694 lines
22 KiB
C
694 lines
22 KiB
C
#include <stdbool.h>
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#include <stdint.h>
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#include <immintrin.h>
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#include <string.h>
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typedef uint64_t fe4[4];
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typedef uint8_t fiat_uint1;
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typedef int8_t fiat_int1;
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static __inline__ uint64_t fiat_value_barrier_u64(uint64_t a) {
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__asm__("" : "+r"(a) : /* no inputs */);
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return a;
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}
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__attribute__((target("adx,bmi2")))
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static inline void fe4_mul(fe4 out, const fe4 x, const fe4 y) { fiat_curve25519_adx_mul(out, x, y); }
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__attribute__((target("adx,bmi2")))
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static inline void fe4_sq(fe4 out, const fe4 x) { fiat_curve25519_adx_square(out, x); }
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/*
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* The function fiat_mulx_u64 is a multiplication, returning the full double-width result.
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*
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* Postconditions:
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* out1 = (arg1 * arg2) mod 2^64
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* out2 = ⌊arg1 * arg2 / 2^64⌋
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*
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* Input Bounds:
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* arg1: [0x0 ~> 0xffffffffffffffff]
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* arg2: [0x0 ~> 0xffffffffffffffff]
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* Output Bounds:
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* out1: [0x0 ~> 0xffffffffffffffff]
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* out2: [0x0 ~> 0xffffffffffffffff]
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*/
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__attribute__((target("adx,bmi2")))
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static inline void fiat_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) {
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// NOTE: edited after generation
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#if defined(_M_X64)
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unsigned long long t;
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*out1 = _umul128(arg1, arg2, &t);
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*out2 = t;
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#elif defined(_M_ARM64)
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*out1 = arg1 * arg2;
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*out2 = __umulh(arg1, arg2);
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#else
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unsigned __int128 t = (unsigned __int128)arg1 * arg2;
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*out1 = t;
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*out2 = (t >> 64);
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#endif
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}
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/*
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* The function fiat_addcarryx_u64 is an addition with carry.
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*
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* Postconditions:
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* out1 = (arg1 + arg2 + arg3) mod 2^64
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* out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋
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*
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* Input Bounds:
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* arg1: [0x0 ~> 0x1]
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* arg2: [0x0 ~> 0xffffffffffffffff]
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* arg3: [0x0 ~> 0xffffffffffffffff]
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* Output Bounds:
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* out1: [0x0 ~> 0xffffffffffffffff]
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* out2: [0x0 ~> 0x1]
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*/
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__attribute__((target("adx,bmi2")))
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static inline void fiat_addcarryx_u64(uint64_t* out1, fiat_uint1* out2, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) {
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// NOTE: edited after generation
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#if defined(__has_builtin)
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# if __has_builtin(__builtin_ia32_addcarryx_u64)
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# define addcarry64 __builtin_ia32_addcarryx_u64
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# endif
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#endif
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#if defined(addcarry64)
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long long unsigned int t;
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*out2 = addcarry64(arg1, arg2, arg3, &t);
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*out1 = t;
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#elif defined(_M_X64)
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long long unsigned int t;
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*out2 = _addcarry_u64(arg1, arg2, arg3, out1);
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*out1 = t;
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#else
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arg2 += arg1;
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arg1 = arg2 < arg1;
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uint64_t ret = arg2 + arg3;
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arg1 += ret < arg2;
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*out1 = ret;
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*out2 = arg1;
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#endif
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#undef addcarry64
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}
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/*
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* The function fiat_subborrowx_u64 is a subtraction with borrow.
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*
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* Postconditions:
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* out1 = (-arg1 + arg2 + -arg3) mod 2^64
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* out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋
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*
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* Input Bounds:
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* arg1: [0x0 ~> 0x1]
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* arg2: [0x0 ~> 0xffffffffffffffff]
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* arg3: [0x0 ~> 0xffffffffffffffff]
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* Output Bounds:
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* out1: [0x0 ~> 0xffffffffffffffff]
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* out2: [0x0 ~> 0x1]
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*/
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__attribute__((target("adx,bmi2")))
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static inline void fiat_subborrowx_u64(uint64_t* out1, fiat_uint1* out2, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) {
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#if defined(__has_builtin)
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# if __has_builtin(__builtin_ia32_subborrow_u64)
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# define subborrow64 __builtin_ia32_subborrow_u64
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# endif
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#endif
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#if defined(subborrow64)
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long long unsigned int t;
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*out2 = subborrow64(arg1, arg2, arg3, &t);
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*out1 = t;
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#elif defined(_M_X64)
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long long unsigned int t;
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*out2 = _subborrow_u64(arg1, arg2, arg3, &t); // NOTE: edited after generation
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*out1 = t;
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#else
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*out1 = arg2 - arg3 - arg1;
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*out2 = (arg2 < arg3) | ((arg2 == arg3) & arg1);
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#endif
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#undef subborrow64
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}
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/*
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* The function fiat_cmovznz_u64 is a single-word conditional move.
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*
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* Postconditions:
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* out1 = (if arg1 = 0 then arg2 else arg3)
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*
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* Input Bounds:
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* arg1: [0x0 ~> 0x1]
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* arg2: [0x0 ~> 0xffffffffffffffff]
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* arg3: [0x0 ~> 0xffffffffffffffff]
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* Output Bounds:
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* out1: [0x0 ~> 0xffffffffffffffff]
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*/
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__attribute__((target("adx,bmi2")))
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static inline void fiat_cmovznz_u64(uint64_t* out1, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) {
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fiat_uint1 x1;
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uint64_t x2;
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uint64_t x3;
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x1 = (!(!arg1));
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x2 = ((fiat_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
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x3 = ((fiat_value_barrier_u64(x2) & arg3) | (fiat_value_barrier_u64((~x2)) & arg2));
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*out1 = x3;
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}
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/*
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* Input Bounds:
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* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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__attribute__((target("adx,bmi2")))
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static void fe4_add(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) {
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uint64_t x1;
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fiat_uint1 x2;
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uint64_t x3;
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fiat_uint1 x4;
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uint64_t x5;
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fiat_uint1 x6;
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uint64_t x7;
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fiat_uint1 x8;
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uint64_t x9;
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uint64_t x10;
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fiat_uint1 x11;
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uint64_t x12;
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fiat_uint1 x13;
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uint64_t x14;
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fiat_uint1 x15;
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uint64_t x16;
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fiat_uint1 x17;
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uint64_t x18;
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uint64_t x19;
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fiat_uint1 x20;
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fiat_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
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fiat_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
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fiat_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
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fiat_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
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fiat_cmovznz_u64(&x9, x8, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and
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fiat_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
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fiat_addcarryx_u64(&x12, &x13, x11, x3, 0x0);
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fiat_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
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fiat_addcarryx_u64(&x16, &x17, x15, x7, 0x0);
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fiat_cmovznz_u64(&x18, x17, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and
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fiat_addcarryx_u64(&x19, &x20, 0x0, x10, x18);
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out1[0] = x19;
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out1[1] = x12;
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out1[2] = x14;
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out1[3] = x16;
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}
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/*
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* Input Bounds:
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* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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__attribute__((target("adx,bmi2")))
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static void fe4_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) {
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uint64_t x1;
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uint64_t x2;
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fiat_uint1 x3;
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uint64_t x4;
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uint64_t x5;
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fiat_uint1 x6;
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uint64_t x7;
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uint64_t x8;
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fiat_uint1 x9;
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uint64_t x10;
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uint64_t x11;
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fiat_uint1 x12;
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uint64_t x13;
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uint64_t x14;
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fiat_uint1 x15;
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uint64_t x16;
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fiat_uint1 x17;
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uint64_t x18;
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fiat_uint1 x19;
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uint64_t x20;
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fiat_uint1 x21;
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uint64_t x22;
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uint64_t x23;
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fiat_uint1 x24;
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x1 = (arg2[0]);
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fiat_subborrowx_u64(&x2, &x3, 0x0, (arg1[0]), x1);
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x4 = (arg2[1]);
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fiat_subborrowx_u64(&x5, &x6, x3, (arg1[1]), x4);
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x7 = (arg2[2]);
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fiat_subborrowx_u64(&x8, &x9, x6, (arg1[2]), x7);
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x10 = (arg2[3]);
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fiat_subborrowx_u64(&x11, &x12, x9, (arg1[3]), x10);
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fiat_cmovznz_u64(&x13, x12, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and
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fiat_subborrowx_u64(&x14, &x15, 0x0, x2, x13);
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fiat_subborrowx_u64(&x16, &x17, x15, x5, 0x0);
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fiat_subborrowx_u64(&x18, &x19, x17, x8, 0x0);
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fiat_subborrowx_u64(&x20, &x21, x19, x11, 0x0);
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fiat_cmovznz_u64(&x22, x21, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and
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fiat_subborrowx_u64(&x23, &x24, 0x0, x14, x22);
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out1[0] = x23;
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out1[1] = x16;
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out1[2] = x18;
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out1[3] = x20;
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}
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/*
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* Input Bounds:
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* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* arg2: [0x0 ~> 0x3ffffffffffffff] // NOTE: this is not any uint64!
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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__attribute__((target("adx,bmi2")))
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static void fe4_scmul(uint64_t out1[4], const uint64_t arg1[4], uint64_t arg2) {
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uint64_t x1;
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uint64_t x2;
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uint64_t x3;
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uint64_t x4;
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uint64_t x5;
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fiat_uint1 x6;
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uint64_t x7;
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uint64_t x8;
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uint64_t x9;
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fiat_uint1 x10;
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uint64_t x11;
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uint64_t x12;
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uint64_t x13;
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fiat_uint1 x14;
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uint64_t x15;
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uint64_t x16;
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uint64_t x17;
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fiat_uint1 x18;
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uint64_t x19;
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fiat_uint1 x20;
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uint64_t x21;
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fiat_uint1 x22;
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uint64_t x23;
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fiat_uint1 x24;
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uint64_t x25;
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uint64_t x26;
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fiat_uint1 x27;
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fiat_mulx_u64(&x1, &x2, (arg1[0]), arg2);
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fiat_mulx_u64(&x3, &x4, (arg1[1]), arg2);
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fiat_addcarryx_u64(&x5, &x6, 0x0, x2, x3);
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fiat_mulx_u64(&x7, &x8, (arg1[2]), arg2);
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fiat_addcarryx_u64(&x9, &x10, x6, x4, x7);
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fiat_mulx_u64(&x11, &x12, (arg1[3]), arg2);
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fiat_addcarryx_u64(&x13, &x14, x10, x8, x11);
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fiat_mulx_u64(&x15, &x16, (x12 + (uint64_t)x14), UINT8_C(0x26));
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fiat_addcarryx_u64(&x17, &x18, 0x0, x1, x15);
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fiat_addcarryx_u64(&x19, &x20, x18, x5, 0x0);
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fiat_addcarryx_u64(&x21, &x22, x20, x9, 0x0);
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fiat_addcarryx_u64(&x23, &x24, x22, x13, 0x0);
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fiat_cmovznz_u64(&x25, x24, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and
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fiat_addcarryx_u64(&x26, &x27, 0x0, x17, x25);
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out1[0] = x26;
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out1[1] = x19;
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out1[2] = x21;
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out1[3] = x23;
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}
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/*
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* Input Bounds:
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* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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__attribute__((target("adx,bmi2")))
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static void fe4_canon(uint64_t out1[4], const uint64_t arg1[4]) {
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uint64_t x1;
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fiat_uint1 x2;
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uint64_t x3;
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fiat_uint1 x4;
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uint64_t x5;
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fiat_uint1 x6;
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uint64_t x7;
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fiat_uint1 x8;
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uint64_t x9;
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uint64_t x10;
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uint64_t x11;
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uint64_t x12;
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uint64_t x13;
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fiat_uint1 x14;
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uint64_t x15;
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fiat_uint1 x16;
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uint64_t x17;
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fiat_uint1 x18;
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uint64_t x19;
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fiat_uint1 x20;
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uint64_t x21;
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uint64_t x22;
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uint64_t x23;
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uint64_t x24;
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fiat_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), UINT64_C(0xffffffffffffffed));
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fiat_subborrowx_u64(&x3, &x4, x2, (arg1[1]), UINT64_C(0xffffffffffffffff));
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fiat_subborrowx_u64(&x5, &x6, x4, (arg1[2]), UINT64_C(0xffffffffffffffff));
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fiat_subborrowx_u64(&x7, &x8, x6, (arg1[3]), UINT64_C(0x7fffffffffffffff));
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fiat_cmovznz_u64(&x9, x8, x1, (arg1[0]));
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fiat_cmovznz_u64(&x10, x8, x3, (arg1[1]));
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fiat_cmovznz_u64(&x11, x8, x5, (arg1[2]));
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fiat_cmovznz_u64(&x12, x8, x7, (arg1[3]));
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fiat_subborrowx_u64(&x13, &x14, 0x0, x9, UINT64_C(0xffffffffffffffed));
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fiat_subborrowx_u64(&x15, &x16, x14, x10, UINT64_C(0xffffffffffffffff));
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fiat_subborrowx_u64(&x17, &x18, x16, x11, UINT64_C(0xffffffffffffffff));
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fiat_subborrowx_u64(&x19, &x20, x18, x12, UINT64_C(0x7fffffffffffffff));
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fiat_cmovznz_u64(&x21, x20, x13, x9);
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fiat_cmovznz_u64(&x22, x20, x15, x10);
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fiat_cmovznz_u64(&x23, x20, x17, x11);
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fiat_cmovznz_u64(&x24, x20, x19, x12);
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out1[0] = x21;
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out1[1] = x22;
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out1[2] = x23;
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out1[3] = x24;
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}
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/*
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* Input Bounds:
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* arg1: [0x0 ~> 0x1]
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* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* Output Bounds:
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* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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* out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
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*/
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__attribute__((target("adx,bmi2")))
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static void fe4_cswap(uint64_t out1[4], uint64_t out2[4], fiat_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) {
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uint64_t x1;
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uint64_t x2;
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uint64_t x3;
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uint64_t x4;
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uint64_t x5;
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uint64_t x6;
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uint64_t x7;
|
|
uint64_t x8;
|
|
// NOTE: clang 14 for Zen 2 uses YMM registers
|
|
fiat_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
|
|
fiat_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
|
|
fiat_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
|
|
fiat_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
|
|
fiat_cmovznz_u64(&x5, arg1, (arg3[0]), (arg2[0]));
|
|
fiat_cmovznz_u64(&x6, arg1, (arg3[1]), (arg2[1]));
|
|
fiat_cmovznz_u64(&x7, arg1, (arg3[2]), (arg2[2]));
|
|
fiat_cmovznz_u64(&x8, arg1, (arg3[3]), (arg2[3]));
|
|
out1[0] = x1;
|
|
out1[1] = x2;
|
|
out1[2] = x3;
|
|
out1[3] = x4;
|
|
out2[0] = x5;
|
|
out2[1] = x6;
|
|
out2[2] = x7;
|
|
out2[3] = x8;
|
|
}
|
|
|
|
// The following functions are adaped from crypto/curve25519/curve25519.c
|
|
// It would be desirable to share the code, but with the current field
|
|
// implementations both 4-limb and 5-limb versions of the curve-level code need
|
|
// to be included in builds targetting an unknown variant of x86_64.
|
|
|
|
__attribute__((target("adx,bmi2")))
|
|
static void fe4_invert(fe4 out, const fe4 z) {
|
|
fe4 t0;
|
|
fe4 t1;
|
|
fe4 t2;
|
|
fe4 t3;
|
|
int i;
|
|
|
|
fe4_sq(t0, z);
|
|
fe4_sq(t1, t0);
|
|
for (i = 1; i < 2; ++i) {
|
|
fe4_sq(t1, t1);
|
|
}
|
|
fe4_mul(t1, z, t1);
|
|
fe4_mul(t0, t0, t1);
|
|
fe4_sq(t2, t0);
|
|
fe4_mul(t1, t1, t2);
|
|
fe4_sq(t2, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe4_sq(t2, t2);
|
|
}
|
|
fe4_mul(t1, t2, t1);
|
|
fe4_sq(t2, t1);
|
|
for (i = 1; i < 10; ++i) {
|
|
fe4_sq(t2, t2);
|
|
}
|
|
fe4_mul(t2, t2, t1);
|
|
fe4_sq(t3, t2);
|
|
for (i = 1; i < 20; ++i) {
|
|
fe4_sq(t3, t3);
|
|
}
|
|
fe4_mul(t2, t3, t2);
|
|
fe4_sq(t2, t2);
|
|
for (i = 1; i < 10; ++i) {
|
|
fe4_sq(t2, t2);
|
|
}
|
|
fe4_mul(t1, t2, t1);
|
|
fe4_sq(t2, t1);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe4_sq(t2, t2);
|
|
}
|
|
fe4_mul(t2, t2, t1);
|
|
fe4_sq(t3, t2);
|
|
for (i = 1; i < 100; ++i) {
|
|
fe4_sq(t3, t3);
|
|
}
|
|
fe4_mul(t2, t3, t2);
|
|
fe4_sq(t2, t2);
|
|
for (i = 1; i < 50; ++i) {
|
|
fe4_sq(t2, t2);
|
|
}
|
|
fe4_mul(t1, t2, t1);
|
|
fe4_sq(t1, t1);
|
|
for (i = 1; i < 5; ++i) {
|
|
fe4_sq(t1, t1);
|
|
}
|
|
fe4_mul(out, t1, t0);
|
|
}
|
|
|
|
__attribute__((noinline)) // https://github.com/rust-lang/rust/issues/116573
|
|
__attribute__((target("adx,bmi2")))
|
|
void x25519_scalar_mult_adx(uint8_t out[32], const uint8_t scalar[32],
|
|
const uint8_t point[32]) {
|
|
uint8_t e[32];
|
|
memcpy(e, scalar, 32);
|
|
e[0] &= 248;
|
|
e[31] &= 127;
|
|
e[31] |= 64;
|
|
|
|
// The following implementation was transcribed to Coq and proven to
|
|
// correspond to unary scalar multiplication in affine coordinates given that
|
|
// x1 != 0 is the x coordinate of some point on the curve. It was also checked
|
|
// in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2
|
|
// = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the
|
|
// underlying field, so it applies to Curve25519 itself and the quadratic
|
|
// twist of Curve25519. It was not proven in Coq that prime-field arithmetic
|
|
// correctly simulates extension-field arithmetic on prime-field values.
|
|
// The decoding of the byte array representation of e was not considered.
|
|
// Specification of Montgomery curves in affine coordinates:
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
|
|
// Proof that these form a group that is isomorphic to a Weierstrass curve:
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
|
|
// Coq transcription and correctness proof of the loop (where scalarbits=255):
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
|
|
// preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0
|
|
fe4 x1, x2 = {1}, z2 = {0}, x3, z3 = {1}, tmp0, tmp1;
|
|
OPENSSL_memcpy(x1, point, sizeof(fe4));
|
|
x1[3] &= (uint64_t)(-1)>>1;
|
|
OPENSSL_memcpy(x3, x1, sizeof(fe4));
|
|
|
|
unsigned swap = 0;
|
|
int pos;
|
|
for (pos = 254; pos >= 0; --pos) {
|
|
// loop invariant as of right before the test, for the case where x1 != 0:
|
|
// pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero
|
|
// let r := e >> (pos+1) in the following equalities of projective points:
|
|
// to_xz (r*P) === if swap then (x3, z3) else (x2, z2)
|
|
// to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
|
|
// x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P)
|
|
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
|
|
swap ^= b;
|
|
fe4_cswap(x2, x3, swap, x2, x3);
|
|
fe4_cswap(z2, z3, swap, z2, z3);
|
|
swap = b;
|
|
// Coq transcription of ladderstep formula (called from transcribed loop):
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
|
|
// <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
|
|
// x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
|
|
// x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
|
|
fe4_sub(tmp0, x3, z3);
|
|
fe4_sub(tmp1, x2, z2);
|
|
fe4_add(x2, x2, z2);
|
|
fe4_add(z2, x3, z3);
|
|
fe4_mul(z3, tmp0, x2);
|
|
fe4_mul(z2, z2, tmp1);
|
|
fe4_sq(tmp0, tmp1);
|
|
fe4_sq(tmp1, x2);
|
|
fe4_add(x3, z3, z2);
|
|
fe4_sub(z2, z3, z2);
|
|
fe4_mul(x2, tmp1, tmp0);
|
|
fe4_sub(tmp1, tmp1, tmp0);
|
|
fe4_sq(z2, z2);
|
|
fe4_scmul(z3, tmp1, 121666);
|
|
fe4_sq(x3, x3);
|
|
fe4_add(tmp0, tmp0, z3);
|
|
fe4_mul(z3, x1, z2);
|
|
fe4_mul(z2, tmp1, tmp0);
|
|
}
|
|
// here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2)
|
|
fe4_cswap(x2, x3, swap, x2, x3);
|
|
fe4_cswap(z2, z3, swap, z2, z3);
|
|
|
|
fe4_invert(z2, z2);
|
|
fe4_mul(x2, x2, z2);
|
|
fe4_canon(x2, x2);
|
|
OPENSSL_memcpy(out, x2, sizeof(fe4));
|
|
}
|
|
|
|
typedef struct {
|
|
fe4 X;
|
|
fe4 Y;
|
|
fe4 Z;
|
|
fe4 T;
|
|
} ge_p3_4;
|
|
|
|
typedef struct {
|
|
fe4 yplusx;
|
|
fe4 yminusx;
|
|
fe4 xy2d;
|
|
} ge_precomp_4;
|
|
|
|
__attribute__((target("adx,bmi2")))
|
|
static void inline_x25519_ge_dbl_4(ge_p3_4 *r, const ge_p3_4 *p, bool skip_t) {
|
|
// Transcribed from a Coq function proven against affine coordinates.
|
|
// https://github.com/mit-plv/fiat-crypto/blob/9943ba9e7d8f3e1c0054b2c94a5edca46ea73ef8/src/Curves/Edwards/XYZT/Basic.v#L136-L165
|
|
fe4 trX, trZ, trT, t0, cX, cY, cZ, cT;
|
|
fe4_sq(trX, p->X);
|
|
fe4_sq(trZ, p->Y);
|
|
fe4_sq(trT, p->Z);
|
|
fe4_add(trT, trT, trT);
|
|
fe4_add(cY, p->X, p->Y);
|
|
fe4_sq(t0, cY);
|
|
fe4_add(cY, trZ, trX);
|
|
fe4_sub(cZ, trZ, trX);
|
|
fe4_sub(cX, t0, cY);
|
|
fe4_sub(cT, trT, cZ);
|
|
fe4_mul(r->X, cX, cT);
|
|
fe4_mul(r->Y, cY, cZ);
|
|
fe4_mul(r->Z, cZ, cT);
|
|
if (!skip_t) {
|
|
fe4_mul(r->T, cX, cY);
|
|
}
|
|
}
|
|
|
|
__attribute__((target("adx,bmi2")))
|
|
__attribute__((always_inline)) // 4% speedup with clang14 and zen2
|
|
static inline void
|
|
ge_p3_add_p3_precomp_4(ge_p3_4 *r, const ge_p3_4 *p, const ge_precomp_4 *q) {
|
|
fe4 A, B, C, YplusX, YminusX, D, X3, Y3, Z3, T3;
|
|
// Transcribed from a Coq function proven against affine coordinates.
|
|
// https://github.com/mit-plv/fiat-crypto/blob/a36568d1d73aff5d7accc79fd28be672882f9c17/src/Curves/Edwards/XYZT/Precomputed.v#L38-L56
|
|
fe4_add(YplusX, p->Y, p->X);
|
|
fe4_sub(YminusX, p->Y, p->X);
|
|
fe4_mul(A, YplusX, q->yplusx);
|
|
fe4_mul(B, YminusX, q->yminusx);
|
|
fe4_mul(C, q->xy2d, p->T);
|
|
fe4_add(D, p->Z, p->Z);
|
|
fe4_sub(X3, A, B);
|
|
fe4_add(Y3, A, B);
|
|
fe4_add(Z3, D, C);
|
|
fe4_sub(T3, D, C);
|
|
fe4_mul(r->X, X3, T3);
|
|
fe4_mul(r->Y, Y3, Z3);
|
|
fe4_mul(r->Z, Z3, T3);
|
|
fe4_mul(r->T, X3, Y3);
|
|
}
|
|
|
|
__attribute__((always_inline)) // 25% speedup with clang14 and zen2
|
|
static inline void table_select_4(ge_precomp_4 *t, const int pos,
|
|
const signed char b) {
|
|
uint8_t bnegative = constant_time_msb_w(b);
|
|
uint8_t babs = b - ((bnegative & b) << 1);
|
|
|
|
uint8_t t_bytes[3][32] = {
|
|
{constant_time_is_zero_w(b) & 1}, {constant_time_is_zero_w(b) & 1}, {0}};
|
|
#if defined(__clang__)
|
|
__asm__("" : "+m" (t_bytes) : /*no inputs*/);
|
|
#endif
|
|
OPENSSL_STATIC_ASSERT(sizeof(t_bytes) == sizeof(k25519Precomp[pos][0]), "");
|
|
for (int i = 0; i < 8; i++) {
|
|
constant_time_conditional_memxor(t_bytes, k25519Precomp[pos][i],
|
|
sizeof(t_bytes),
|
|
constant_time_eq_w(babs, 1 + i));
|
|
}
|
|
|
|
OPENSSL_STATIC_ASSERT(sizeof(t_bytes) == sizeof(ge_precomp_4), "");
|
|
|
|
// fe4 uses saturated 64-bit limbs, so converting from bytes is just a copy.
|
|
OPENSSL_memcpy(t, t_bytes, sizeof(ge_precomp_4));
|
|
|
|
fe4 xy2d_neg = {0};
|
|
fe4_sub(xy2d_neg, xy2d_neg, t->xy2d);
|
|
constant_time_conditional_memcpy(t->yplusx, t_bytes[1], sizeof(fe4),
|
|
bnegative);
|
|
constant_time_conditional_memcpy(t->yminusx, t_bytes[0], sizeof(fe4),
|
|
bnegative);
|
|
constant_time_conditional_memcpy(t->xy2d, xy2d_neg, sizeof(fe4), bnegative);
|
|
}
|
|
|
|
// h = a * B
|
|
// where a = a[0]+256*a[1]+...+256^31 a[31]
|
|
// B is the Ed25519 base point (x,4/5) with x positive.
|
|
//
|
|
// Preconditions:
|
|
// a[31] <= 127
|
|
__attribute__((noinline)) // https://github.com/rust-lang/rust/issues/116573
|
|
__attribute__((target("adx,bmi2")))
|
|
void x25519_ge_scalarmult_base_adx(uint8_t h[4][32], const uint8_t a[32]) {
|
|
signed char e[64];
|
|
signed char carry;
|
|
|
|
for (unsigned i = 0; i < 32; ++i) {
|
|
e[2 * i + 0] = (a[i] >> 0) & 15;
|
|
e[2 * i + 1] = (a[i] >> 4) & 15;
|
|
}
|
|
// each e[i] is between 0 and 15
|
|
// e[63] is between 0 and 7
|
|
|
|
carry = 0;
|
|
for (unsigned i = 0; i < 63; ++i) {
|
|
e[i] += carry;
|
|
carry = e[i] + 8;
|
|
carry >>= 4;
|
|
e[i] -= carry << 4;
|
|
}
|
|
e[63] += carry;
|
|
// each e[i] is between -8 and 8
|
|
|
|
ge_p3_4 r = {{0}, {1}, {1}, {0}};
|
|
for (unsigned i = 1; i < 64; i += 2) {
|
|
ge_precomp_4 t;
|
|
table_select_4(&t, i / 2, e[i]);
|
|
ge_p3_add_p3_precomp_4(&r, &r, &t);
|
|
}
|
|
|
|
inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true);
|
|
inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true);
|
|
inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true);
|
|
inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/false);
|
|
|
|
for (unsigned i = 0; i < 64; i += 2) {
|
|
ge_precomp_4 t;
|
|
table_select_4(&t, i / 2, e[i]);
|
|
ge_p3_add_p3_precomp_4(&r, &r, &t);
|
|
}
|
|
|
|
// fe4 uses saturated 64-bit limbs, so converting to bytes is just a copy.
|
|
// Satisfy stated precondition of fiat_25519_from_bytes; tests pass either way
|
|
fe4_canon(r.X, r.X);
|
|
fe4_canon(r.Y, r.Y);
|
|
fe4_canon(r.Z, r.Z);
|
|
fe4_canon(r.T, r.T);
|
|
OPENSSL_STATIC_ASSERT(sizeof(ge_p3_4) == sizeof(uint8_t[4][32]), "");
|
|
OPENSSL_memcpy(h, &r, sizeof(ge_p3_4));
|
|
}
|