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c_kzg_4844.c
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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.
*/
/**
* @file c_kzg_4844.c
*
* Minimal implementation of the polynomial commitments API for EIP-4844.
*/
#include "c_kzg_4844.h"
#include <assert.h>
#include <inttypes.h>
#include <stdlib.h>
#include <string.h>
///////////////////////////////////////////////////////////////////////////////
// Macros
///////////////////////////////////////////////////////////////////////////////
/** Returns C_KZG_BADARGS if the condition is not met. */
#define CHECK(cond) \
if (!(cond)) return C_KZG_BADARGS
/** Returns number of elements in a statically defined array. */
#define NUM_ELEMENTS(a) (sizeof(a) / sizeof(a[0]))
/**
* Helper macro to release memory allocated on the heap. Unlike free(),
* c_kzg_free() macro sets the pointer value to NULL after freeing it.
*/
#define c_kzg_free(p) \
do { \
free(p); \
(p) = NULL; \
} while (0)
///////////////////////////////////////////////////////////////////////////////
// Types
///////////////////////////////////////////////////////////////////////////////
/** Internal representation of a polynomial. */
typedef struct {
fr_t evals[FIELD_ELEMENTS_PER_BLOB];
} Polynomial;
///////////////////////////////////////////////////////////////////////////////
// Constants
///////////////////////////////////////////////////////////////////////////////
/** The domain separator for the Fiat-Shamir protocol. */
static const char *FIAT_SHAMIR_PROTOCOL_DOMAIN = "FSBLOBVERIFY_V1_";
/** The domain separator for a random challenge. */
static const char *RANDOM_CHALLENGE_KZG_BATCH_DOMAIN = "RCKZGBATCH___V1_";
/** Length of the domain strings above. */
#define DOMAIN_STR_LENGTH 16
/** The number of bytes in a g1 point. */
#define BYTES_PER_G1 48
/** The number of bytes in a g2 point. */
#define BYTES_PER_G2 96
/** The number of g1 points in a trusted setup. */
#define TRUSTED_SETUP_NUM_G1_POINTS FIELD_ELEMENTS_PER_BLOB
/** The number of g2 points in a trusted setup. */
#define TRUSTED_SETUP_NUM_G2_POINTS 65
// clang-format off
/** Deserialized form of the G1 identity/infinity point. */
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 first 32 roots of unity in the finite field F_r.
* SCALE2_ROOT_OF_UNITY[i] is a 2^i'th root of unity.
*
* 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 blst_fr_from_uint64() 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".
*
* In the formula above, the restriction can be slightly relaxed to `r` being a non-square.
* This is easy to check: We just require that r^((q-1)/2) == -1. Instead of
* 7, we could use 10, 13, 14, 15, 20... to create the 2^i'th roots of unity below.
* Generally, 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}};
/** 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};
/** This used to represent a missing element. It's a invalid value. */
static const fr_t FR_NULL = {
0xffffffffffffffffL, 0xffffffffffffffffL,
0xffffffffffffffffL, 0xffffffffffffffffL};
// clang-format on
///////////////////////////////////////////////////////////////////////////////
// Memory Allocation Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Wrapped malloc() that reports failures to allocate.
*
* @remark Will return C_KZG_BADARGS if the requested size is zero.
*
* @param[out] out Pointer to the allocated space
* @param[in] size The number of bytes to be allocated
*/
static C_KZG_RET c_kzg_malloc(void **out, size_t size) {
*out = NULL;
if (size == 0) return C_KZG_BADARGS;
*out = malloc(size);
return *out != NULL ? C_KZG_OK : C_KZG_MALLOC;
}
/**
* Wrapped calloc() that reports failures to allocate.
*
* @remark Will return C_KZG_BADARGS if the requested size is zero.
*
* @param[out] out Pointer to the allocated space
* @param[in] count The number of elements
* @param[in] size The size of each element
*/
static C_KZG_RET c_kzg_calloc(void **out, size_t count, size_t size) {
*out = NULL;
if (count == 0 || size == 0) return C_KZG_BADARGS;
*out = calloc(count, size);
return *out != NULL ? C_KZG_OK : C_KZG_MALLOC;
}
/**
* Allocate memory for an array of G1 group elements.
*
* @remark Free the space later using c_kzg_free().
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of G1 elements to be allocated
*/
static C_KZG_RET new_g1_array(g1_t **x, size_t n) {
return c_kzg_calloc((void **)x, n, sizeof(g1_t));
}
/**
* Allocate memory for an array of G2 group elements.
*
* @remark Free the space later using c_kzg_free().
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of G2 elements to be allocated
*/
static C_KZG_RET new_g2_array(g2_t **x, size_t n) {
return c_kzg_calloc((void **)x, n, sizeof(g2_t));
}
/**
* Allocate memory for an array of field elements.
*
* @remark Free the space later using c_kzg_free().
*
* @param[out] x Pointer to the allocated space
* @param[in] n The number of field elements to be allocated
*/
static C_KZG_RET new_fr_array(fr_t **x, size_t n) {
return c_kzg_calloc((void **)x, n, sizeof(fr_t));
}
///////////////////////////////////////////////////////////////////////////////
// Helper Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Get the minimum of two unsigned integers.
*
* @param[in] a An unsigned integer
* @param[in] b An unsigned integer
*
* @return Whichever value is smaller.
*/
static inline size_t min(size_t a, size_t b) {
return a < b ? a : b;
}
/**
* Test whether the operand is one in the finite field.
*
* @param[in] p The field element to be checked
*
* @retval true The element is one
* @retval false The element is not one
*/
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 the operand is zero in the finite field.
*
* @param[in] p The field element to be checked
*
* @retval true The element is zero
* @retval false The element is not zero
*/
static bool fr_is_zero(const fr_t *p) {
uint64_t a[4];
blst_uint64_from_fr(a, p);
return a[0] == 0 && 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];
}
/**
* Test whether the operand is null (all 0xff's).
*
* @param[in] p The field element to be checked
*
* @retval true The element is null
* @retval false The element is not null
*/
static bool fr_is_null(const fr_t *p) {
return fr_equal(p, &FR_NULL);
}
/**
* Divide a field element by another.
*
* @remark The behaviour for @p b == 0 is unspecified.
*
* @remark This function does support in-place computation, i.e. @p out == @p a
* or @p out == @p b work.
*
* @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);
}
/**
* 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.
*
* @remark This function does support in-place computation, i.e. @p a == @p out
* works.
*
* @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) {
blst_fr_mul(out, out, &tmp);
}
if ((n >>= 1) == 0) break;
blst_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] out The field element equivalent of @p n
* @param[in] 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};
blst_fr_from_uint64(out, vals);
}
/**
* Montgomery batch inversion in finite field.
*
* @remark Return C_KZG_BADARGS if a zero is found in the input. In this case,
* the `out` output array has already been mutated.
*
* @remark This function does not support in-place computation (i.e. `a` MUST
* NOT point to the same place as `out`)
*
* @remark This function only supports len > 0.
*
* @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 The number of field elements
*/
static C_KZG_RET fr_batch_inv(fr_t *out, const fr_t *a, int len) {
int i;
assert(len > 0);
assert(a != out);
fr_t accumulator = FR_ONE;
for (i = 0; i < len; i++) {
out[i] = accumulator;
blst_fr_mul(&accumulator, &accumulator, &a[i]);
}
/* Bail on any zero input */
if (fr_is_zero(&accumulator)) {
return C_KZG_BADARGS;
}
blst_fr_eucl_inverse(&accumulator, &accumulator);
for (i = len - 1; i >= 0; i--) {
blst_fr_mul(&out[i], &out[i], &accumulator);
blst_fr_mul(&accumulator, &accumulator, &a[i]);
}
return C_KZG_OK;
}
/**
* Multiply a G1 group element by a field element.
*
* @param[out] out @p a * @p b
* @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);
/* The last argument is the number of bits in the scalar */
blst_p1_mult(out, a, s.b, 8 * sizeof(blst_scalar));
}
/**
* Multiply a G2 group element by a field element.
*
* @param[out] out @p a * @p b
* @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);
/* The last argument is the number of bits in the scalar */
blst_p2_mult(out, a, s.b, 8 * sizeof(blst_scalar));
}
/**
* 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);
}
/**
* 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(>_point, &loop0, &loop1);
blst_final_exp(>_point, >_point);
return blst_fp12_is_one(>_point);
}
///////////////////////////////////////////////////////////////////////////////
// Bytes Conversion Helper Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Serialize a G1 group element into bytes.
*
* @param[out] out A 48-byte array to store the serialized G1 element
* @param[in] in The G1 element to be serialized
*/
static void bytes_from_g1(Bytes48 *out, const g1_t *in) {
blst_p1_compress(out->bytes, in);
}
/**
* Serialize a BLS field element into bytes.
*
* @param[out] out A 32-byte array to store the serialized field element
* @param[in] in The field element to be serialized
*/
static void bytes_from_bls_field(Bytes32 *out, const fr_t *in) {
blst_scalar s;
blst_scalar_from_fr(&s, in);
blst_bendian_from_scalar(out->bytes, &s);
}
/**
* Serialize a 64-bit unsigned integer into bytes.
*
* @remark The output format is big-endian.
*
* @param[out] out An 8-byte array to store the serialized integer
* @param[in] n The integer to be serialized
*/
static void bytes_from_uint64(uint8_t out[8], uint64_t n) {
for (int i = 7; i >= 0; i--) {
out[i] = n & 0xFF;
n >>= 8;
}
}
///////////////////////////////////////////////////////////////////////////////
// BLS12-381 Helper Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Map bytes to a BLS field element.
*
* @param[out] out The field element to store the result
* @param[in] b A 32-byte array containing the input
*/
static void hash_to_bls_field(fr_t *out, const Bytes32 *b) {
blst_scalar tmp;
blst_scalar_from_bendian(&tmp, b->bytes);
blst_fr_from_scalar(out, &tmp);
}
/**
* Convert untrusted bytes to a trusted and validated BLS scalar field
* element.
*
* @param[out] out The field element to store the deserialized data
* @param[in] b A 32-byte array containing the serialized field element
*/
static C_KZG_RET bytes_to_bls_field(fr_t *out, const Bytes32 *b) {
blst_scalar tmp;
blst_scalar_from_bendian(&tmp, b->bytes);
if (!blst_scalar_fr_check(&tmp)) return C_KZG_BADARGS;
blst_fr_from_scalar(out, &tmp);
return C_KZG_OK;
}
/**
* Perform BLS validation required by the types KZGProof and KZGCommitment.
*
* @remark This function deviates from the spec because it returns (via an
* output argument) the g1 point. This way is more efficient (faster)
* but the function name is a bit misleading.
*
* @param[out] out The output g1 point
* @param[in] b The proof/commitment bytes
*/
static C_KZG_RET validate_kzg_g1(g1_t *out, const Bytes48 *b) {
blst_p1_affine p1_affine;
/* Convert the bytes to a p1 point */
/* The uncompress routine checks that the point is on the curve */
if (blst_p1_uncompress(&p1_affine, b->bytes) != BLST_SUCCESS)
return C_KZG_BADARGS;
blst_p1_from_affine(out, &p1_affine);
/* The point at infinity is accepted! */
if (blst_p1_is_inf(out)) return C_KZG_OK;
/* The point must be on the right subgroup */
if (!blst_p1_in_g1(out)) return C_KZG_BADARGS;
return C_KZG_OK;
}
/**
* Convert untrusted bytes into a trusted and validated KZGCommitment.
*
* @param[out] out The output commitment
* @param[in] b The commitment bytes
*/
static C_KZG_RET bytes_to_kzg_commitment(g1_t *out, const Bytes48 *b) {
return validate_kzg_g1(out, b);
}
/**
* Convert untrusted bytes into a trusted and validated KZGProof.
*
* @param[out] out The output proof
* @param[in] b The proof bytes
*/
static C_KZG_RET bytes_to_kzg_proof(g1_t *out, const Bytes48 *b) {
return validate_kzg_g1(out, b);
}
/**
* Deserialize a Blob (array of bytes) into a Polynomial (array of field
* elements).
*
* @param[out] p The output polynomial (array of field elements)
* @param[in] blob The blob (an array of bytes)
*/
static C_KZG_RET blob_to_polynomial(Polynomial *p, const Blob *blob) {
C_KZG_RET ret;
for (size_t i = 0; i < FIELD_ELEMENTS_PER_BLOB; i++) {
ret = bytes_to_bls_field(
&p->evals[i], (Bytes32 *)&blob->bytes[i * BYTES_PER_FIELD_ELEMENT]
);
if (ret != C_KZG_OK) return ret;
}
return C_KZG_OK;
}
/* Input size to the Fiat-Shamir challenge computation. */
#define CHALLENGE_INPUT_SIZE \
(DOMAIN_STR_LENGTH + 16 + BYTES_PER_BLOB + BYTES_PER_COMMITMENT)
/**
* Return the Fiat-Shamir challenge required to verify `blob` and
* `commitment`.
*
* @remark This function should compute challenges even if `n==0`.
*
* @param[out] eval_challenge_out The evaluation challenge
* @param[in] blob A blob
* @param[in] commitment A commitment
*/
static void compute_challenge(
fr_t *eval_challenge_out, const Blob *blob, const g1_t *commitment
) {
Bytes32 eval_challenge;
uint8_t bytes[CHALLENGE_INPUT_SIZE];
/* Pointer tracking `bytes` for writing on top of it */
uint8_t *offset = bytes;
/* Copy domain separator */
memcpy(offset, FIAT_SHAMIR_PROTOCOL_DOMAIN, DOMAIN_STR_LENGTH);
offset += DOMAIN_STR_LENGTH;
/* Copy polynomial degree (16-bytes, big-endian) */
bytes_from_uint64(offset, 0);
offset += sizeof(uint64_t);
bytes_from_uint64(offset, FIELD_ELEMENTS_PER_BLOB);
offset += sizeof(uint64_t);
/* Copy blob */
memcpy(offset, blob->bytes, BYTES_PER_BLOB);
offset += BYTES_PER_BLOB;
/* Copy commitment */
bytes_from_g1((Bytes48 *)offset, commitment);
offset += BYTES_PER_COMMITMENT;
/* Make sure we wrote the entire buffer */
assert(offset == bytes + CHALLENGE_INPUT_SIZE);
/* Now let's create the challenge! */
blst_sha256(eval_challenge.bytes, bytes, CHALLENGE_INPUT_SIZE);
hash_to_bls_field(eval_challenge_out, &eval_challenge);
}
/**
* 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`.
*
* This function computes the result naively without using Pippenger's
* algorithm.
*/
static void g1_lincomb_naive(
g1_t *out, const g1_t *p, const fr_t *coeffs, uint64_t len
) {
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);
}
}
/**
* 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`.
*
* @remark This function MUST NOT be called with the point at infinity in `p`.
*
* @remark While this function is significantly faster than
* `g1_lincomb_naive()`, we refrain from using it in security-critical places
* (like verification) because the blst Pippenger code has not been
* audited. In those critical places, we prefer using `g1_lincomb_naive()` which
* is much simpler.
*
* @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.
*/
static C_KZG_RET g1_lincomb_fast(
g1_t *out, const g1_t *p, const fr_t *coeffs, uint64_t len
) {
C_KZG_RET ret;
void *scratch = NULL;
blst_p1_affine *p_affine = NULL;
blst_scalar *scalars = NULL;
/* Tunable parameter: must be at least 2 since blst fails for 0 or 1 */
if (len < 8) {
g1_lincomb_naive(out, p, coeffs, len);
} else {
/* blst's implementation of the Pippenger method */
size_t scratch_size = blst_p1s_mult_pippenger_scratch_sizeof(len);
ret = c_kzg_malloc(&scratch, scratch_size);
if (ret != C_KZG_OK) goto out;
ret = c_kzg_calloc((void **)&p_affine, len, sizeof(blst_p1_affine));
if (ret != C_KZG_OK) goto out;
ret = c_kzg_calloc((void **)&scalars, len, sizeof(blst_scalar));
if (ret != C_KZG_OK) goto out;
/* 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 (uint64_t 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, 255, scratch
);
}
ret = C_KZG_OK;
out:
c_kzg_free(scratch);
c_kzg_free(p_affine);
c_kzg_free(scalars);
return ret;
}
/**
* Compute and return [ x^0, x^1, ..., x^{n-1} ].
*
* @remark `out` is left untouched if `n == 0`.
*
* @param[out] out The array to store the powers
* @param[in] x The field element to raise to powers
* @param[in] n The number of powers to compute
*/
static void compute_powers(fr_t *out, const fr_t *x, uint64_t n) {
fr_t current_power = FR_ONE;
for (uint64_t i = 0; i < n; i++) {
out[i] = current_power;
blst_fr_mul(¤t_power, ¤t_power, x);
}
}
///////////////////////////////////////////////////////////////////////////////
// Polynomials Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Evaluate a polynomial in evaluation form at a given point.
*
* @param[out] out The result of the evaluation
* @param[in] p The polynomial in evaluation form
* @param[in] x The point to evaluate the polynomial at
* @param[in] s The trusted setup
*/
static C_KZG_RET evaluate_polynomial_in_evaluation_form(
fr_t *out, const Polynomial *p, const fr_t *x, const KZGSettings *s
) {
C_KZG_RET ret;
fr_t tmp;
fr_t *inverses_in = NULL;
fr_t *inverses = NULL;
uint64_t i;
const fr_t *roots_of_unity = s->roots_of_unity;
ret = new_fr_array(&inverses_in, FIELD_ELEMENTS_PER_BLOB);
if (ret != C_KZG_OK) goto out;
ret = new_fr_array(&inverses, FIELD_ELEMENTS_PER_BLOB);
if (ret != C_KZG_OK) goto out;
for (i = 0; i < FIELD_ELEMENTS_PER_BLOB; i++) {
/*
* If the point to evaluate at is one of the evaluation points by which
* the polynomial is given, we can just return the result directly.
* Note that special-casing this is necessary, as the formula below
* would divide by zero otherwise.
*/
if (fr_equal(x, &roots_of_unity[i])) {
*out = p->evals[i];
ret = C_KZG_OK;
goto out;
}
blst_fr_sub(&inverses_in[i], x, &roots_of_unity[i]);
}
ret = fr_batch_inv(inverses, inverses_in, FIELD_ELEMENTS_PER_BLOB);
if (ret != C_KZG_OK) goto out;
*out = FR_ZERO;
for (i = 0; i < FIELD_ELEMENTS_PER_BLOB; i++) {
blst_fr_mul(&tmp, &inverses[i], &roots_of_unity[i]);
blst_fr_mul(&tmp, &tmp, &p->evals[i]);
blst_fr_add(out, out, &tmp);
}
fr_from_uint64(&tmp, FIELD_ELEMENTS_PER_BLOB);
fr_div(out, out, &tmp);
fr_pow(&tmp, x, FIELD_ELEMENTS_PER_BLOB);
blst_fr_sub(&tmp, &tmp, &FR_ONE);
blst_fr_mul(out, out, &tmp);
out:
c_kzg_free(inverses_in);
c_kzg_free(inverses);
return ret;
}
///////////////////////////////////////////////////////////////////////////////
// KZG Functions
///////////////////////////////////////////////////////////////////////////////
/**
* Compute a KZG commitment from a polynomial (in monomial form).
*
* @param[out] out The resulting commitment
* @param[in] p The polynomial to commit to
* @param[in] n The polynomial length
* @param[in] s The trusted setup
*/
static C_KZG_RET poly_to_kzg_commitment_monomial(
g1_t *out, const fr_t *p, size_t n, const KZGSettings *s
) {
return g1_lincomb_fast(out, s->g1_values, p, n);
}
/**
* Compute a KZG commitment from a polynomial (in lagrange form).
*
* @param[out] out The resulting commitment
* @param[in] p The polynomial to commit to
* @param[in] n The polynomial length
* @param[in] s The trusted setup
*/
C_KZG_RET poly_to_kzg_commitment_lagrange(
g1_t *out, const fr_t *p, size_t n, const KZGSettings *s
) {
return g1_lincomb_fast(out, s->g1_values_lagrange, p, n);
}
/**
* Convert a blob to a KZG commitment.
*
* @param[out] out The resulting commitment
* @param[in] blob The blob representing the polynomial to be committed to
* @param[in] s The trusted setup
*/
C_KZG_RET blob_to_kzg_commitment(
KZGCommitment *out, const Blob *blob, const KZGSettings *s
) {
C_KZG_RET ret;
Polynomial p;
g1_t commitment;
ret = blob_to_polynomial(&p, blob);
if (ret != C_KZG_OK) return ret;
ret = poly_to_kzg_commitment_lagrange(
&commitment, p.evals, FIELD_ELEMENTS_PER_BLOB, s
);
if (ret != C_KZG_OK) return ret;
bytes_from_g1(out, &commitment);
return C_KZG_OK;
}
/* Forward function declaration */
static C_KZG_RET verify_kzg_proof_impl(
bool *ok,
const g1_t *commitment,
const fr_t *z,
const fr_t *y,
const g1_t *proof,
const KZGSettings *s
);
/**
* Verify a KZG proof claiming that `p(z) == y`.
*
* @param[out] ok True if the proofs are valid, otherwise false
* @param[in] commitment The KZG commitment corresponding to poly p(x)
* @param[in] z The evaluation point
* @param[in] y The claimed evaluation result
* @param[in] kzg_proof The KZG proof
* @param[in] s The trusted setup
*/
C_KZG_RET verify_kzg_proof(
bool *ok,
const Bytes48 *commitment_bytes,
const Bytes32 *z_bytes,
const Bytes32 *y_bytes,
const Bytes48 *proof_bytes,
const KZGSettings *s
) {
C_KZG_RET ret;
fr_t z_fr, y_fr;
g1_t commitment_g1, proof_g1;
*ok = false;
/* Convert untrusted inputs to trusted inputs */
ret = bytes_to_kzg_commitment(&commitment_g1, commitment_bytes);
if (ret != C_KZG_OK) return ret;
ret = bytes_to_bls_field(&z_fr, z_bytes);
if (ret != C_KZG_OK) return ret;
ret = bytes_to_bls_field(&y_fr, y_bytes);
if (ret != C_KZG_OK) return ret;
ret = bytes_to_kzg_proof(&proof_g1, proof_bytes);
if (ret != C_KZG_OK) return ret;
/* Call helper to do pairings check */
return verify_kzg_proof_impl(
ok, &commitment_g1, &z_fr, &y_fr, &proof_g1, s
);
}
/**
* Helper function: Verify KZG proof claiming that `p(z) == y`.
*
* Given a @p commitment to a polynomial, a @p proof for @p z, and the
* claimed value @p y at @p z, 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] z The point at which the proof is to be checked
* (opened)
* @param[in] y The claimed value of the polynomial at @p z
* @param[in] proof A proof of the value of the polynomial at the
* point @p z
* @param[in] s The trusted setup
*/
static C_KZG_RET verify_kzg_proof_impl(
bool *ok,
const g1_t *commitment,
const fr_t *z,
const fr_t *y,
const g1_t *proof,
const KZGSettings *s
) {
g2_t x_g2, X_minus_z;
g1_t y_g1, P_minus_y;