; + + for (size_t i = 0; i < NWORDS_FIELD; i++) { + SUBC(borrow, a[i], sike_params.prime[i], borrow, a[i]); + } + mask = 0 - (crypto_word_t)borrow; + + borrow = 0; + for (size_t i = 0; i < NWORDS_FIELD; i++) { + ADDC(borrow, a[i], sike_params.prime[i] & mask, borrow, a[i]); + } +} + +// GF(p^2) multiplication using Montgomery arithmetic, c = a*b in GF(p^2). +// Inputs: a = a0+a1*i and b = b0+b1*i, where a0, a1, b0, b1 are in [0, 2*p-1] +// Output: c = c0+c1*i, where c0, c1 are in [0, 2*p-1] +void sike_fp2mul_mont(const f2elm_t a, const f2elm_t b, f2elm_t c) { + felm_t t1, t2; + dfelm_t tt1, tt2, tt3; + crypto_word_t mask; + + mp_addfast(a->c0, a->c1, t1); // t1 = a0+a1 + mp_addfast(b->c0, b->c1, t2); // t2 = b0+b1 + sike_mpmul(a->c0, b->c0, tt1); // tt1 = a0*b0 + sike_mpmul(a->c1, b->c1, tt2); // tt2 = a1*b1 + sike_mpmul(t1, t2, tt3); // tt3 = (a0+a1)*(b0+b1) + mp_dblsubfast(tt1, tt2, tt3); // tt3 = (a0+a1)*(b0+b1) - a0*b0 - a1*b1 + mask = mp_subfast(tt1, tt2, tt1); // tt1 = a0*b0 - a1*b1. If tt1 < 0 then mask = 0xFF..F, else if tt1 >= 0 then mask = 0x00..0 + + for (size_t i = 0; i < NWORDS_FIELD; i++) { + t1[i] = sike_params.prime[i] & mask; + } + + sike_fprdc(tt3, c->c1); // c[1] = (a0+a1)*(b0+b1) - a0*b0 - a1*b1 + mp_addfast(&tt1[NWORDS_FIELD], t1, &tt1[NWORDS_FIELD]); + sike_fprdc(tt1, c->c0); // c[0] = a0*b0 - a1*b1 +} + +// GF(p^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2). +void sike_fp2inv_mont(f2elm_t a) { + f2elm_t t1; + + fpsqr_mont(a->c0, t1->c0); // t10 = a0^2 + fpsqr_mont(a->c1, t1->c1); // t11 = a1^2 + sike_fpadd(t1->c0, t1->c1, t1->c0); // t10 = a0^2+a1^2 + fpinv_mont(t1->c0); // t10 = (a0^2+a1^2)^-1 + sike_fpneg(a->c1); // a = a0-i*a1 + sike_fpmul_mont(a->c0, t1->c0, a->c0); + sike_fpmul_mont(a->c1, t1->c0, a->c1); // a = (a0-i*a1)*(a0^2+a1^2)^-1 +} |