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[release/4.x] Cherry pick: Replace Secret Sharing implementation (#5655…
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-^- ___ ___ | ||
(- -) (= =) | Y & +--? | ||
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/--x-m- /--n-n---xXx--/--yY------ | ||
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// Copyright (c) Microsoft Corporation. All rights reserved. | ||
// Licensed under the Apache 2.0 License. | ||
#include "sharing.h" | ||
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#include "ccf/crypto/entropy.h" | ||
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#include <stdexcept> | ||
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namespace crypto | ||
{ | ||
/* PRIME FIELD | ||
For simplicity, we use a finite field F[prime] where all operations | ||
are defined in plain uint64_t arithmetic, and we reduce after every | ||
operation. This is not meant to be efficient. Compared to e.g. GF(2^n), the | ||
main drawback is that we need to hash the "raw secret" to obtain a | ||
uniformly-distributed secret. | ||
*/ | ||
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using element = uint64_t; | ||
constexpr element prime = (1ul << 31) - 1ul; // a notorious Mersenne prime | ||
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static element reduce(uint64_t x) | ||
{ | ||
return (x % prime); | ||
} | ||
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static element mul(element x, element y) | ||
{ | ||
return ((x * y) % prime); | ||
} | ||
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static element add(element x, element y) | ||
{ | ||
return ((x + y) % prime); | ||
} | ||
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static element sub(element x, element y) | ||
{ | ||
return ((prime + x - y)) % prime; | ||
} | ||
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// naive algorithm, used only to compute coefficients, not for use on secrets! | ||
static element exp(element x, size_t n) | ||
{ | ||
element y = 1; | ||
while (n > 0) | ||
{ | ||
if (n & 1) | ||
y = mul(y, x); | ||
x = mul(x, x); | ||
n >>= 1; | ||
} | ||
return y; | ||
} | ||
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static element inv(element x) | ||
{ | ||
if (x == 0) | ||
{ | ||
throw std::invalid_argument("division by zero"); | ||
} | ||
return exp(x, prime - 2); | ||
} | ||
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// This function is specific to prime=2^31-1. | ||
// We assume the lower 31 bits are uniformly distributed, | ||
// and retry if they are all set to get uniformity in F[prime]. | ||
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static element sample(const crypto::EntropyPtr& entropy) | ||
{ | ||
uint64_t res = prime; | ||
while (res == prime) | ||
{ | ||
res = entropy->random64() & prime; | ||
} | ||
return res; | ||
} | ||
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/* POLYNOMIAL SHARING AND INTERPOLATION */ | ||
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static void sample_polynomial( | ||
element p[], size_t degree, const crypto::EntropyPtr& entropy) | ||
{ | ||
for (size_t i = 0; i <= degree; i++) | ||
{ | ||
p[i] = sample(entropy); | ||
} | ||
} | ||
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static element eval(element p[], size_t degree, element x) | ||
{ | ||
element y = 0, x_i = 1; | ||
for (size_t i = 0; i <= degree; i++) | ||
{ | ||
// x_i == x^i | ||
y = add(y, mul(p[i], x_i)); | ||
x_i = mul(x, x_i); | ||
} | ||
return y; | ||
} | ||
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void sample_secret_and_shares( | ||
Share& raw_secret, const std::span<Share>& shares, size_t threshold) | ||
{ | ||
if (shares.size() < 1) | ||
{ | ||
throw std::invalid_argument("insufficient number of shares"); | ||
} | ||
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if (threshold < 1 || threshold > shares.size()) | ||
{ | ||
throw std::invalid_argument("invalid threshold"); | ||
} | ||
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size_t degree = threshold - 1; | ||
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raw_secret.x = 0; | ||
for (size_t s = 0; s < shares.size(); s++) | ||
{ | ||
shares[s].x = s + 1; | ||
} | ||
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auto entropy = crypto::create_entropy(); | ||
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for (size_t limb = 0; limb < LIMBS; limb++) | ||
{ | ||
element p[degree + 1]; /*SECRET*/ | ||
sample_polynomial(p, degree, entropy); | ||
raw_secret.y[limb] = p[0]; | ||
for (size_t s = 0; s < shares.size(); s++) | ||
{ | ||
shares[s].y[limb] = eval(p, degree, shares[s].x); | ||
} | ||
} | ||
} | ||
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void recover_unauthenticated_secret( | ||
Share& raw_secret, const std::span<Share const>& shares, size_t threshold) | ||
{ | ||
if (shares.size() < threshold) | ||
{ | ||
throw std::invalid_argument("insufficient input shares"); | ||
} | ||
// We systematically reduce the input shares instead of checking they are | ||
// well-formed. | ||
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size_t degree = threshold - 1; | ||
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// Precomputes Lagrange coefficients for interpolating p(0). No secrets | ||
// involved. | ||
element lagrange[degree + 1]; | ||
for (size_t i = 0; i <= degree; i++) | ||
{ | ||
element numerator = 1, denominator = 1; | ||
for (size_t j = 0; j <= degree; j++) | ||
{ | ||
if (i != j) | ||
{ | ||
numerator = mul(numerator, reduce(shares[j].x)); | ||
denominator = | ||
mul(denominator, sub(reduce(shares[j].x), reduce(shares[i].x))); | ||
} | ||
} | ||
if (denominator == 0) | ||
{ | ||
throw std::invalid_argument("duplicate input share"); | ||
} | ||
lagrange[i] = mul(numerator, inv(denominator)); | ||
} | ||
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// Interpolate every limb of the secret. Constant-time on y values. | ||
raw_secret.x = 0; | ||
for (size_t limb = 0; limb < LIMBS; limb++) | ||
{ | ||
element y = 0; | ||
for (size_t i = 0; i <= degree; i++) | ||
{ | ||
y = add(y, mul(lagrange[i], reduce(shares[i].y[limb]))); | ||
} | ||
raw_secret.y[limb] = y; | ||
} | ||
} | ||
} |
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