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c-kzg-4844/min-src/c_kzg_4844.c

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/*
* Copyright 2021 Benjamin Edgington
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "c_kzg_4844.h"
#include <inttypes.h>
#include <stdlib.h>
#include <string.h>
/**
* Wrapped `malloc()` that reports failures to allocate.
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of bytes to be allocated
* @retval C_CZK_OK All is well
* @retval C_CZK_MALLOC Memory allocation failed
*/
static C_KZG_RET c_kzg_malloc(void **x, size_t n) {
if (n > 0) {
*x = malloc(n);
return *x != NULL ? C_KZG_OK : C_KZG_MALLOC;
}
*x = NULL;
return C_KZG_OK;
}
#define CHECK(cond) \
if (!(cond)) return C_KZG_BADARGS
#define TRY(result) \
{ \
C_KZG_RET ret = (result); \
if (ret == C_KZG_MALLOC) return ret; \
if (ret != C_KZG_OK) return C_KZG_ERROR; \
}
/**
* Allocate memory for an array of G1 group elements.
*
* @remark Free the space later using `free()`.
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of G1 elements to be allocated
* @retval C_CZK_OK All is well
* @retval C_CZK_MALLOC Memory allocation failed
*/
static C_KZG_RET new_g1_array(g1_t **x, size_t n) {
return c_kzg_malloc((void **)x, n * sizeof **x);
}
/**
* Allocate memory for an array of G2 group elements.
*
* @remark Free the space later using `free()`.
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of G2 elements to be allocated
* @retval C_CZK_OK All is well
* @retval C_CZK_MALLOC Memory allocation failed
*/
static C_KZG_RET new_g2_array(g2_t **x, size_t n) {
return c_kzg_malloc((void **)x, n * sizeof **x);
}
/**
* Allocate memory for an array of field elements.
*
* @remark Free the space later using `free()`.
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of field elements to be allocated
* @retval C_CZK_OK All is well
* @retval C_CZK_MALLOC Memory allocation failed
*/
static C_KZG_RET new_fr_array(fr_t **x, size_t n) {
return c_kzg_malloc((void **)x, n * sizeof **x);
}
/**
* Fast log base 2 of a byte.
*
* Corresponds to the index of the highest bit set in the byte. Adapted from
* https://graphics.stanford.edu/~seander/bithacks.html#IntegerLog.
*
* @param[in] b A non-zero byte
* @return The index of the highest set bit
*/
static int log_2_byte(byte b) {
int r, shift;
r = (b > 0xF) << 2;
b >>= r;
shift = (b > 0x3) << 1;
b >>= (shift + 1);
r |= shift | b;
return r;
}
/** The zero field element */
static const fr_t fr_zero = {0L, 0L, 0L, 0L};
/** This is 1 in Blst's `blst_fr` limb representation. Crazy but true. */
static const fr_t fr_one = {0x00000001fffffffeL, 0x5884b7fa00034802L, 0x998c4fefecbc4ff5L, 0x1824b159acc5056fL};
/**
* Create a field element from an array of four 64-bit unsigned integers.
*
* @param out The field element equivalent of @p vals
* @param vals The array of 64-bit integers to be converted, little-endian ordering of the 64-bit words
*/
static void fr_from_uint64s(fr_t *out, const uint64_t vals[4]) {
blst_fr_from_uint64(out, vals);
}
/**
* Test whether the operand is one in the finite field.
*
* @param p The field element to be checked
* @retval true The element is one
* @retval false The element is not one
*
* @todo See if there is a more efficient way to check for one in the finite field.
*/
static bool fr_is_one(const fr_t *p) {
uint64_t a[4];
blst_uint64_from_fr(a, p);
return a[0] == 1 && a[1] == 0 && a[2] == 0 && a[3] == 0;
}
/**
* Test whether two field elements are equal.
*
* @param[in] aa The first element
* @param[in] bb The second element
* @retval true if @p aa and @p bb are equal
* @retval false otherwise
*/
static bool fr_equal(const fr_t *aa, const fr_t *bb) {
uint64_t a[4], b[4];
blst_uint64_from_fr(a, aa);
blst_uint64_from_fr(b, bb);
return a[0] == b[0] && a[1] == b[1] && a[2] == b[2] && a[3] == b[3];
}
/**
* Add two field elements.
*
* @param[out] out @p a plus @p b in the field
* @param[in] a Field element
* @param[in] b Field element
*/
static void fr_add(fr_t *out, const fr_t *a, const fr_t *b) {
blst_fr_add(out, a, b);
}
/**
* Subtract one field element from another.
*
* @param[out] out @p a minus @p b in the field
* @param[in] a Field element
* @param[in] b Field element
*/
static void fr_sub(fr_t *out, const fr_t *a, const fr_t *b) {
blst_fr_sub(out, a, b);
}
/**
* Multiply two field elements.
*
* @param[out] out @p a multiplied by @p b in the field
* @param[in] a Multiplicand
* @param[in] b Multiplier
*/
static void fr_mul(fr_t *out, const fr_t *a, const fr_t *b) {
blst_fr_mul(out, a, b);
}
/**
* Division of two field elements.
*
* @param[out] out @p a divided by @p b in the field
* @param[in] a The dividend
* @param[in] b The divisor
*/
static void fr_div(fr_t *out, const fr_t *a, const fr_t *b) {
blst_fr tmp;
blst_fr_eucl_inverse(&tmp, b);
blst_fr_mul(out, a, &tmp);
}
/**
* Square a field element.
*
* @param[out] out @p a squared
* @param[in] a A field element
*/
static void fr_sqr(fr_t *out, const fr_t *a) {
blst_fr_sqr(out, a);
}
/**
* Exponentiation of a field element.
*
* Uses square and multiply for log(@p n) performance.
*
* @remark A 64-bit exponent is sufficient for our needs here.
*
* @param[out] out @p a raised to the power of @p n
* @param[in] a The field element to be exponentiated
* @param[in] n The exponent
*/
static void fr_pow(fr_t *out, const fr_t *a, uint64_t n) {
fr_t tmp = *a;
*out = fr_one;
while (true) {
if (n & 1) {
fr_mul(out, out, &tmp);
}
if ((n >>= 1) == 0) break;
fr_sqr(&tmp, &tmp);
}
}
/**
* Create a field element from a single 64-bit unsigned integer.
*
* @remark This can only generate a tiny fraction of possible field elements, and is mostly useful for testing.
*
* @param out The field element equivalent of @p n
* @param n The 64-bit integer to be converted
*/
static void fr_from_uint64(fr_t *out, uint64_t n) {
uint64_t vals[] = {n, 0, 0, 0};
fr_from_uint64s(out, vals);
}
/**
* Inverse of a field element.
*
* @param[out] out The inverse of @p a
* @param[in] a A field element
*/
static void fr_inv(fr_t *out, const fr_t *a) {
blst_fr_eucl_inverse(out, a);
}
/**
* Montgomery batch inversion in finite field
*
* @param[out] out The inverses of @p a, length @p len
* @param[in] a A vector of field elements, length @p len
* @param[in] len Length
*/
static C_KZG_RET fr_batch_inv(fr_t *out, const fr_t *a, size_t len) {
fr_t *prod;
fr_t inv;
size_t i;
TRY(new_fr_array(&prod, len));
prod[0] = a[0];
for(i = 1; i < len; i++) {
fr_mul(&prod[i], &a[i], &prod[i - 1]);
}
blst_fr_eucl_inverse(&inv, &prod[len - 1]);
for(i = len - 1; i > 0; i--) {
fr_mul(&out[i], &inv, &prod[i - 1]);
fr_mul(&inv, &a[i], &inv);
}
out[0] = inv;
free(prod);
return C_KZG_OK;
}
/** The G1 identity/infinity */
static const g1_t g1_identity = {{0L, 0L, 0L, 0L, 0L, 0L}, {0L, 0L, 0L, 0L, 0L, 0L}, {0L, 0L, 0L, 0L, 0L, 0L}};
/** The G1 generator */
static const g1_t g1_generator = {{0x5cb38790fd530c16L, 0x7817fc679976fff5L, 0x154f95c7143ba1c1L, 0xf0ae6acdf3d0e747L,
0xedce6ecc21dbf440L, 0x120177419e0bfb75L},
{0xbaac93d50ce72271L, 0x8c22631a7918fd8eL, 0xdd595f13570725ceL, 0x51ac582950405194L,
0x0e1c8c3fad0059c0L, 0x0bbc3efc5008a26aL},
{0x760900000002fffdL, 0xebf4000bc40c0002L, 0x5f48985753c758baL, 0x77ce585370525745L,
0x5c071a97a256ec6dL, 0x15f65ec3fa80e493L}};
/** The G2 generator */
static const g2_t g2_generator = {{{{0xf5f28fa202940a10L, 0xb3f5fb2687b4961aL, 0xa1a893b53e2ae580L, 0x9894999d1a3caee9L,
0x6f67b7631863366bL, 0x058191924350bcd7L},
{0xa5a9c0759e23f606L, 0xaaa0c59dbccd60c3L, 0x3bb17e18e2867806L, 0x1b1ab6cc8541b367L,
0xc2b6ed0ef2158547L, 0x11922a097360edf3L}}},
{{{0x4c730af860494c4aL, 0x597cfa1f5e369c5aL, 0xe7e6856caa0a635aL, 0xbbefb5e96e0d495fL,
0x07d3a975f0ef25a2L, 0x0083fd8e7e80dae5L},
{0xadc0fc92df64b05dL, 0x18aa270a2b1461dcL, 0x86adac6a3be4eba0L, 0x79495c4ec93da33aL,
0xe7175850a43ccaedL, 0x0b2bc2a163de1bf2L}}},
{{{0x760900000002fffdL, 0xebf4000bc40c0002L, 0x5f48985753c758baL, 0x77ce585370525745L,
0x5c071a97a256ec6dL, 0x15f65ec3fa80e493L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L,
0x0000000000000000L, 0x0000000000000000L}}}};
/**
* Add or double G1 points.
*
* This is safe if the two points are the same.
*
* @param[out] out @p a plus @p b in the group
* @param[in] a G1 group point
* @param[in] b G1 group point
*/
static void g1_add_or_dbl(g1_t *out, const g1_t *a, const g1_t *b) {
blst_p1_add_or_double(out, a, b);
}
/**
* Multiply a G1 group element by a field element.
*
* This "undoes" the Blst constant-timedness. FFTs do a lot of multiplication by one, so constant time is rather slow.
*
* @param[out] out [@p b]@p a
* @param[in] a The G1 group element
* @param[in] b The multiplier
*/
static void g1_mul(g1_t *out, const g1_t *a, const fr_t *b) {
blst_scalar s;
blst_scalar_from_fr(&s, b);
// Count the number of bytes to be multiplied.
int i = sizeof(blst_scalar);
while (i && !s.b[i - 1]) --i;
if (i == 0) {
*out = g1_identity;
} else if (i == 1 && s.b[0] == 1) {
*out = *a;
} else {
// Count the number of bits to be multiplied.
blst_p1_mult(out, a, s.b, 8 * i - 7 + log_2_byte(s.b[i - 1]));
}
}
/**
* Subtraction of G1 group elements.
*
* @param[out] out @p a - @p b
* @param[in] a A G1 group element
* @param[in] b The G1 group element to be subtracted
*/
static void g1_sub(g1_t *out, const g1_t *a, const g1_t *b) {
g1_t bneg = *b;
blst_p1_cneg(&bneg, true);
blst_p1_add_or_double(out, a, &bneg);
}
/**
* Subtraction of G2 group elements.
*
* @param[out] out @p a - @p b
* @param[in] a A G2 group element
* @param[in] b The G2 group element to be subtracted
*/
static void g2_sub(g2_t *out, const g2_t *a, const g2_t *b) {
g2_t bneg = *b;
blst_p2_cneg(&bneg, true);
blst_p2_add_or_double(out, a, &bneg);
}
/**
* Multiply a G2 group element by a field element.
*
* @param[out] out [@p b]@p a
* @param[in] a The G2 group element
* @param[in] b The multiplier
*/
static void g2_mul(g2_t *out, const g2_t *a, const fr_t *b) {
blst_scalar s;
blst_scalar_from_fr(&s, b);
blst_p2_mult(out, a, s.b, 8 * sizeof(blst_scalar));
}
/**
* Utility function to test whether the argument is a power of two.
*
* @remark This method returns `true` for `is_power_of_two(0)` which is a bit weird, but not an issue in the contexts in
* which we use it.
*
* @param[in] n The number to test
* @retval true if @p n is a power of two or zero
* @retval false otherwise
*/
static bool is_power_of_two(uint64_t n) {
return (n & (n - 1)) == 0;
}
/**
* The first 32 roots of unity in the finite field F_r.
*
* For element `{A, B, C, D}`, the field element value is `A + B * 2^64 + C * 2^128 + D * 2^192`. This format may be
* converted to an `fr_t` type via the #fr_from_uint64s library function.
*
* The decimal values may be calculated with the following Python code:
* @code{.py}
* MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513
* PRIMITIVE_ROOT = 7
* [pow(PRIMITIVE_ROOT, (MODULUS - 1) // (2**i), MODULUS) for i in range(32)]
* @endcode
*
* Note: Being a "primitive root" in this context means that r^k != 1 for any k < q-1 where q is the modulus. So
* powers of r generate the field. This is also known as being a "primitive element".
*
* This is easy to check for: we just require that r^((q-1)/2) != 1. Instead of 5, we could use 7, 10, 13, 14, 15, 20...
* to create the roots of unity below. There are a lot of primitive roots:
* https://crypto.stanford.edu/pbc/notes/numbertheory/gen.html
*/
static const uint64_t scale2_root_of_unity[][4] = {
{0x0000000000000001L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0xffffffff00000000L, 0x53bda402fffe5bfeL, 0x3339d80809a1d805L, 0x73eda753299d7d48L},
{0x0001000000000000L, 0xec03000276030000L, 0x8d51ccce760304d0L, 0x0000000000000000L},
{0x7228fd3397743f7aL, 0xb38b21c28713b700L, 0x8c0625cd70d77ce2L, 0x345766f603fa66e7L},
{0x53ea61d87742bcceL, 0x17beb312f20b6f76L, 0xdd1c0af834cec32cL, 0x20b1ce9140267af9L},
{0x360c60997369df4eL, 0xbf6e88fb4c38fb8aL, 0xb4bcd40e22f55448L, 0x50e0903a157988baL},
{0x8140d032f0a9ee53L, 0x2d967f4be2f95155L, 0x14a1e27164d8fdbdL, 0x45af6345ec055e4dL},
{0x5130c2c1660125beL, 0x98d0caac87f5713cL, 0xb7c68b4d7fdd60d0L, 0x6898111413588742L},
{0x4935bd2f817f694bL, 0x0a0865a899e8deffL, 0x6b368121ac0cf4adL, 0x4f9b4098e2e9f12eL},
{0x4541b8ff2ee0434eL, 0xd697168a3a6000feL, 0x39feec240d80689fL, 0x095166525526a654L},
{0x3c28d666a5c2d854L, 0xea437f9626fc085eL, 0x8f4de02c0f776af3L, 0x325db5c3debf77a1L},
{0x4a838b5d59cd79e5L, 0x55ea6811be9c622dL, 0x09f1ca610a08f166L, 0x6d031f1b5c49c834L},
{0xe206da11a5d36306L, 0x0ad1347b378fbf96L, 0xfc3e8acfe0f8245fL, 0x564c0a11a0f704f4L},
{0x6fdd00bfc78c8967L, 0x146b58bc434906acL, 0x2ccddea2972e89edL, 0x485d512737b1da3dL},
{0x034d2ff22a5ad9e1L, 0xae4622f6a9152435L, 0xdc86b01c0d477fa6L, 0x56624634b500a166L},
{0xfbd047e11279bb6eL, 0xc8d5f51db3f32699L, 0x483405417a0cbe39L, 0x3291357ee558b50dL},
{0xd7118f85cd96b8adL, 0x67a665ae1fcadc91L, 0x88f39a78f1aeb578L, 0x2155379d12180caaL},
{0x08692405f3b70f10L, 0xcd7f2bd6d0711b7dL, 0x473a2eef772c33d6L, 0x224262332d8acbf4L},
{0x6f421a7d8ef674fbL, 0xbb97a3bf30ce40fdL, 0x652f717ae1c34bb0L, 0x2d3056a530794f01L},
{0x194e8c62ecb38d9dL, 0xad8e16e84419c750L, 0xdf625e80d0adef90L, 0x520e587a724a6955L},
{0xfece7e0e39898d4bL, 0x2f69e02d265e09d9L, 0xa57a6e07cb98de4aL, 0x03e1c54bcb947035L},
{0xcd3979122d3ea03aL, 0x46b3105f04db5844L, 0xc70d0874b0691d4eL, 0x47c8b5817018af4fL},
{0xc6e7a6ffb08e3363L, 0xe08fec7c86389beeL, 0xf2d38f10fbb8d1bbL, 0x0abe6a5e5abcaa32L},
{0x5616c57de0ec9eaeL, 0xc631ffb2585a72dbL, 0x5121af06a3b51e3cL, 0x73560252aa0655b2L},
{0x92cf4deb77bd779cL, 0x72cf6a8029b7d7bcL, 0x6e0bcd91ee762730L, 0x291cf6d68823e687L},
{0xce32ef844e11a51eL, 0xc0ba12bb3da64ca5L, 0x0454dc1edc61a1a3L, 0x019fe632fd328739L},
{0x531a11a0d2d75182L, 0x02c8118402867ddcL, 0x116168bffbedc11dL, 0x0a0a77a3b1980c0dL},
{0xe2d0a7869f0319edL, 0xb94f1101b1d7a628L, 0xece8ea224f31d25dL, 0x23397a9300f8f98bL},
{0xd7b688830a4f2089L, 0x6558e9e3f6ac7b41L, 0x99e276b571905a7dL, 0x52dd465e2f094256L},
{0x474650359d8e211bL, 0x84d37b826214abc6L, 0x8da40c1ef2bb4598L, 0x0c83ea7744bf1beeL},
{0x694341f608c9dd56L, 0xed3a181fabb30adcL, 0x1339a815da8b398fL, 0x2c6d4e4511657e1eL},
{0x63e7cb4906ffc93fL, 0xf070bb00e28a193dL, 0xad1715b02e5713b5L, 0x4b5371495990693fL}};
/**
* Discrete fourier transforms over arrays of G1 group elements.
*
* Also known as [number theoretic
* transforms](https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general)#Number-theoretic_transform).
*
* @remark Functions here work only for lengths that are a power of two.
*/
/**
* Fast Fourier Transform.
*
* Recursively divide and conquer.
*
* @param[out] out The results (array of length @p n)
* @param[in] in The input data (array of length @p n * @p stride)
* @param[in] stride The input data stride
* @param[in] roots Roots of unity (array of length @p n * @p roots_stride)
* @param[in] roots_stride The stride interval among the roots of unity
* @param[in] n Length of the FFT, must be a power of two
*/
static void fft_g1_fast(g1_t *out, const g1_t *in, uint64_t stride, const fr_t *roots, uint64_t roots_stride,
uint64_t n) {
uint64_t half = n / 2;
if (half > 0) { // Tunable parameter
fft_g1_fast(out, in, stride * 2, roots, roots_stride * 2, half);
fft_g1_fast(out + half, in + stride, stride * 2, roots, roots_stride * 2, half);
for (uint64_t i = 0; i < half; i++) {
g1_t y_times_root;
g1_mul(&y_times_root, &out[i + half], &roots[i * roots_stride]);
g1_sub(&out[i + half], &out[i], &y_times_root);
g1_add_or_dbl(&out[i], &out[i], &y_times_root);
}
} else {
*out = *in;
}
}
/**
* The main entry point for forward and reverse FFTs over the finite field.
*
* @param[out] out The results (array of length @p n)
* @param[in] in The input data (array of length @p n)
* @param[in] inverse `false` for forward transform, `true` for inverse transform
* @param[in] n Length of the FFT, must be a power of two
* @param[in] fs Pointer to previously initialised FFTSettings structure with `max_width` at least @p n.
* @retval C_CZK_OK All is well
* @retval C_CZK_BADARGS Invalid parameters were supplied
*/
static C_KZG_RET fft_g1(g1_t *out, const g1_t *in, bool inverse, uint64_t n, const FFTSettings *fs) {
uint64_t stride = fs->max_width / n;
CHECK(n <= fs->max_width);
CHECK(is_power_of_two(n));
if (inverse) {
fr_t inv_len;
fr_from_uint64(&inv_len, n);
fr_inv(&inv_len, &inv_len);
fft_g1_fast(out, in, 1, fs->reverse_roots_of_unity, stride, n);
for (uint64_t i = 0; i < n; i++) {
g1_mul(&out[i], &out[i], &inv_len);
}
} else {
fft_g1_fast(out, in, 1, fs->expanded_roots_of_unity, stride, n);
}
return C_KZG_OK;
}
/**
* Generate powers of a root of unity in the field for use in the FFTs.
*
* @remark @p root must be such that @p root ^ @p width is equal to one, but no smaller power of @p root is equal to
* one.
*
* @param[out] out The generated powers of the root of unity (array size @p width + 1)
* @param[in] root A root of unity
* @param[in] width One less than the size of @p out
* @retval C_CZK_OK All is well
* @retval C_CZK_BADARGS Invalid parameters were supplied
*/
static C_KZG_RET expand_root_of_unity(fr_t *out, const fr_t *root, uint64_t width) {
out[0] = fr_one;
out[1] = *root;
for (uint64_t i = 2; !fr_is_one(&out[i - 1]); i++) {
CHECK(i <= width);
fr_mul(&out[i], &out[i - 1], root);
}
CHECK(fr_is_one(&out[width]));
return C_KZG_OK;
}
/**
* Reverse the bits in a byte.
*
* From https://graphics.stanford.edu/~seander/bithacks.html#ReverseByteWith64BitsDiv
*
* @param a A byte
* @return A byte that is bit-reversed with respect to @p a
*
* @todo Benchmark some of the other bit-reversal options in the list. Maybe.
*/
#define rev_byte(a) ((((a)&0xff) * 0x0202020202ULL & 0x010884422010ULL) % 1023)
/**
* Reverse the bits in a 32 bit word.
*
* @param a A 32 bit unsigned integer
* @return A 32 bit unsigned integer that is bit-reversed with respect to @p a
*/
#define rev_4byte(a) (rev_byte(a) << 24 | rev_byte((a) >> 8) << 16 | rev_byte((a) >> 16) << 8 | rev_byte((a) >> 24))
/**
* Calculate log base two of a power of two.
*
* In other words, the bit index of the one bit.
*
* @remark Works only for n a power of two, and only for n up to 2^31.
*
* @param[in] n The power of two
* @return the log base two of n
*/
static int log2_pow2(uint32_t n) {
const uint32_t b[] = {0xAAAAAAAA, 0xCCCCCCCC, 0xF0F0F0F0, 0xFF00FF00, 0xFFFF0000};
register uint32_t r;
r = (n & b[0]) != 0;
r |= ((n & b[1]) != 0) << 1;
r |= ((n & b[2]) != 0) << 2;
r |= ((n & b[3]) != 0) << 3;
r |= ((n & b[4]) != 0) << 4;
return r;
}
/**
* Reverse the bit order in a 32 bit integer.
*
* @remark This simply wraps the macro to enforce the type check.
*
* @param[in] a The integer to be reversed
* @return An integer with the bits of @p a reversed
*/
static uint32_t reverse_bits(uint32_t a) {
return rev_4byte(a);
}
/**
* Reorder an array in reverse bit order of its indices.
*
* @remark Operates in-place on the array.
* @remark Can handle arrays of any type: provide the element size in @p size.
*
* @param[in,out] values The array, which is re-ordered in-place
* @param[in] size The size in bytes of an element of the array
* @param[in] n The length of the array, must be a power of two less that 2^32
* @retval C_CZK_OK All is well
* @retval C_CZK_BADARGS Invalid parameters were supplied
*/
static C_KZG_RET reverse_bit_order(void *values, size_t size, uint64_t n) {
CHECK(n >> 32 == 0);
CHECK(is_power_of_two(n));
// Pointer arithmetic on `void *` is naughty, so cast to something definite
byte *v = values;
byte tmp[size];
int unused_bit_len = 32 - log2_pow2(n);
for (uint32_t i = 0; i < n; i++) {
uint32_t r = reverse_bits(i) >> unused_bit_len;
if (r > i) {
// Swap the two elements
memcpy(tmp, v + (i * size), size);
memcpy(v + (i * size), v + (r * size), size);
memcpy(v + (r * size), tmp, size);
}
}
return C_KZG_OK;
}
/**
* Initialise an FFTSettings structure.
*
* Space is allocated for, and arrays are populated with, powers of the roots of unity. The two arrays contain the same
* values in reverse order for convenience in inverse FFTs.
*
* `max_width` is the maximum size of FFT that can be calculated with these settings, and is a power of two by
* construction. The same settings may be used to calculated FFTs of smaller power sizes.
*
* @remark As with all functions prefixed `new_`, this allocates memory that needs to be reclaimed by calling the
* corresponding `free_` function. In this case, #free_fft_settings.
* @remark These settings may be used for FFTs on both field elements and G1 group elements.
*
* @param[out] fs The new settings
* @param[in] max_scale Log base 2 of the max FFT size to be used with these settings
* @retval C_CZK_OK All is well
* @retval C_CZK_BADARGS Invalid parameters were supplied
* @retval C_CZK_ERROR An internal error occurred
* @retval C_CZK_MALLOC Memory allocation failed
*/
static C_KZG_RET new_fft_settings(FFTSettings *fs, unsigned int max_scale) {
fr_t root_of_unity;
fs->max_width = (uint64_t)1 << max_scale;
CHECK((max_scale < sizeof scale2_root_of_unity / sizeof scale2_root_of_unity[0]));
fr_from_uint64s(&root_of_unity, scale2_root_of_unity[max_scale]);
// Allocate space for the roots of unity
TRY(new_fr_array(&fs->expanded_roots_of_unity, fs->max_width + 1));
TRY(new_fr_array(&fs->reverse_roots_of_unity, fs->max_width + 1));
TRY(new_fr_array(&fs->roots_of_unity, fs->max_width));
// Populate the roots of unity
TRY(expand_root_of_unity(fs->expanded_roots_of_unity, &root_of_unity, fs->max_width));
// Populate reverse roots of unity
for (uint64_t i = 0; i <= fs->max_width; i++) {
fs->reverse_roots_of_unity[i] = fs->expanded_roots_of_unity[fs->max_width - i];
}
// Permute the roots of unity
memcpy(fs->roots_of_unity, fs->expanded_roots_of_unity, sizeof(fr_t) * fs->max_width);
TRY(reverse_bit_order(fs->roots_of_unity, sizeof(fr_t), fs->max_width));
return C_KZG_OK;
}
/**
* Free the memory that was previously allocated by #new_fft_settings.
*
* @param fs The settings to be freed
*/
static void free_fft_settings(FFTSettings *fs) {
free(fs->expanded_roots_of_unity);
free(fs->reverse_roots_of_unity);
free(fs->roots_of_unity);
fs->max_width = 0;
}
/**
* Free the memory that was previously allocated by #new_kzg_settings.
*
* @param ks The settings to be freed
*/
static void free_kzg_settings(KZGSettings *ks) {
free(ks->g1_values);
free(ks->g2_values);
ks->length = 0;
}
/**
* Perform pairings and test whether the outcomes are equal in G_T.
*
* Tests whether `e(a1, a2) == e(b1, b2)`.
*
* @param[in] a1 A G1 group point for the first pairing
* @param[in] a2 A G2 group point for the first pairing
* @param[in] b1 A G1 group point for the second pairing
* @param[in] b2 A G2 group point for the second pairing
* @retval true The pairings were equal
* @retval false The pairings were not equal
*/
static bool pairings_verify(const g1_t *a1, const g2_t *a2, const g1_t *b1, const g2_t *b2) {
blst_fp12 loop0, loop1, gt_point;
blst_p1_affine aa1, bb1;
blst_p2_affine aa2, bb2;
// As an optimisation, we want to invert one of the pairings,
// so we negate one of the points.
g1_t a1neg = *a1;
blst_p1_cneg(&a1neg, true);
blst_p1_to_affine(&aa1, &a1neg);
blst_p1_to_affine(&bb1, b1);
blst_p2_to_affine(&aa2, a2);
blst_p2_to_affine(&bb2, b2);
blst_miller_loop(&loop0, &aa2, &aa1);
blst_miller_loop(&loop1, &bb2, &bb1);
blst_fp12_mul(&gt_point, &loop0, &loop1);
blst_final_exp(&gt_point, &gt_point);
return blst_fp12_is_one(&gt_point);
}
void bytes_from_g1(uint8_t out[48], const g1_t *in) {
blst_p1_compress(out, in);
}
void uint64s_from_BLSFieldElement(uint64_t out[4], const BLSFieldElement *in) {
blst_uint64_from_fr(out, in);
}
C_KZG_RET load_trusted_setup(KZGSettings *out, FILE *in) {
uint64_t n2, i;
int j; uint8_t c[96];
blst_p1_affine g1_affine;
blst_p2_affine g2_affine;
g1_t *g1_projective;
fscanf(in, "%" SCNu64, &out->length);
fscanf(in, "%" SCNu64, &n2);
TRY(new_g1_array(&out->g1_values, out->length));
TRY(new_g2_array(&out->g2_values, n2));
TRY(new_g1_array(&g1_projective, out->length));
for (i = 0; i < out->length; i++) {
for (j = 0; j < 48; j++) {
fscanf(in, "%2hhx", &c[j]);
}
blst_p1_uncompress(&g1_affine, c);
blst_p1_from_affine(&g1_projective[i], &g1_affine);
}
for (i = 0; i < n2; i++) {
for (j = 0; j < 96; j++) {
fscanf(in, "%2hhx", &c[j]);
}
blst_p2_uncompress(&g2_affine, c);
blst_p2_from_affine(&out->g2_values[i], &g2_affine);
}
unsigned int max_scale = 0;
while (((uint64_t)1 << max_scale) < out->length) max_scale++;
out->fs = (FFTSettings*)malloc(sizeof(FFTSettings));
TRY(new_fft_settings((FFTSettings*)out->fs, max_scale));
TRY(fft_g1(out->g1_values, g1_projective, true, out->length, out->fs));
free(g1_projective);
return C_KZG_OK;
}
void free_trusted_setup(KZGSettings *s) {
free_fft_settings((FFTSettings*)s->fs);
free_kzg_settings(s);
}
void compute_powers(fr_t out[], const fr_t *x, uint64_t n) {
uint64_t i = 0;
out[i] = fr_one;
while (++i < n) fr_mul(&out[i], &out[i-1], x);
}
void bytes_to_bls_field(BLSFieldElement *out, const uint8_t bytes[32]) {
blst_scalar tmp;
blst_scalar_from_lendian(&tmp, bytes);
blst_fr_from_scalar(out, &tmp);
}
/**
* Compute linear combinations of a sequence of vectors with some scalars
*/
void vector_lincomb(fr_t out[], const fr_t* vectors[], const fr_t* scalars[], uint64_t n, uint64_t m) {
fr_t tmp;
uint64_t i, j;
for (j = 0; j < m; j++)
out[j] = fr_zero;
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++) {
fr_mul(&tmp, scalars[i], vectors[i * m + j]);
fr_add(&out[j], &out[j], &tmp);
}
}
}
/**
* Calculate a linear combination of G1 group elements.
*
* Calculates `[coeffs_0]p_0 + [coeffs_1]p_1 + ... + [coeffs_n]p_n` where `n` is `len - 1`.
*
* @param[out] out The resulting sum-product
* @param[in] p Array of G1 group elements, length @p len
* @param[in] coeffs Array of field elements, length @p len
* @param[in] len The number of group/field elements
*
* For the benefit of future generations (since Blst has no documentation to speak of),
* there are two ways to pass the arrays of scalars and points into `blst_p1s_mult_pippenger()`.
*
* 1. Pass `points` as an array of pointers to the points, and pass `scalars` as an array of pointers to the scalars,
* each of length @p len.
* 2. Pass an array where the first element is a pointer to the contiguous array of points and the second is null, and
* similarly for scalars.
*
* We do the second of these to save memory here.
*/
void g1_lincomb(g1_t *out, const g1_t *p, const fr_t *coeffs, const uint64_t len) {
if (len < 8) { // Tunable parameter: must be at least 2 since Blst fails for 0 or 1
// Direct approach
g1_t tmp;
*out = g1_identity;
for (uint64_t i = 0; i < len; i++) {
g1_mul(&tmp, &p[i], &coeffs[i]);
blst_p1_add_or_double(out, out, &tmp);
}
} else {
// Blst's implementation of the Pippenger method
void *scratch = malloc(blst_p1s_mult_pippenger_scratch_sizeof(len));
blst_p1_affine *p_affine = malloc(len * sizeof(blst_p1_affine));
blst_scalar *scalars = malloc(len * sizeof(blst_scalar));
// Transform the points to affine representation
const blst_p1 *p_arg[2] = {p, NULL};
blst_p1s_to_affine(p_affine, p_arg, len);
// Transform the field elements to 256-bit scalars
for (int i = 0; i < len; i++) {
blst_scalar_from_fr(&scalars[i], &coeffs[i]);
}
// Call the Pippenger implementation
const byte *scalars_arg[2] = {(byte *)scalars, NULL};
const blst_p1_affine *points_arg[2] = {p_affine, NULL};
blst_p1s_mult_pippenger(out, points_arg, len, scalars_arg, 256, scratch);
// Tidy up
free(scratch);
free(p_affine);
free(scalars);
}
}
void blob_to_kzg_commitment(KZGCommitment *out, const BLSFieldElement blob[], const KZGSettings *s) {
g1_lincomb(out, s->g1_values, blob, s->length);
}
/**
* Check a KZG proof at a point against a commitment.
*
* Given a @p commitment to a polynomial, a @p proof for @p x, and the claimed value @p y at @p x, verify the claim.
*
* @param[out] out `true` if the proof is valid, `false` if not
* @param[in] commitment The commitment to a polynomial
* @param[in] x The point at which the proof is to be checked (opened)
* @param[in] y The claimed value of the polynomial at @p x
* @param[in] proof A proof of the value of the polynomial at the point @p x
* @param[in] ks The settings containing the secrets, previously initialised with #new_kzg_settings
* @retval C_CZK_OK All is well
*/
C_KZG_RET verify_kzg_proof(bool *out, const g1_t *commitment, const fr_t *x, const fr_t *y,
const g1_t *proof, const KZGSettings *ks) {
g2_t x_g2, s_minus_x;
g1_t y_g1, commitment_minus_y;
g2_mul(&x_g2, &g2_generator, x);
g2_sub(&s_minus_x, &ks->g2_values[1], &x_g2);
g1_mul(&y_g1, &g1_generator, y);
g1_sub(&commitment_minus_y, commitment, &y_g1);
*out = pairings_verify(&commitment_minus_y, &g2_generator, proof, &s_minus_x);
return C_KZG_OK;
}
C_KZG_RET alloc_polynomial(PolynomialEvalForm *out, uint64_t length) {
out->length = length;
return new_fr_array(&out->values, length);
}
void free_polynomial(PolynomialEvalForm *p) {
p->length = 0;
free(p->values);
}
/**
* Compute KZG proof for polynomial in Lagrange form at position x
*
* @param[out] out The combined proof as a single G1 element
* @param[in] p The polynomial in Lagrange form
* @param[in] x The generator x-value for the evaluation points
* @param[in] s The settings containing the secrets, previously initialised with #new_kzg_settings
* @retval C_KZG_OK All is well
* @retval C_KZG_ERROR An internal error occurred
* @retval C_KZG_MALLOC Memory allocation failed
*/
C_KZG_RET compute_kzg_proof(KZGProof *out, const PolynomialEvalForm *p, const BLSFieldElement *x, const KZGSettings *s) {
CHECK(p->length <= s->length);
BLSFieldElement y;
TRY(evaluate_polynomial_in_evaluation_form(&y, p, x, s));
fr_t tmp, tmp2;
PolynomialEvalForm q;
const fr_t *roots_of_unity = s->fs->roots_of_unity;
uint64_t i, m = 0;
TRY(alloc_polynomial(&q, p->length));
fr_t *inverses_in, *inverses;
TRY(new_fr_array(&inverses_in, p->length));
TRY(new_fr_array(&inverses, p->length));
for (i = 0; i < q.length; i++) {
if (fr_equal(x, &roots_of_unity[i])) {
m = i + 1;
continue;
}
// (p_i - y) / (ω_i - x)
fr_sub(&q.values[i], &p->values[i], &y);
fr_sub(&inverses_in[i], &roots_of_unity[i], x);
}
TRY(fr_batch_inv(inverses, inverses_in, q.length));
for (i = 0; i < q.length; i++) {
fr_mul(&q.values[i], &q.values[i], &inverses[i]);
}
if (m) { // ω_m == x
q.values[--m] = fr_zero;
for (i=0; i < q.length; i++) {
if (i == m) continue;
// (p_i - y) * ω_i / (x * (x - ω_i))
fr_sub(&tmp, x, &roots_of_unity[i]);
fr_mul(&inverses_in[i], &tmp, x);
}
TRY(fr_batch_inv(inverses, inverses_in, q.length));
for (i=0; i < q.length; i++) {
fr_sub(&tmp2, &p->values[i], &y);
fr_mul(&tmp, &tmp2, &inverses[i]);
fr_mul(&tmp, &tmp, &roots_of_unity[i]);
fr_add(&q.values[m], &q.values[m], &tmp);
}
}
free(inverses_in);
free(inverses);
g1_lincomb(out, s->g1_values, p->values, p->length);
return C_KZG_OK;
}
C_KZG_RET evaluate_polynomial_in_evaluation_form(BLSFieldElement *out, const PolynomialEvalForm *p, const BLSFieldElement *x, const KZGSettings *s) {
fr_t tmp, *inverses_in, *inverses;
uint64_t i;
const uint64_t stride = s->fs->max_width / p->length;
const fr_t *roots_of_unity = s->fs->roots_of_unity;
TRY(new_fr_array(&inverses_in, p->length));
TRY(new_fr_array(&inverses, p->length));
for (i = 0; i < p->length; i++) {
if (fr_equal(x, &roots_of_unity[i * stride])) {
*out = p->values[i];
free(inverses_in);
free(inverses);
return C_KZG_OK;
}
fr_sub(&inverses_in[i], x, &roots_of_unity[i * stride]);
}
TRY(fr_batch_inv(inverses, inverses_in, p->length));
*out = fr_zero;
for (i = 0; i < p->length; i++) {
fr_mul(&tmp, &inverses[i], &roots_of_unity[i * stride]);
fr_mul(&tmp, &tmp, &p->values[i]);
fr_add(out, out, &tmp);
}
fr_from_uint64(&tmp, p->length);
fr_div(out, out, &tmp);
fr_pow(&tmp, x, p->length);
fr_sub(&tmp, &tmp, &fr_one);
fr_mul(out, out, &tmp);
free(inverses_in);
free(inverses);
return C_KZG_OK;
}
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