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Reimplement Felt::mul_mod and Felt::mod_inverse #15

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2 changes: 2 additions & 0 deletions crates/starknet-types-core/Cargo.toml
Original file line number Diff line number Diff line change
Expand Up @@ -19,6 +19,8 @@ lambdaworks-crypto = { git = "https://github.com/lambdaclass/lambdaworks.git", r

arbitrary = { version = "1.3.0", optional = true, default-features = false }
num-traits = { version = "0.2.16", default-features = false }
num-bigint = {version = "0.4.4", default-features = false}
num-integer = {version = "0.1.45", default-features = false}

[features]
default = ["std", "serde", "curve"]
Expand Down
118 changes: 106 additions & 12 deletions crates/starknet-types-core/src/felt.rs
Original file line number Diff line number Diff line change
@@ -1,7 +1,9 @@
use core::ops::{Add, Neg};
use core::ops::{Add, Mul, Neg};

use bitvec::array::BitArray;
use num_traits::{FromPrimitive, ToPrimitive, Zero};
use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{FromPrimitive, One, ToPrimitive, Zero};

#[cfg(target_pointer_width = "64")]
pub type BitArrayStore = [u64; 4];
Expand Down Expand Up @@ -32,6 +34,7 @@ use arbitrary::{self, Arbitrary, Unstructured};
pub struct Felt(pub(crate) FieldElement<Stark252PrimeField>);

/// A non-zero [Felt].
#[derive(Debug, Clone, Copy)]
pub struct NonZeroFelt(FieldElement<Stark252PrimeField>);

#[derive(Debug)]
Expand Down Expand Up @@ -170,14 +173,47 @@ impl Felt {
Self(self.0.pow(exponent.0.representative()))
}

/// Modular multiplication between `self` and `rhs` modulo `p`.
// Implemention taken from Jonathan Lei's starknet-rs
// https://github.com/xJonathanLEI/starknet-rs/blob/a3a0050f80e90bd40303256a85783f4b5b18258c/starknet-crypto/src/fe_utils.rs#L20
/// Modular multiplication between `self` and `rhs` in modulo `p`.
pub fn mul_mod(&self, rhs: &Self, p: &NonZeroFelt) -> Self {
(self * rhs).div_rem(p).1
let multiplicand = BigInt::from_bytes_be(num_bigint::Sign::Plus, &self.to_bytes_be());
let multiplier = BigInt::from_bytes_be(num_bigint::Sign::Plus, &rhs.to_bytes_be());
let modulus = BigInt::from_bytes_be(num_bigint::Sign::Plus, &p.0.to_bytes_be());

let result = multiplicand.mul(multiplier).mod_floor(&modulus);

let (_, buffer) = result.to_bytes_be();
let mut result = [0u8; 32];

result[(32 - buffer.len())..].copy_from_slice(&buffer[..]);

// safe .unwrap()
Felt::from_bytes_be(&result).unwrap()
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}

/// Modular inverse of `self` modulo `p`.
pub fn inverse_mod(&self, p: &NonZeroFelt) -> Option<Self> {
self.inverse().map(|x| x.div_rem(p).1)
// Implemention taken from Jonathan Lei's starknet-rs
// https://github.com/xJonathanLEI/starknet-rs/blob/a3a0050f80e90bd40303256a85783f4b5b18258c/starknet-crypto/src/fe_utils.rs#L46
/// Multiplicative inverse of `self` in modulo `p`.
pub fn mod_inverse(&self, p: &NonZeroFelt) -> Option<Self> {
let operand = BigInt::from_bytes_be(num_bigint::Sign::Plus, &self.0.to_bytes_be());
let modulus = BigInt::from_bytes_be(num_bigint::Sign::Plus, &p.0.to_bytes_be());

let extended_gcd = operand.extended_gcd(&modulus);
if extended_gcd.gcd != BigInt::one() {
return None;
}
let result = if extended_gcd.x < BigInt::zero() {
extended_gcd.x + modulus
} else {
extended_gcd.x
};

let (_, buffer) = result.to_bytes_be();
let mut result = [0u8; 32];
result[(32 - buffer.len())..].copy_from_slice(&buffer[..]);

Felt::from_bytes_be(&result).ok()
}

/// Remainder of dividing `self` by `n` as integers.
Expand Down Expand Up @@ -829,7 +865,6 @@ mod test {
use crate::felt_arbitrary::nonzero_felt;
use core::ops::Shl;
use proptest::prelude::*;

#[cfg(feature = "serde")]
use serde_test::{assert_de_tokens, assert_ser_tokens, Configure, Token};

Expand Down Expand Up @@ -1030,14 +1065,17 @@ mod test {
#[test]
fn inverse_mod_of_zero_is_none(p in nonzero_felt()) {
let nzp = NonZeroFelt(p.0);
prop_assert!(Felt::ZERO.inverse_mod(&nzp).is_none());
prop_assert!(Felt::ZERO.mod_inverse(&nzp).is_none());
}

#[test]
fn inverse_mod_in_range(x in nonzero_felt(), p in nonzero_felt()) {
fn inverse_mod_in_range_peter(x in nonzero_felt(), p in nonzero_felt()) {
let nzp = NonZeroFelt(p.0);
prop_assert!(x.inverse_mod(&nzp) <= Some(Felt::MAX));
prop_assert!(x.inverse_mod(&nzp) < Some(p));
let Some(result) = x.mod_inverse(&nzp) else { return Ok(()) };

prop_assert!(result <= Felt::MAX);
prop_assert!(result < p);
prop_assert!(result.mul_mod(&x, &nzp) == Felt::ONE);
}

#[test]
Expand Down Expand Up @@ -1388,4 +1426,60 @@ mod test {
)
);
}

#[test]
fn inverse_and_mul_mod() {
let nzps: Vec<NonZeroFelt> = [
Felt::from(5_i32).try_into().unwrap(),
Felt::from_hex("0x5").unwrap().try_into().unwrap(),
Felt::from_hex("0x1234").unwrap().try_into().unwrap(),
Felt::from_hex("0xabcdef123").unwrap().try_into().unwrap(),
Felt::from_hex("0xffffffffffffff")
.unwrap()
.try_into()
.unwrap(),
Felt::from_hex("0xfffffffffffffffffffffffffffffff")
.unwrap()
.try_into()
.unwrap(),
Felt::MAX.try_into().unwrap(),
]
.to_vec();
let nums = [
Felt::from_hex("0x0").unwrap(),
Felt::from_hex("0x1").unwrap(),
Felt::from_hex("0x2").unwrap(),
Felt::from_hex("0x5").unwrap(),
Felt::from_hex("0x123abc").unwrap(),
Felt::from_hex("0xabcdef9812367312").unwrap(),
Felt::from_hex("0xffffffffffffffffffffffffffffff").unwrap(),
Felt::from_hex("0xffffffffffffffffffffffffffffffffffffffffff").unwrap(),
Felt::MAX,
];

for felt in nums {
for nzp in nzps.iter() {
let result = felt.mod_inverse(nzp);
if result.is_some() {
assert_eq!(result.unwrap().mul_mod(&felt, nzp), Felt::ONE);
}
}
}
}

#[test]
fn check_mul_mod() {
let x = Felt::from_dec_str(
"3618502788666131213697322783095070105623107215331596699973092056135872020480",
)
.unwrap();
let y = Felt::from_dec_str("46118400291").unwrap();
let p: NonZeroFelt = Felt::from_dec_str("123987312893120893724347692364")
.unwrap()
.try_into()
.unwrap();
let expected_result = Felt::from_dec_str("68082278891996790254001523512").unwrap();

assert_eq!(x.mul_mod(&y, &p), expected_result);
}
}