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It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Affero General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Affero General Public License for more details. + + You should have received a copy of the GNU Affero General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If your software can interact with users remotely through a computer +network, you should also make sure that it provides a way for users to +get its source. For example, if your program is a web application, its +interface could display a "Source" link that leads users to an archive +of the code. There are many ways you could offer source, and different +solutions will be better for different programs; see section 13 for the +specific requirements. + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU AGPL, see +. diff --git a/README.md b/README.md new file mode 100644 index 0000000..6a50dc5 --- /dev/null +++ b/README.md @@ -0,0 +1,17 @@ +# DualRing-rs + +Rust implementation of [DualRing-PRF](https://eprint.iacr.org/2024/985), a post-quantum [ring signature](https://en.wikipedia.org/wiki/Ring_signature) scheme based on the Legendre PRF. + +Early development, not working yet. I focus on implementing the non-linkable version first, then the linkable version will follow. + +At the time I started this project, DualRing-PRF seemed to be the most performant post-quantum linkable ring signature. + +## License + +[Support me via LiberaPay](https://liberapay.com/tuxmain/donate) + +GNU AGPL v3, CopyLeft 2025 Pascal Engélibert [(why copyleft?)](https://txmn.tk/blog/why-copyleft/) + +This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, version 3 of the License. +This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details. +You should have received a copy of the GNU Affero General Public License along with this program. If not, see https://www.gnu.org/licenses/. diff --git a/rustfmt.toml b/rustfmt.toml new file mode 100644 index 0000000..26b2841 --- /dev/null +++ b/rustfmt.toml @@ -0,0 +1,9 @@ +hard_tabs = true +newline_style = "Unix" +imports_granularity = "Crate" + +unstable_features = true +format_code_in_doc_comments = true +format_macro_bodies = true +format_macro_matchers = true +format_strings = true diff --git a/src/lib.rs b/src/lib.rs new file mode 100644 index 0000000..8d39dac --- /dev/null +++ b/src/lib.rs @@ -0,0 +1,623 @@ +#![feature(array_chunks)] +#![feature(split_array)] + +// To be more explicit about all the variable names +#![allow(clippy::let_and_return)] +// Have you seen how many indices the vectors have? +#![allow(clippy::type_complexity)] + +mod util; + +use bytemuck::{bytes_of, bytes_of_mut, cast_slice, cast_slice_mut}; +use num_modular::{ModularCoreOps, ModularPow, ModularUnaryOps}; +use rand::seq::SliceRandom; +use rand_core::CryptoRngCore; +use sha3::{ + Shake128, + digest::{ExtendableOutput, Update, XofReader}, +}; +use std::marker::PhantomData; + +const P: u128 = 0x7fff_ffff_ffff_ffff_ffff_ffff_ffff_ffff; + +/// L_K(a) Legendre PRF +fn legendre_prf(a: u128) -> u128 { + 1.subm(a.powm(0x3fffffffffffffffffffffffffffffff, &P), &P) / 2 +} + +fn random_fp(mut rng: impl CryptoRngCore) -> u128 { + let mut bytes = [0; 16]; + rng.fill_bytes(&mut bytes); + // approximate modulo to avoid complex multi-register arithmetic + bytes[0] &= 0x7f; + u128::from_be_bytes(bytes) + // Generated number is in [0..P] + // Proba(0 = x mod P) = 2^-126 + // so we are in in the ring [0..P-1] with overwhelming probability +} + +pub struct DualRing { + /// B + b: usize, + /// M + m: usize, + /// N + n: usize, + /// tau + tau: usize, +} + +impl DualRing { + pub fn new_fast() -> Self { + Self { + b: 10, + m: 127, + n: 16, + tau: 74, + } + } + + pub fn keygen(rng: impl CryptoRngCore) -> (u128, [u128; 2 * 254]) { + let sk = random_fp(rng); + let pk = Self::power_residue_prf_l(sk); + (sk, pk) + } + + pub fn sign( + &self, + ring: &[[u128; 2 * 254]], + sk: u128, + sk_index: usize, + m: &[u8], + mut rng: impl CryptoRngCore, + ) { + // Phase 1 + + let mut salt = [0; 32]; + rng.fill_bytes(&mut salt); + + /*let challenges: Vec<([u8; L], Vec)> = ring.iter().enumerate().map(|(i, pk_i)| { + if i == sk_index { + ([0; L], Vec::new()) + } else { + let mut challenge_seed = [0; L]; + rng.fill_bytes(&mut challenge_seed); + let mut challenge = vec![0; self.tau as usize * self.b as usize]; + Self::expand_indices(&challenge_seed, L as _, &mut challenge); + (challenge_seed, challenge) + } + }).collect();*/ + let challenges: Vec<[u8; 16]> = (0..ring.len()) + .map(|i| { + let mut challenge = [0; 16]; + if i != sk_index { + rng.fill_bytes(&mut challenge); + } + challenge + }) + .collect(); + + struct Share { + k: u128, + a: u128, + b: u128, + c: u128, + r: Vec, + c_mask: Vec<[u8; 32]>, + c_mpc: [u8; 32], + } + + struct Execution { + sd_mask: Vec, + mask: Vec>, + /// [b] + r_sum: Vec, + t: Vec, + dk: u128, + dc: u128, + shares: Vec, + indices: Vec>, + /// [k][j][b] + d_indices: Vec>>, + epsilon: u128, + lambda: Vec, + } + + let mut executions: Vec = (0..self.tau) + .map(|e| { + let mut sd_mask_e = vec![0u128; self.m]; + rng.fill_bytes(bytes_of_mut(&mut sd_mask_e[0])); + Self::expand_tree(&mut sd_mask_e); + + let mask_e: Vec> = (0..self.m) + .map(|k| { + let mut mask_e_k = vec![0u128; self.n]; + mask_e_k[0] = sd_mask_e[k]; + Self::expand_tree(&mut mask_e_k); + mask_e_k + }) + .collect(); + + let mut sd_mpc_e = vec![0u128; self.n]; + rng.fill_bytes(bytes_of_mut(&mut sd_mpc_e[0])); + Self::expand_tree(&mut sd_mpc_e); + + let mut shares: Vec = (0..self.n) + .map(|i| { + let mut buf = vec![0; (4 + self.b) * size_of::()]; + Self::expand(&sd_mpc_e[i].to_be_bytes(), &mut buf); + let mut buf_iter = buf.array_chunks(); + let k_e_i = u128::from_be_bytes(*buf_iter.next().unwrap()); + let a_e_i = u128::from_be_bytes(*buf_iter.next().unwrap()); + let b_e_i = u128::from_be_bytes(*buf_iter.next().unwrap()); + let c_e_i = u128::from_be_bytes(*buf_iter.next().unwrap()); + let r_e_i: Vec = (0..self.b) + .zip(buf_iter) + .map(|(_bi, r_e_i_bi)| u128::from_be_bytes(*r_e_i_bi)) + .collect(); + let c_mpc_e_i = Self::hash([ + &salt[..], + &e.to_be_bytes(), + &i.to_be_bytes(), + &sd_mpc_e[i].to_be_bytes(), + ]); + let c_mask_e_i: Vec<[u8; 32]> = mask_e + .iter() + .enumerate() + .map(|(k, mask_e_k)| { + Self::hash([ + &salt[..], + &e.to_be_bytes(), + &k.to_be_bytes(), + &i.to_be_bytes(), + &mask_e_k[i].to_be_bytes(), + ]) + }) + .collect(); + Share { + k: k_e_i, + a: a_e_i, + b: b_e_i, + c: c_e_i, + r: r_e_i, + c_mask: c_mask_e_i, + c_mpc: c_mpc_e_i, + } + }) + .collect(); + + let dk_e: u128 = sk.subm( + shares + .iter() + .map(|share| share.k) + .fold(0, |x, y| x.addm(y, &P)), + &P, + ); + shares[0].k = shares[0].k.addm(dk_e, &P); + + let a_e_sum = shares + .iter() + .map(|share| share.a) + .fold(0, |x, y| x.addm(y, &P)); + let b_e_sum = shares + .iter() + .map(|share| share.b) + .fold(0, |x, y| x.addm(y, &P)); + let c_e_sum = shares + .iter() + .map(|share| share.c) + .fold(0, |x, y| x.addm(y, &P)); + let dc_e = a_e_sum.mulm(b_e_sum, &P).subm(c_e_sum, &P); + shares[0].c = shares[0].c.addm(dc_e, &P); + + let indices_e: Vec> = challenges + .iter() + .enumerate() + .map(|(j, challenge)| { + let mut indices_e_j = vec![0; self.b]; + if j != sk_index { + Self::expand_indices(challenge, 2 * 254, &mut indices_e_j); + } + indices_e_j + }) + .collect(); + + let (r_sum_e, t_e): (Vec, Vec) = (0..self.b) + .map(|b| { + let r_e_b = shares + .iter() + .map(|share| share.r[b]) + .fold(0, |x, y| x.addm(y, &P)); + let t_e_b = legendre_prf(r_e_b).subm( + indices_e + .iter() + .map(|indices_e_j| { + if indices_e_j.is_empty() { + 0 + } else { + ring[sk_index][indices_e_j[b] as usize] + } + }) + .fold(0, |x, y| x.addm(y, &P)), + &P, + ); + (r_e_b, t_e_b) + }) + .collect(); + + Execution { + sd_mask: sd_mask_e, + mask: mask_e, + r_sum: r_sum_e, + t: t_e, + dk: dk_e, + dc: dc_e, + shares, + indices: indices_e, + d_indices: Vec::new(), + epsilon: 0, + lambda: Vec::new(), + } + }) + .collect(); + + // Concatenate lots of stuff to be hashed! + let s1 = executions + .iter() + .flat_map(|e| { + [cast_slice(&e.t), bytes_of(&e.dk), bytes_of(&e.dc)] + .into_iter() + .chain( + e.shares + .iter() + .flat_map(|share| [cast_slice(&share.c_mask), &share.c_mpc].into_iter()), + ) + }); + + // Phase 2 + + let h1 = Self::hash( + [&salt[..], m] + .into_iter() + .chain(ring.iter().map(|pk| cast_slice(pk))) + .chain(s1), + ); + + let signer_challenge = u128::from_be_bytes(*h1.split_array_ref::<16>().0) + ^ challenges + .iter() + .map(|c| u128::from_be_bytes(*c)) + .fold(0, |x, y| x ^ y); + + // TODO optimize: hold only 1 copy of indices_e_pi for all e + // (they are all the same if I get it right from part 2, line 4) + for e in executions.iter_mut() { + Self::expand_indices( + &signer_challenge.to_be_bytes(), + 2 * 254, + &mut e.indices[sk_index], + ); + } + + let s2: Vec<[u8; 32]> = executions + .iter_mut() + .enumerate() + .map(|(e_index, e)| { + let (c_d_e, d_indices_e, accs_e): ( + Vec>, + Vec>>, + Vec<[u8; 32]>, + ) = e.mask + .iter() + .enumerate() + .map(|(k, mask_e_k)| { + let mask_e_k_sum = mask_e_k.iter().fold(0, |x, y| x.addm(y, &P)); + let (c_d_e_k, d_indices_e_k): (Vec<[u8; 32]>, Vec>) = e + .indices + .iter() + .map(|indices_e_j| { + let d_indices_e_k_j: Vec = indices_e_j + .iter() + .map(|index_e_j_b| { + (*index_e_j_b as u128).subm(mask_e_k_sum, &P) + }) + .collect(); + let c_d_e_k_j = Self::hash([ + &salt, + cast_slice(&[e_index as u32, k as u32]), + cast_slice(&d_indices_e_k_j), + ]); + (c_d_e_k_j, d_indices_e_k_j) + }) + .collect(); + + let mut phi: Vec = (0..ring.len()).collect(); + phi.shuffle(&mut rng); + + let acc_e_k = + Self::compute_tree_root(phi.iter().map(|i| c_d_e_k[*i]).collect()); + + (c_d_e_k, d_indices_e_k, acc_e_k) + }) + .collect(); + e.d_indices = d_indices_e; + + let acc_e = Self::hash( + [salt.as_slice(), &e_index.to_be_bytes()] + .into_iter() + .chain(accs_e.iter().map(|acc_e_k| acc_e_k.as_slice())), + ); + + acc_e + }) + .collect(); + + // Phase 3 + + let h2 = Self::hash( + [h1.as_slice()] + .into_iter() + .chain(s2.iter().map(|i| i.as_slice())), + ); + let mut kbar = vec![0; self.tau]; + Self::expand_indices(&h2, self.m as u32, &mut kbar); + + // Phase 4 + + let s3: Vec> = executions + .iter() + .map(|e| { + let o_e: Vec = e.indices[sk_index] + .iter() + .zip(e.r_sum.iter()) + .map(|(indices_e_pi_b, r_e_b)| { + let o_e_b = r_e_b.mulm(sk.addm(*indices_e_pi_b as u128, &P), &P); + o_e_b + }) + .collect(); + o_e + }) + .collect(); + + // Phase 5 + + let h3 = Self::hash( + [h2.as_slice()] + .into_iter() + .chain(s3.iter().map(|o_e| cast_slice(o_e))), + ); + + let mut buf = vec![0; self.tau * (self.b + 1) * size_of::()]; + Self::expand(&h3, &mut buf); + let mut buf_iter = buf.array_chunks(); + for e in executions.iter_mut() { + e.epsilon = u128::from_be_bytes(*buf_iter.next().unwrap()) & P; + e.lambda = (0..self.b) + .map(|_b| u128::from_be_bytes(*buf_iter.next().unwrap()) & P) + .collect(); + } + + // Phase 6 + + let mut h4_hasher = Shake128::default(); + h4_hasher.update(&h3); + + for ((e, kbar_e), o_e) in executions.iter().zip(kbar.iter()).zip(s3.iter()) { + let (alpha_e, beta_e): (Vec, Vec) = e + .shares + .iter() + .map(|share| { + let alpha_e_i = share.a.addm(share.k.mulm(e.epsilon, &P), &P); + let beta_e_i = share.b.addm( + share + .r + .iter() + .zip(e.lambda.iter()) + .map(|(r_e_i_b, lambda_e_b)| r_e_i_b.mulm(lambda_e_b, &P)) + .fold(0, |x, y| x.addm(y, &P)), + &P, + ); + (alpha_e_i, beta_e_i) + }) + .collect(); + + let alpha_e_sum = alpha_e.iter().fold(0, |x, y| x.addm(y, &P)); + let beta_e_sum = beta_e.iter().fold(0, |x, y| x.addm(y, &P)); + + let (z_e, mut zp_e): (Vec, Vec) = e.shares.iter().zip(e.mask[*kbar_e as usize].iter()).enumerate().map(|(i, (share_e_i, mask_e_kbar_e_i))| { + let (z_e_i, zp_e_i) = e + .lambda + .iter() + .zip(share_e_i.r.iter()) + .zip(e.d_indices[*kbar_e as usize][sk_index].iter()) + .map(|((lambda_e_b, r_e_i_b), d_index_e_kbar_pi_b)| { + let factor = lambda_e_b.mulm(r_e_i_b, &P); + (factor.mulm(d_index_e_kbar_pi_b, &P), factor.mulm(if i == 0 { + mask_e_kbar_e_i.addm(d_index_e_kbar_pi_b, &P) + } else { + *mask_e_kbar_e_i + }, &P)) + }) + .fold((0, 0), |x, y| (x.0.subm(y.0, &P), x.1.subm(y.1, &P))); + (z_e_i, zp_e_i) + }).collect(); + let z_e_sum = z_e.iter().fold(0, |x, y| x.addm(y, &P)); + let d_z_e = z_e_sum.subm(zp_e.iter().fold(0, |x, y| x.addm(y, &P)), &P); + zp_e[0] = e.lambda.iter().zip(o_e.iter()).map(|(lambda_e_b, o_e_b)| lambda_e_b.mulm(o_e_b, &P)).fold(zp_e[0].addm(d_z_e, &P), |x, y| x.addm(y, &P)); + let gamma_e: Vec = e.shares.iter().zip(zp_e.iter()).map(|(share_e_i, zp_e_i)| { + let gamma_e_i = alpha_e_sum.mulm(share_e_i.b, &P) + .addm(beta_e_sum.mulm(share_e_i.a, &P), &P) + .subm(share_e_i.c, &P) + .addm(e.epsilon.mulm(zp_e_i, &P), &P); + gamma_e_i + }).collect(); + + // We also hash the corresponding vectors, so what use is to hash their sums? + //h4_hasher.update(bytes_of(&alpha_e_sum)); + //h4_hasher.update(bytes_of(&beta_e_sum)); + + h4_hasher.update(cast_slice(&alpha_e)); + h4_hasher.update(cast_slice(&beta_e)); + h4_hasher.update(cast_slice(&gamma_e)); + } + + // Phase 7 + + let mut h4_reader = h4_hasher.finalize_xof(); + let mut h4 = [0; 32]; + h4_reader.read(&mut h4); + let mut ibar = vec![0; self.tau]; + Self::expand_indices(&h4, self.n as u32, &mut ibar); + + // Phase 8 + + + } + + /// L_K^k(a) + fn power_residue_prf(a: u128) -> u128 { + // for k=2, this is the Legendre PRF + legendre_prf(a) + } + + fn power_residue_prf_l(a: u128) -> [u128; 2 * 254] { + // TODO generate uniform list + #[rustfmt::skip] + const LIST: [u128; 2*254] = [0; 2*254]; + let mut res = [0; 2 * 254]; + for (res_i, l_i) in res.iter_mut().zip(LIST.iter()) { + *res_i = Self::power_residue_prf(a + l_i); + } + res + } + + fn expand(input: &[u8], output: &mut [u8]) { + // TODO generic + let mut hasher = Shake128::default(); + hasher.update(input); + let mut reader = hasher.finalize_xof(); + reader.read(output); + } + + fn expand_indices(input: &[u8], modulus: u32, output: &mut [u32]) { + // TODO generic + let mut hasher = Shake128::default(); + hasher.update(input); + let mut reader = hasher.finalize_xof(); + reader.read(cast_slice_mut(output)); + for i in output.iter_mut() { + *i %= modulus; + } + } + + fn hash<'a>(input: impl IntoIterator) -> [u8; 32] { + // TODO generic + let mut output = [0; 32]; + let mut hasher = Shake128::default(); + for item in input { + hasher.update(item); + } + let mut reader = hasher.finalize_xof(); + reader.read(&mut output); + output + } + + /// Seed is the first element + fn expand_tree(tree: &mut [u128]) { + for i in 0..tree.len() / 2 - 1 { + let (tree1, tree2) = tree.split_at_mut(2 * i + 1); + Self::expand(bytes_of(&tree1[i]), cast_slice_mut(&mut tree2[0..2])); + } + } + + /// Compute Merkle tree root + // TODO salt? + fn compute_tree_root(mut input: Vec<[u8; 32]>) -> [u8; 32] { + while input.len() > 1 { + if input.len() % 2 == 1 { + input.push(*input.last().unwrap()); + } + for i in (0..input.len()).step_by(2) { + let mut hasher = Shake128::default(); + hasher.update(&input[i]); + hasher.update(&input[i + 1]); + let mut reader = hasher.finalize_xof(); + reader.read(&mut input[i / 2]); + } + input.truncate(input.len() / 2); + } + input[0] + } + + /// Compute authentication path from given input's index to root + /// Returns the siblings of the path, from leaf to root + fn compute_tree_proof(mut input: Vec<[u8; 32]>, mut index: usize) -> Vec<[u8; 32]> { + let mut path = Vec::new(); + // TODO do not compute useless branches + // input.len().next_power_of_two()-1 + while input.len() > 1 { + if input.len() % 2 == 1 { + input.push(*input.last().unwrap()); + } + path.push(input[index ^ 1]); + for i in (0..input.len()).step_by(2) { + let mut hasher = Shake128::default(); + hasher.update(&input[i]); + hasher.update(&input[i + 1]); + let mut reader = hasher.finalize_xof(); + reader.read(&mut input[i / 2]); + } + input.truncate(input.len() / 2); + index /= 2; + } + path + } + + fn tree_root_from_path(mut leaf: [u8; 32], mut index: usize, path: &[[u8; 32]]) -> [u8; 32] { + for sibling in path { + let mut hasher = Shake128::default(); + if index % 2 == 0 { + hasher.update(&leaf); + hasher.update(sibling); + } else { + hasher.update(sibling); + hasher.update(&leaf); + } + let mut reader = hasher.finalize_xof(); + reader.read(&mut leaf); + index /= 2; + } + leaf + } +} + +#[cfg(test)] +mod tests { + use rand::Rng; + + use super::*; + + #[test] + fn test_merkle_tree() { + let mut rng = rand::thread_rng(); + for len in 1usize..32 { + let input: Vec<[u8; 32]> = (0..len).map(|_i| rng.r#gen()).collect(); + let root = DualRing::compute_tree_root(input.clone()); + for index in 0..len { + let path = DualRing::compute_tree_proof(input.clone(), index); + assert_eq!(root, DualRing::tree_root_from_path(input[index], index, &path)); + } + } + } + + #[test] + fn test_sign() { + let mut rng = rand::thread_rng(); + let signer = DualRing::new_fast(); + let m = b"Hello world!"; + let l = 10; + let (sks, pks): (Vec, Vec<[u128; 2 * 254]>) = (0..l).map(|_j| DualRing::keygen(&mut rng)).collect(); + let sk_index = 4; + signer.sign(&pks, sks[sk_index], sk_index, m, &mut rng); + } +} diff --git a/src/util.rs b/src/util.rs new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/src/util.rs @@ -0,0 +1 @@ +