From afc0759480d3336d4b58f4cf33975bb53d5ede84 Mon Sep 17 00:00:00 2001 From: parazyd Date: Thu, 12 Aug 2021 17:19:48 +0200 Subject: [PATCH] halo2: Add poseidon hash primitives --- examples/halo2/src/lib.rs | 2 + examples/halo2/src/primitives.rs | 1 + examples/halo2/src/primitives/poseidon.rs | 363 ++++ .../halo2/src/primitives/poseidon/grain.rs | 193 ++ examples/halo2/src/primitives/poseidon/mds.rs | 123 ++ .../src/primitives/poseidon/nullifier.rs | 1619 +++++++++++++++++ .../src/primitives/poseidon/test_vectors.rs | 632 +++++++ 7 files changed, 2933 insertions(+) create mode 100644 examples/halo2/src/lib.rs create mode 100644 examples/halo2/src/primitives.rs create mode 100644 examples/halo2/src/primitives/poseidon.rs create mode 100644 examples/halo2/src/primitives/poseidon/grain.rs create mode 100644 examples/halo2/src/primitives/poseidon/mds.rs create mode 100644 examples/halo2/src/primitives/poseidon/nullifier.rs create mode 100644 examples/halo2/src/primitives/poseidon/test_vectors.rs diff --git a/examples/halo2/src/lib.rs b/examples/halo2/src/lib.rs new file mode 100644 index 000000000..ebcca690d --- /dev/null +++ b/examples/halo2/src/lib.rs @@ -0,0 +1,2 @@ +pub mod circuit; +pub mod primitives; diff --git a/examples/halo2/src/primitives.rs b/examples/halo2/src/primitives.rs new file mode 100644 index 000000000..4395ce1cd --- /dev/null +++ b/examples/halo2/src/primitives.rs @@ -0,0 +1 @@ +pub mod poseidon; diff --git a/examples/halo2/src/primitives/poseidon.rs b/examples/halo2/src/primitives/poseidon.rs new file mode 100644 index 000000000..2b17d9acd --- /dev/null +++ b/examples/halo2/src/primitives/poseidon.rs @@ -0,0 +1,363 @@ +use std::array; +use std::fmt; +use std::iter; +use std::marker::PhantomData; + +use halo2::arithmetic::FieldExt; + +pub(crate) mod grain; +pub(crate) mod mds; + +#[cfg(test)] +pub(crate) mod test_vectors; + +mod nullifier; +pub use nullifier::OrchardNullifier; + +use grain::SboxType; + +/// The type used to hold permutation state. +pub type State = [F; T]; + +/// The type used to hold duplex sponge state. +pub type SpongeState = [Option; RATE]; + +/// The type used to hold the MDS matrix and its inverse. +pub type Mds = [[F; T]; T]; + +/// A specification for a Poseidon permutation. +pub trait Spec { + /// The number of full rounds for this specification. + /// + /// This must be an even number. + fn full_rounds() -> usize; + + /// The number of partial rounds for this specification. + fn partial_rounds() -> usize; + + /// The S-box for this specification. + fn sbox(val: F) -> F; + + /// Side-loaded index of the first correct and secure MDS that will be generated by + /// the reference implementation. + /// + /// This is used by the default implementation of [`Spec::constants`]. If you are + /// hard-coding the constants, you may leave this unimplemented. + fn secure_mds(&self) -> usize; + + /// Generates `(round_constants, mds, mds^-1)` corresponding to this specification. + fn constants(&self) -> (Vec<[F; T]>, Mds, Mds) { + let r_f = Self::full_rounds(); + let r_p = Self::partial_rounds(); + + let mut grain = grain::Grain::new(SboxType::Pow, T as u16, r_f as u16, r_p as u16); + + let round_constants = (0..(r_f + r_p)) + .map(|_| { + let mut rc_row = [F::zero(); T]; + for (rc, value) in rc_row + .iter_mut() + .zip((0..T).map(|_| grain.next_field_element())) + { + *rc = value; + } + rc_row + }) + .collect(); + + let (mds, mds_inv) = mds::generate_mds::(&mut grain, self.secure_mds()); + + (round_constants, mds, mds_inv) + } +} + +/// Runs the Poseidon permutation on the given state. +pub(crate) fn permute, const T: usize, const RATE: usize>( + state: &mut State, + mds: &Mds, + round_constants: &[[F; T]], +) { + let r_f = S::full_rounds() / 2; + let r_p = S::partial_rounds(); + + let apply_mds = |state: &mut State| { + let mut new_state = [F::zero(); T]; + // Matrix multiplication + #[allow(clippy::needless_range_loop)] + for i in 0..T { + for j in 0..T { + new_state[i] += mds[i][j] * state[j]; + } + } + *state = new_state; + }; + + let full_round = |state: &mut State, rcs: &[F; T]| { + for (word, rc) in state.iter_mut().zip(rcs.iter()) { + *word = S::sbox(*word + rc); + } + apply_mds(state); + }; + + let part_round = |state: &mut State, rcs: &[F; T]| { + for (word, rc) in state.iter_mut().zip(rcs.iter()) { + *word += rc; + } + // In a partial round, the S-box is only applied to the first state word. + state[0] = S::sbox(state[0]); + apply_mds(state); + }; + + iter::empty() + .chain(iter::repeat(&full_round as &dyn Fn(&mut State, &[F; T])).take(r_f)) + .chain(iter::repeat(&part_round as &dyn Fn(&mut State, &[F; T])).take(r_p)) + .chain(iter::repeat(&full_round as &dyn Fn(&mut State, &[F; T])).take(r_f)) + .zip(round_constants.iter()) + .fold(state, |state, (round, rcs)| { + round(state, rcs); + state + }); +} + +fn poseidon_duplex, const T: usize, const RATE: usize>( + state: &mut State, + input: &SpongeState, + pad_and_add: &dyn Fn(&mut State, &SpongeState), + mds_matrix: &Mds, + round_constants: &[[F; T]], +) -> SpongeState { + pad_and_add(state, input); + + permute::(state, mds_matrix, round_constants); + + let mut output = [None; RATE]; + for (word, value) in output.iter_mut().zip(state.iter()) { + *word = Some(*value); + } + output +} + +pub(crate) enum Sponge { + Absorbing(SpongeState), + Squeezing(SpongeState), +} + +impl Sponge { + pub(crate) fn absorb(val: F) -> Self { + let mut input = [None; RATE]; + input[0] = Some(val); + Sponge::Absorbing(input) + } +} + +/// A Poseidon duplex sponge. +pub struct Duplex, const T: usize, const RATE: usize> { + sponge: Sponge, + state: State, + pad_and_add: Box, &SpongeState)>, + mds_matrix: Mds, + round_constants: Vec<[F; T]>, + _marker: PhantomData, +} + +impl, const T: usize, const RATE: usize> Duplex { + /// Constructs a new duplex sponge for the given Poseidon specification. + pub fn new( + spec: S, + initial_capacity_element: F, + pad_and_add: Box, &SpongeState)>, + ) -> Self { + let (round_constants, mds_matrix, _) = spec.constants(); + + let input = [None; RATE]; + let mut state = [F::zero(); T]; + state[RATE] = initial_capacity_element; + + Duplex { + sponge: Sponge::Absorbing(input), + state, + pad_and_add, + mds_matrix, + round_constants, + _marker: PhantomData::default(), + } + } + + /// Absorbs an element into the sponge. + pub fn absorb(&mut self, value: F) { + match self.sponge { + Sponge::Absorbing(ref mut input) => { + for entry in input.iter_mut() { + if entry.is_none() { + *entry = Some(value); + return; + } + } + + // We've already absorbed as many elements as we can + let _ = poseidon_duplex::( + &mut self.state, + input, + &self.pad_and_add, + &self.mds_matrix, + &self.round_constants, + ); + self.sponge = Sponge::absorb(value); + } + Sponge::Squeezing(_) => { + // Drop the remaining output elements + self.sponge = Sponge::absorb(value); + } + } + } + + /// Squeezes an element from the sponge. + pub fn squeeze(&mut self) -> F { + loop { + match self.sponge { + Sponge::Absorbing(ref input) => { + self.sponge = Sponge::Squeezing(poseidon_duplex::( + &mut self.state, + input, + &self.pad_and_add, + &self.mds_matrix, + &self.round_constants, + )); + } + Sponge::Squeezing(ref mut output) => { + for entry in output.iter_mut() { + if let Some(e) = entry.take() { + return e; + } + } + + // We've already squeezed out all available elements + self.sponge = Sponge::Absorbing([None; RATE]); + } + } + } + } +} + +/// A domain in which a Poseidon hash function is being used. +pub trait Domain, const T: usize, const RATE: usize>: + Copy + fmt::Debug +{ + /// The initial capacity element, encoding this domain. + fn initial_capacity_element(&self) -> F; + + fn padding(&self) -> SpongeState; + + /// Returns a function that will update the given state with the given input to a + /// duplex permutation round, applying padding according to this domain specification. + fn pad_and_add(&self) -> Box, &SpongeState)>; +} + +/// A Poseidon hash function used with constant input length. +/// +/// Domain specified in section 4.2 of https://eprint.iacr.org/2019/458.pdf +#[derive(Clone, Copy, Debug)] +pub struct ConstantLength; + +impl, const T: usize, const RATE: usize, const L: usize> + Domain for ConstantLength +{ + fn initial_capacity_element(&self) -> F { + // Capacity value is $length \cdot 2^64 + (o-1)$ where o is the output length. + // We hard-code an output length of 1. + F::from_u128((L as u128) << 64) + } + + fn padding(&self) -> SpongeState { + // For constant-input-length hashing, padding consists of the field elements being + // zero. + let mut padding = [None; RATE]; + for word in padding.iter_mut().skip(L) { + *word = Some(F::zero()); + } + padding + } + + fn pad_and_add(&self) -> Box, &SpongeState)> { + Box::new(|state, input| { + // `Iterator::zip` short-circuits when one iterator completes, so this will only + // mutate the rate portion of the state. + for (word, value) in state.iter_mut().zip(input.iter()) { + // For constant-input-length hashing, padding consists of the field + // elements being zero, so we don't add anything to the state. + if let Some(value) = value { + *word += value; + } + } + }) + } +} + +/// A Poseidon hash function, built around a duplex sponge. +pub struct Hash< + F: FieldExt, + S: Spec, + D: Domain, + const T: usize, + const RATE: usize, +> { + duplex: Duplex, + domain: D, +} + +impl< + F: FieldExt, + S: Spec, + D: Domain, + const T: usize, + const RATE: usize, + > Hash +{ + /// Initializes a new hasher. + pub fn init(spec: S, domain: D) -> Self { + Hash { + duplex: Duplex::new( + spec, + domain.initial_capacity_element(), + domain.pad_and_add(), + ), + domain, + } + } +} + +impl, const T: usize, const RATE: usize, const L: usize> + Hash, T, RATE> +{ + /// Hashes the given input. + pub fn hash(mut self, message: [F; L]) -> F { + for value in array::IntoIter::new(message) { + self.duplex.absorb(value); + } + self.duplex.squeeze() + } +} + +#[cfg(test)] +mod tests { + use halo2::arithmetic::FieldExt; + use pasta_curves::pallas; + + use super::{permute, ConstantLength, Hash, OrchardNullifier, Spec}; + + #[test] + fn orchard_spec_equivalence() { + let message = [pallas::Base::from_u64(6), pallas::Base::from_u64(42)]; + + let (round_constants, mds, _) = OrchardNullifier.constants(); + + let hasher = Hash::init(OrchardNullifier, ConstantLength); + let result = hasher.hash(message); + + // The result should be equivalent to just directly applying the permutation and + // taking the first state element as the output. + let mut state = [message[0], message[1], pallas::Base::from_u128(2 << 64)]; + permute::<_, OrchardNullifier, 3, 2>(&mut state, &mds, &round_constants); + assert_eq!(state[0], result); + } +} diff --git a/examples/halo2/src/primitives/poseidon/grain.rs b/examples/halo2/src/primitives/poseidon/grain.rs new file mode 100644 index 000000000..c2446c871 --- /dev/null +++ b/examples/halo2/src/primitives/poseidon/grain.rs @@ -0,0 +1,193 @@ +//! The Grain LFSR in self-shrinking mode, as used by Poseidon. + +use std::marker::PhantomData; + +use bitvec::prelude::*; +use halo2::arithmetic::FieldExt; + +const STATE: usize = 80; + +#[derive(Debug, Clone, Copy)] +pub(super) enum FieldType { + /// GF(2^n) + #[allow(dead_code)] + Binary, + /// GF(p) + PrimeOrder, +} + +impl FieldType { + fn tag(&self) -> u8 { + match self { + FieldType::Binary => 0, + FieldType::PrimeOrder => 1, + } + } +} + +#[derive(Debug, Clone, Copy)] +pub(super) enum SboxType { + /// x^alpha + Pow, + /// x^(-1) + #[allow(dead_code)] + Inv, +} + +impl SboxType { + fn tag(&self) -> u8 { + match self { + SboxType::Pow => 0, + SboxType::Inv => 1, + } + } +} + +pub(super) struct Grain { + state: BitArr!(for 80, in Msb0, u8), + next_bit: usize, + _field: PhantomData, +} + +impl Grain { + pub(super) fn new(sbox: SboxType, t: u16, r_f: u16, r_p: u16) -> Self { + // Initialize the LFSR state. + let mut state = bitarr![Msb0, u8; 1; STATE]; + let mut set_bits = |offset: usize, len, value| { + // Poseidon reference impl sets initial state bits in MSB order. + for i in 0..len { + *state.get_mut(offset + len - 1 - i).unwrap() = (value >> i) & 1 != 0; + } + }; + set_bits(0, 2, FieldType::PrimeOrder.tag() as u16); + set_bits(2, 4, sbox.tag() as u16); + set_bits(6, 12, F::NUM_BITS as u16); + set_bits(18, 12, t); + set_bits(30, 10, r_f); + set_bits(40, 10, r_p); + + let mut grain = Grain { + state, + next_bit: STATE, + _field: PhantomData::default(), + }; + + // Discard the first 160 bits. + for _ in 0..20 { + grain.load_next_8_bits(); + grain.next_bit = STATE; + } + + grain + } + + fn load_next_8_bits(&mut self) { + let mut new_bits = 0u8; + for i in 0..8 { + new_bits |= ((self.state[i + 62] + ^ self.state[i + 51] + ^ self.state[i + 38] + ^ self.state[i + 23] + ^ self.state[i + 13] + ^ self.state[i]) as u8) + << i; + } + self.state.rotate_left(8); + self.next_bit -= 8; + for i in 0..8 { + *self.state.get_mut(self.next_bit + i).unwrap() = (new_bits >> i) & 1 != 0; + } + } + + fn get_next_bit(&mut self) -> bool { + if self.next_bit == STATE { + self.load_next_8_bits(); + } + let ret = self.state[self.next_bit]; + self.next_bit += 1; + ret + } + + /// Returns the next field element from this Grain instantiation. + pub(super) fn next_field_element(&mut self) -> F { + // Loop until we get an element in the field. + loop { + let mut bytes = F::Repr::default(); + + // Poseidon reference impl interprets the bits as a repr in MSB order, because + // it's easy to do that in Python. Meanwhile, our field elements all use LSB + // order. There's little motivation to diverge from the reference impl; these + // are all constants, so we aren't introducing big-endianness into the rest of + // the circuit (assuming unkeyed Poseidon, but we probably wouldn't want to + // implement Grain inside a circuit, so we'd use a different round constant + // derivation function there). + let view = bytes.as_mut(); + for (i, bit) in self.take(F::NUM_BITS as usize).enumerate() { + // If we diverged from the reference impl and interpreted the bits in LSB + // order, we would remove this line. + let i = F::NUM_BITS as usize - 1 - i; + + view[i / 8] |= if bit { 1 << (i % 8) } else { 0 }; + } + + if let Some(f) = F::from_repr(bytes) { + break f; + } + } + } + + /// Returns the next field element from this Grain instantiation, without using + /// rejection sampling. + pub(super) fn next_field_element_without_rejection(&mut self) -> F { + let mut bytes = [0u8; 64]; + + // Poseidon reference impl interprets the bits as a repr in MSB order, because + // it's easy to do that in Python. Additionally, it does not use rejection + // sampling in cases where the constants don't specifically need to be uniformly + // random for security. We do not provide APIs that take a field-element-sized + // array and reduce it modulo the field order, because those are unsafe APIs to + // offer generally (accidentally using them can lead to divergence in consensus + // systems due to not rejecting canonical forms). + // + // Given that we don't want to diverge from the reference implementation, we hack + // around this restriction by serializing the bits into a 64-byte array and then + // calling F::from_bytes_wide. PLEASE DO NOT COPY THIS INTO YOUR OWN CODE! + let view = bytes.as_mut(); + for (i, bit) in self.take(F::NUM_BITS as usize).enumerate() { + // If we diverged from the reference impl and interpreted the bits in LSB + // order, we would remove this line. + let i = F::NUM_BITS as usize - 1 - i; + + view[i / 8] |= if bit { 1 << (i % 8) } else { 0 }; + } + + F::from_bytes_wide(&bytes) + } +} + +impl Iterator for Grain { + type Item = bool; + + fn next(&mut self) -> Option { + // Evaluate bits in pairs: + // - If the first bit is a 1, output the second bit. + // - If the first bit is a 0, discard the second bit. + while !self.get_next_bit() { + self.get_next_bit(); + } + Some(self.get_next_bit()) + } +} + +#[cfg(test)] +mod tests { + use pasta_curves::Fp; + + use super::{Grain, SboxType}; + + #[test] + fn grain() { + let mut grain = Grain::::new(SboxType::Pow, 3, 8, 56); + let _f = grain.next_field_element(); + } +} diff --git a/examples/halo2/src/primitives/poseidon/mds.rs b/examples/halo2/src/primitives/poseidon/mds.rs new file mode 100644 index 000000000..62ecb312d --- /dev/null +++ b/examples/halo2/src/primitives/poseidon/mds.rs @@ -0,0 +1,123 @@ +use halo2::arithmetic::FieldExt; + +use super::{grain::Grain, Mds}; + +pub(super) fn generate_mds( + grain: &mut Grain, + mut select: usize, +) -> (Mds, Mds) { + let (xs, ys, mds) = loop { + // Generate two [F; T] arrays of unique field elements. + let (xs, ys) = loop { + let mut vals: Vec<_> = (0..2 * T) + .map(|_| grain.next_field_element_without_rejection()) + .collect(); + + // Check that we have unique field elements. + let mut unique = vals.clone(); + unique.sort_unstable(); + unique.dedup(); + if vals.len() == unique.len() { + let rhs = vals.split_off(T); + break (vals, rhs); + } + }; + + // We need to ensure that the MDS is secure. Instead of checking the MDS against + // the relevant algorithms directly, we witness a fixed number of MDS matrices + // that we need to sample from the given Grain state before obtaining a secure + // matrix. This can be determined out-of-band via the reference implementation in + // Sage. + if select != 0 { + select -= 1; + continue; + } + + // Generate a Cauchy matrix, with elements a_ij in the form: + // a_ij = 1/(x_i + y_j); x_i + y_j != 0 + // + // It would be much easier to use the alternate definition: + // a_ij = 1/(x_i - y_j); x_i - y_j != 0 + // + // These are clearly equivalent on `y <- -y`, but it is easier to work with the + // negative formulation, because ensuring that xs ∪ ys is unique implies that + // x_i - y_j != 0 by construction (whereas the positive case does not hold). It + // also makes computation of the matrix inverse simpler below (the theorem used + // was formulated for the negative definition). + // + // However, the Poseidon paper and reference impl use the positive formulation, + // and we want to rely on the reference impl for MDS security, so we use the same + // formulation. + let mut mds = [[F::zero(); T]; T]; + #[allow(clippy::needless_range_loop)] + for i in 0..T { + for j in 0..T { + let sum = xs[i] + ys[j]; + // We leverage the secure MDS selection counter to also check this. + assert!(!sum.is_zero()); + mds[i][j] = sum.invert().unwrap(); + } + } + + break (xs, ys, mds); + }; + + // Compute the inverse. All square Cauchy matrices have a non-zero determinant and + // thus are invertible. The inverse for a Cauchy matrix of the form: + // + // a_ij = 1/(x_i - y_j); x_i - y_j != 0 + // + // has elements b_ij given by: + // + // b_ij = (x_j - y_i) A_j(y_i) B_i(x_j) (Schechter 1959, Theorem 1) + // + // where A_i(x) and B_i(x) are the Lagrange polynomials for xs and ys respectively. + // + // We adapt this to the positive Cauchy formulation by negating ys. + let mut mds_inv = [[F::zero(); T]; T]; + let l = |xs: &[F], j, x: F| { + let x_j = xs[j]; + xs.iter().enumerate().fold(F::one(), |acc, (m, x_m)| { + if m == j { + acc + } else { + // We can invert freely; by construction, the elements of xs are distinct. + acc * (x - x_m) * (x_j - x_m).invert().unwrap() + } + }) + }; + let neg_ys: Vec<_> = ys.iter().map(|y| -*y).collect(); + for i in 0..T { + for j in 0..T { + mds_inv[i][j] = (xs[j] - neg_ys[i]) * l(&xs, j, neg_ys[i]) * l(&neg_ys, i, xs[j]); + } + } + + (mds, mds_inv) +} + +#[cfg(test)] +mod tests { + use pasta_curves::Fp; + + use super::{generate_mds, Grain}; + + #[test] + fn poseidon_mds() { + const T: usize = 3; + let mut grain = Grain::new(super::super::grain::SboxType::Pow, T as u16, 8, 56); + let (mds, mds_inv) = generate_mds::(&mut grain, 0); + + // Verify that MDS * MDS^-1 = I. + #[allow(clippy::needless_range_loop)] + for i in 0..T { + for j in 0..T { + let expected = if i == j { Fp::one() } else { Fp::zero() }; + assert_eq!( + (0..T).fold(Fp::zero(), |acc, k| acc + (mds[i][k] * mds_inv[k][j])), + expected + ); + } + } + } +} diff --git a/examples/halo2/src/primitives/poseidon/nullifier.rs b/examples/halo2/src/primitives/poseidon/nullifier.rs new file mode 100644 index 000000000..69fb30f5e --- /dev/null +++ b/examples/halo2/src/primitives/poseidon/nullifier.rs @@ -0,0 +1,1619 @@ +use halo2::arithmetic::Field; +use pasta_curves::pallas; + +use super::{Mds, Spec}; + +/// Poseidon-128 using the $x^5$ S-box, with a width of 3 field elements, and the +/// standard number of rounds for 128-bit security "with margin". +/// +/// The standard specification for this set of parameters uses $R_F = 8, R_P = 56$. +/// This is conveniently an even number of partial rounds, making it easier to +/// construct a Halo 2 circuit. +#[derive(Debug)] +pub struct OrchardNullifier; + +impl Spec for OrchardNullifier { + fn full_rounds() -> usize { + 8 + } + + fn partial_rounds() -> usize { + 56 + } + + fn sbox(val: pallas::Base) -> pallas::Base { + val.pow_vartime(&[5]) + } + + fn secure_mds(&self) -> usize { + unimplemented!() + } + + fn constants( + &self, + ) -> ( + Vec<[pallas::Base; 3]>, + Mds, + Mds, + ) { + (ROUND_CONSTANTS[..].to_vec(), MDS, MDS_INV) + } +} + +// $ sage generate_parameters_grain.sage 1 0 255 3 8 56 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001 +// Number of round constants: 192 +// Round constants for GF(p): +const ROUND_CONSTANTS: [[pallas::Base; 3]; 64] = [ + [ + pallas::Base::from_raw([ + 0x5753_8c25_9642_6303, + 0x4e71_162f_3100_3b70, + 0x353f_628f_76d1_10f3, + 0x360d_7470_611e_473d, + ]), + pallas::Base::from_raw([ + 0xbdb7_4213_bf63_188b, + 0x4908_ac2f_12eb_e06f, + 0x5dc3_c6c5_febf_aa31, + 0x2bab_94d7_ae22_2d13, + ]), + pallas::Base::from_raw([ + 0x0939_d927_53cc_5dc8, + 0xef77_e7d7_3676_6c5d, + 0x2bf0_3e1a_29aa_871f, + 0x150c_93fe_f652_fb1c, + ]), + ], + [ + pallas::Base::from_raw([ + 0x1425_9dce_5377_82b2, + 0x03cc_0a60_141e_894e, + 0x955d_55db_56dc_57c1, + 0x3270_661e_6892_8b3a, + ]), + pallas::Base::from_raw([ + 0xce9f_b9ff_c345_afb3, + 0xb407_c370_f2b5_a1cc, + 0xa0b7_afe4_e205_7299, + 0x073f_116f_0412_2e25, + ]), + pallas::Base::from_raw([ + 0x8eba_d76f_c715_54d8, + 0x55c9_cd20_61ae_93ca, + 0x7aff_d09c_1f53_f5fd, + 0x2a32_ec5c_4ee5_b183, + ]), + ], + [ + pallas::Base::from_raw([ + 0x2d8c_cbe2_92ef_eead, + 0x634d_24fc_6e25_59f2, + 0x651e_2cfc_7406_28ca, + 0x2703_26ee_039d_f19e, + ]), + pallas::Base::from_raw([ + 0xa068_fc37_c182_e274, + 0x8af8_95bc_e012_f182, + 0xdc10_0fe7_fcfa_5491, + 0x27c6_642a_c633_bc66, + ]), + pallas::Base::from_raw([ + 0x9ca1_8682_e26d_7ff9, + 0x710e_1fb6_ab97_6a45, + 0xd27f_5739_6989_129d, + 0x1bdf_d8b0_1401_c70a, + ]), + ], + [ + pallas::Base::from_raw([ + 0xc832_d824_261a_35ea, + 0xf4f6_fb3f_9054_d373, + 0x14b9_d6a9_c84d_d678, + 0x162a_14c6_2f9a_89b8, + ]), + pallas::Base::from_raw([ + 0xf798_2466_7b5b_6bec, + 0xac0a_1fc7_1e2c_f0c0, + 0x2af6_f79e_3127_feea, + 0x2d19_3e0f_76de_586b, + ]), + pallas::Base::from_raw([ + 0x5d0b_f58d_c8a4_aa94, + 0x4fef_f829_8499_0ff8, + 0x8169_6ef1_104e_674f, + 0x044c_a3cc_4a85_d73b, + ]), + ], + [ + pallas::Base::from_raw([ + 0x6198_785f_0cd6_b9af, + 0xb8d9_e2d4_f314_f46f, + 0x1d04_5341_6d3e_235c, + 0x1cba_f2b3_71da_c6a8, + ]), + pallas::Base::from_raw([ + 0x343e_0761_0f3f_ede5, + 0x293c_4ab0_38fd_bbdc, + 0x0e6c_49d0_61b6_b5f4, + 0x1d5b_2777_692c_205b, + ]), + pallas::Base::from_raw([ + 0xf60e_971b_8d73_b04f, + 0x06a9_adb0_c1e6_f962, + 0xaa30_535b_dd74_9a7e, + 0x2e9b_dbba_3dd3_4bff, + ]), + ], + [ + pallas::Base::from_raw([ + 0x035a_1366_1f22_418b, + 0xde40_fbe2_6d04_7b05, + 0x8bd5_bae3_6969_299f, + 0x2de1_1886_b180_11ca, + ]), + pallas::Base::from_raw([ + 0xbc99_8884_ba96_a721, + 0x2ab9_395c_449b_e947, + 0x0d5b_4a3f_1841_dcd8, + 0x2e07_de17_80b8_a70d, + ]), + pallas::Base::from_raw([ + 0x825e_4c2b_b749_25ca, + 0x2504_40a9_9d6b_8af3, + 0xbbdb_63db_d52d_ad16, + 0x0f69_f185_4d20_ca0c, + ]), + ], + [ + pallas::Base::from_raw([ + 0x816c_0594_22dc_705e, + 0x6ce5_1135_07f9_6de9, + 0x0d13_5dc6_39fb_09a4, + 0x2eb1_b254_17fe_1767, + ]), + pallas::Base::from_raw([ + 0xb8b1_bdf4_953b_d82c, + 0xff36_c661_d26c_c42d, + 0x8c24_cb44_c3fa_b48a, + 0x115c_d0a0_643c_fb98, + ]), + pallas::Base::from_raw([ + 0xde80_1612_311d_04cd, + 0xbb57_ddf1_4e0f_958a, + 0x066d_7378_b999_868b, + 0x26ca_293f_7b2c_462d, + ]), + ], + [ + pallas::Base::from_raw([ + 0xf520_9d14_b248_20ca, + 0x0f16_0bf9_f71e_967f, + 0x2a83_0aa1_6241_2cd9, + 0x17bf_1b93_c4c7_e01a, + ]), + pallas::Base::from_raw([ + 0x05c8_6f2e_7dc2_93c5, + 0xe03c_0354_bd8c_fd38, + 0xa24f_8456_369c_85df, + 0x35b4_1a7a_c4f3_c571, + ]), + pallas::Base::from_raw([ + 0x72ac_156a_f435_d09e, + 0x64e1_4d3b_eb2d_ddde, + 0x4359_2799_4849_bea9, + 0x3b14_8008_0523_c439, + ]), + ], + [ + pallas::Base::from_raw([ + 0x2716_18d8_74b1_4c6d, + 0x08e2_8644_2a2d_3eb2, + 0x4950_856d_c907_d575, + 0x2cc6_8100_31dc_1b0d, + ]), + pallas::Base::from_raw([ + 0x91f3_18c0_9f0c_b566, + 0x9e51_7aa9_3b78_341d, + 0x0596_18e2_afd2_ef99, + 0x25bd_bbed_a1bd_e8c1, + ]), + pallas::Base::from_raw([ + 0xc631_3487_073f_7f7b, + 0x2a5e_d0a2_7b61_926c, + 0xb95f_33c2_5dde_8ac0, + 0x392a_4a87_58e0_6ee8, + ]), + ], + [ + pallas::Base::from_raw([ + 0xe7bb_cef0_2eb5_866c, + 0x5e6a_6fd1_5db8_9365, + 0x9aa6_111f_4de0_0948, + 0x272a_5587_8a08_442b, + ]), + pallas::Base::from_raw([ + 0x9b92_5b3c_5b21_e0e2, + 0xa6eb_ba01_1694_dd12, + 0xefa1_3c4e_60e2_6239, + 0x2d5b_308b_0cf0_2cdf, + ]), + pallas::Base::from_raw([ + 0xef38_c57c_3116_73ac, + 0x44df_f42f_18b4_6c56, + 0xdd5d_293d_72e2_e5f2, + 0x1654_9fc6_af2f_3b72, + ]), + ], + [ + pallas::Base::from_raw([ + 0x9b71_26d9_b468_60df, + 0x7639_8265_3442_0311, + 0xfa69_c3a2_ad52_f76d, + 0x1b10_bb7a_82af_ce39, + ]), + pallas::Base::from_raw([ + 0x90d2_7f6a_00b7_dfc8, + 0xd1b3_6968_ba04_05c0, + 0xc79c_2df7_dc98_a3be, + 0x0f1e_7505_ebd9_1d2f, + ]), + pallas::Base::from_raw([ + 0xff45_7756_b819_bb20, + 0x797f_d6e3_f18e_b1ca, + 0x537a_7497_a3b4_3f46, + 0x2f31_3faf_0d3f_6187, + ]), + ], + [ + pallas::Base::from_raw([ + 0xf0bc_3e73_2ecb_26f6, + 0x5cad_11eb_f0f7_ceb8, + 0xfa3c_a61c_0ed1_5bc5, + 0x3a5c_bb6d_e450_b481, + ]), + pallas::Base::from_raw([ + 0x8655_27cb_ca91_5982, + 0x51ba_a6e2_0f89_2b62, + 0xd920_86e2_53b4_39d6, + 0x3dab_54bc_9bef_688d, + ]), + pallas::Base::from_raw([ + 0x3680_45ac_f2b7_1ae3, + 0x4c24_b33b_410f_efd4, + 0xe280_d316_7012_3f74, + 0x06db_fb42_b979_884d, + ]), + ], + [ + pallas::Base::from_raw([ + 0xa7fc_32d2_2f18_b9d3, + 0xb8d2_de72_e3d2_c9ec, + 0xc6f0_39ea_1973_a63e, + 0x068d_6b46_08aa_e810, + ]), + pallas::Base::from_raw([ + 0x2b5d_fcc5_5725_55df, + 0xb868_a7d7_e1f1_f69a, + 0x0ee2_58c9_b8fd_fccd, + 0x366e_bfaf_a3ad_381c, + ]), + pallas::Base::from_raw([ + 0xe6bc_229e_95bc_76b1, + 0x7ef6_6d89_d044_d022, + 0x04db_3024_f41d_3f56, + 0x3967_8f65_512f_1ee4, + ]), + ], + [ + pallas::Base::from_raw([ + 0xe534_c88f_e53d_85fe, + 0xcf82_c25f_99dc_01a4, + 0xd58b_7750_a3bc_2fe1, + 0x2166_8f01_6a80_63c0, + ]), + pallas::Base::from_raw([ + 0x4bef_429b_c533_1608, + 0xe34d_ea56_439f_e195, + 0x1bc7_4936_3e98_a768, + 0x39d0_0994_a8a5_046a, + ]), + pallas::Base::from_raw([ + 0x770c_956f_60d8_81b3, + 0xb163_d416_05d3_9f99, + 0x6b20_3bbe_12fb_3425, + 0x1f9d_bdc3_f843_1263, + ]), + ], + [ + pallas::Base::from_raw([ + 0x9794_a9f7_c336_eab2, + 0xbe0b_c829_fe5e_66c6, + 0xe5f1_7b9e_0ee0_cab6, + 0x0277_45a9_cddf_ad95, + ]), + pallas::Base::from_raw([ + 0x5202_5657_abd8_aee0, + 0x2fa4_3fe2_0a45_c78d, + 0x788d_695c_61e9_3212, + 0x1cec_0803_c504_b635, + ]), + pallas::Base::from_raw([ + 0xd387_2a95_59a0_3a73, + 0xed50_82c8_dbf3_1365, + 0x7207_7448_ef87_cc6e, + 0x1235_23d7_5e9f_abc1, + ]), + ], + [ + pallas::Base::from_raw([ + 0x0017_79e3_a1d3_57f4, + 0x27fe_ba35_975e_e7e5, + 0xf419_b848_e5d6_94bf, + 0x1723_d145_2c9c_f02d, + ]), + pallas::Base::from_raw([ + 0x9dab_1ee4_dcf9_6622, + 0x21c3_f776_f572_836d, + 0xfcc0_573d_7e61_3694, + 0x1739_d180_a160_10bd, + ]), + pallas::Base::from_raw([ + 0x7029_0452_042d_048d, + 0xfafa_96fb_eb0a_b893, + 0xacce_3239_1794_b627, + 0x2d4e_6354_da9c_c554, + ]), + ], + [ + pallas::Base::from_raw([ + 0x670b_cf6f_8b48_5dcd, + 0x8f3b_d43f_9926_0621, + 0x4a86_9553_c9d0_07f8, + 0x153e_e614_2e53_5e33, + ]), + pallas::Base::from_raw([ + 0xd258_d2e2_b778_2172, + 0x968a_d442_4af8_3700, + 0x635e_f7e7_a430_b486, + 0x0c45_bfd3_a69a_aa65, + ]), + pallas::Base::from_raw([ + 0x0e56_33d2_51f7_3307, + 0x6897_ac0a_8ffa_5ff1, + 0xf2d5_6aec_8314_4600, + 0x0adf_d53b_256a_6957, + ]), + ], + [ + pallas::Base::from_raw([ + 0xac9d_36a8_b751_6d63, + 0x3f87_b28f_1c1b_e4bd, + 0x8cd1_726b_7cba_b8ee, + 0x315d_2ac8_ebdb_ac3c, + ]), + pallas::Base::from_raw([ + 0x299c_e44e_a423_d8e1, + 0xc9bb_60d1_f695_9879, + 0xcfae_c23d_2b16_883f, + 0x1b84_7271_2d02_eef4, + ]), + pallas::Base::from_raw([ + 0xc4a5_4041_98ad_f70c, + 0x367d_2c54_e369_28c9, + 0xbd0b_70fa_2255_eb6f, + 0x3c1c_d07e_fda6_ff24, + ]), + ], + [ + pallas::Base::from_raw([ + 0xbbe5_23ae_f9ab_107a, + 0x4a16_073f_738f_7e0c, + 0x687f_4e51_b2e1_dcd3, + 0x1360_52d2_6bb3_d373, + ]), + pallas::Base::from_raw([ + 0x676c_36c2_4ef9_67dd, + 0x7b3c_fbb8_7303_2681, + 0xc1bd_d859_a123_2a1d, + 0x16c9_6bee_f6a0_a848, + ]), + pallas::Base::from_raw([ + 0x067e_ec7f_2d63_40c4, + 0x0123_87ba_b4f1_662d, + 0x2ab7_fed8_f499_a9fb, + 0x284b_38c5_7ff6_5c26, + ]), + ], + [ + pallas::Base::from_raw([ + 0xaf1d_ff20_4c92_2f86, + 0xfc06_772c_1c04_11a6, + 0x39e2_4219_8897_d17c, + 0x0c59_93d1_75e8_1f66, + ]), + pallas::Base::from_raw([ + 0xbbf5_3f67_b1f8_7b15, + 0xf248_87ad_48e1_7759, + 0xfcda_655d_1ba9_c8f9, + 0x03bf_7a3f_7bd0_43da, + ]), + pallas::Base::from_raw([ + 0x9b5c_d09e_36d8_be62, + 0x4c8f_9cbe_69f0_e827, + 0xb0cf_9995_67f0_0e73, + 0x3188_fe4e_e9f9_fafb, + ]), + ], + [ + pallas::Base::from_raw([ + 0xafea_99a2_ec6c_595a, + 0x3af5_bf77_c1c4_2652, + 0x5a39_768c_480d_61e1, + 0x171f_528c_cf65_8437, + ]), + pallas::Base::from_raw([ + 0x5a05_63b9_b8e9_f1d5, + 0x812c_3286_ee70_0067, + 0x196e_4185_9b35_ef88, + 0x12f4_175c_4ab4_5afc, + ]), + pallas::Base::from_raw([ + 0x0e74_d4d3_6911_8b79, + 0x7e23_e1aa_be96_cfab, + 0x8f8f_dcf8_00a9_ac69, + 0x3a50_9e15_5cb7_ebfd, + ]), + ], + [ + pallas::Base::from_raw([ + 0x9871_2c65_678c_fd30, + 0x984b_c8f2_e4c1_b69e, + 0x1a89_920e_2504_c3b3, + 0x10f2_a685_df4a_27c8, + ]), + pallas::Base::from_raw([ + 0xe8a1_6728_cc9d_4918, + 0x5457_3c93_33c5_6321, + 0x1d8d_93d5_4ab9_1a0e, + 0x09e5_f497_90c8_a0e2, + ]), + pallas::Base::from_raw([ + 0x609a_7403_47cf_5fea, + 0x42d1_7ed6_ee0f_ab7e, + 0x2bf3_5705_d9f8_4a34, + 0x352d_69be_d80e_e3e5, + ]), + ], + [ + pallas::Base::from_raw([ + 0x3a75_8af6_fa84_e0e8, + 0xc634_debd_281b_76a6, + 0x4915_62fa_f2b1_90d3, + 0x058e_e73b_a9f3_f293, + ]), + pallas::Base::from_raw([ + 0x621a_1325_10a4_3904, + 0x092c_b921_19bc_76be, + 0xcd0f_1fc5_5b1a_3250, + 0x232f_99cc_911e_ddd9, + ]), + pallas::Base::from_raw([ + 0xc3b9_7c1e_301b_c213, + 0xf9ef_d52c_a6bc_2961, + 0x86c2_2c6c_5d48_69f0, + 0x201b_eed7_b8f3_ab81, + ]), + ], + [ + pallas::Base::from_raw([ + 0xbf6b_3431_ba94_e9bc, + 0x2938_8842_744a_1210, + 0xa1c9_291d_5860_2f51, + 0x1376_dce6_5800_30c6, + ]), + pallas::Base::from_raw([ + 0x6454_843c_5486_d7b3, + 0x072b_a8b0_2d92_e722, + 0x2b33_56c3_8238_f761, + 0x1793_199e_6fd6_ba34, + ]), + pallas::Base::from_raw([ + 0x06a3_f1d3_b433_311b, + 0x3c66_160d_c62a_acac, + 0x9fee_9c20_c87a_67df, + 0x22de_7a74_88dc_c735, + ]), + ], + [ + pallas::Base::from_raw([ + 0x30d6_e3fd_516b_47a8, + 0xdbe0_b77f_ae77_e1d0, + 0xdf8f_f37f_e2d8_edf8, + 0x3514_d5e9_066b_b160, + ]), + pallas::Base::from_raw([ + 0x1937_7427_137a_81c7, + 0xff45_3d6f_900f_144a, + 0xf919_a00d_abbf_5fa5, + 0x30cd_3006_931a_d636, + ]), + pallas::Base::from_raw([ + 0x5b6a_7422_0692_b506, + 0x8f9e_4b2c_ae2e_bb51, + 0x41f8_1a5c_f613_c8df, + 0x253d_1a5c_5293_4127, + ]), + ], + [ + pallas::Base::from_raw([ + 0x73f6_66cb_86a4_8e8e, + 0x851b_3a59_c990_fafc, + 0xa35e_9613_e7f5_fe92, + 0x035b_461c_02d7_9d19, + ]), + pallas::Base::from_raw([ + 0x7cfb_f86a_3aa0_4780, + 0x92b1_283c_2d5f_ccde, + 0x5bc0_0eed_d56b_93e0, + 0x23a9_9280_79d1_75bd, + ]), + pallas::Base::from_raw([ + 0xf1e4_ccd7_3fa0_0a82, + 0xb5e2_ea34_36ee_f957, + 0xf159_4a07_63c6_11ab, + 0x13a7_785a_e134_ea92, + ]), + ], + [ + pallas::Base::from_raw([ + 0xbbf0_4f52_52de_4279, + 0x3889_c578_6344_6d88, + 0x4962_ae3c_0da1_7e31, + 0x39fc_e308_b7d4_3c57, + ]), + pallas::Base::from_raw([ + 0x3b57_e344_89b5_3fad, + 0xbef0_0a08_c6ed_38d2, + 0xc0fd_f016_62f6_0d22, + 0x1aae_1883_3f8e_1d3a, + ]), + pallas::Base::from_raw([ + 0x5551_3e03_3398_513f, + 0x27c1_b3fd_8f85_d8a8, + 0x8b2e_80c0_64fd_83ed, + 0x1a76_1ce8_2400_af01, + ]), + ], + [ + pallas::Base::from_raw([ + 0x5244_ca74_9b73_e481, + 0xdcf6_af28_30a5_0287, + 0x16dd_1a87_ca22_e1cc, + 0x275a_03e4_5add_a7c3, + ]), + pallas::Base::from_raw([ + 0x58a2_53cf_b6a9_5786, + 0x07e5_6145_3fc5_648b, + 0xeb08_e47e_5fea_bcf8, + 0x2e5a_10f0_8b5a_b8bb, + ]), + pallas::Base::from_raw([ + 0xe033_d82c_efe7_8ce3, + 0xc141_a5b6_d594_bec4, + 0xb84e_9c33_3b29_32f1, + 0x1459_cb85_8720_8473, + ]), + ], + [ + pallas::Base::from_raw([ + 0x5cec_7e7b_338f_be1b, + 0x52f9_332f_bffc_fbbd, + 0x7b92_ce81_0e14_a400, + 0x193a_e592_1d78_b5de, + ]), + pallas::Base::from_raw([ + 0x6022_4be6_7248_e82c, + 0x3743_84f4_a072_8205, + 0x8911_1fb2_c466_0281, + 0x3097_898a_5d00_11a4, + ]), + pallas::Base::from_raw([ + 0x5499_80de_8629_30f5, + 0x1979_b2d1_c465_b4d9, + 0x5717_82fd_96ce_54b4, + 0x378d_97bf_8c86_4ae7, + ]), + ], + [ + pallas::Base::from_raw([ + 0x37ea_32a9_71d1_7884, + 0xdbc7_f5cb_4609_3421, + 0x8813_6287_ce37_6b08, + 0x2eb0_4ea7_c01d_97ec, + ]), + pallas::Base::from_raw([ + 0xead3_726f_1af2_e7b0, + 0x861c_bda4_7680_4e6c, + 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0x63fd_8ac5_7a95_ca8c, + 0x4c0f_7e00_1df4_90aa, + 0x5229_dfaa_0123_1a45, + 0x162a_7c80_f4d2_d12e, + ]), + pallas::Base::from_raw([ + 0x32e6_9efb_22f4_0b96, + 0xcaff_31b4_fda3_2124, + 0x2604_e4af_b09f_8603, + 0x2a0d_6c09_5766_66bb, + ]), + ], + [ + pallas::Base::from_raw([ + 0xc0a0_180f_8cbf_c0d2, + 0xf444_d10d_63a7_4e2c, + 0xe16a_4d60_3d5a_808e, + 0x0978_e5c5_1e1e_5649, + ]), + pallas::Base::from_raw([ + 0x03f4_460e_bc35_1b6e, + 0x0508_7d90_3bda_cfd1, + 0xebe1_9bbd_ce25_1011, + 0x1bdc_ee3a_aca9_cd25, + ]), + pallas::Base::from_raw([ + 0xf619_64bf_3ade_7670, + 0x0c94_7321_e007_5e3f, + 0xe494_7914_0b19_44fd, + 0x1862_cccb_70b5_b885, + ]), + ], + [ + pallas::Base::from_raw([ + 0xc326_7da6_e94a_dc50, + 0x39ee_99c1_cc6e_5dda, + 0xbc26_cc88_3a19_87e1, + 0x1f3e_91d8_63c1_6922, + ]), + pallas::Base::from_raw([ + 0x0f85_b4ac_2c36_7406, + 0xfa66_1465_c656_ad99, + 0xef5c_08f8_478f_663a, + 0x1af4_7a48_a601_6a49, + ]), + pallas::Base::from_raw([ + 0x0eab_cd87_e7d0_1b15, + 0x1c36_98b0_a2e3_da10, + 0x009d_5733_8c69_3505, + 0x3c8e_e901_956e_3d3f, + ]), + ], + [ + pallas::Base::from_raw([ + 0x8b94_7721_8967_3476, + 0xe10c_e2b7_069f_4dbd, + 0x68d0_b024_f591_b520, + 0x1660_a8cd_e7fe_c553, + ]), + pallas::Base::from_raw([ + 0x9d8d_0f67_fdaa_79d5, + 0x3963_c2c1_f558_6e2f, + 0x1303_9363_34dd_1132, + 0x0f6d_9919_29d5_e4e7, + ]), + pallas::Base::from_raw([ + 0x7a43_3091_e1ce_2d3a, + 0x4e7f_da77_0712_f343, + 0xcc62_5eaa_ab52_b4dc, + 0x02b9_cea1_921c_d9f6, + ]), + ], + [ + pallas::Base::from_raw([ + 0x3797_b2d8_3760_43b3, + 0xd8ca_f468_976f_0472, + 0x214f_7c67_84ac_b565, + 0x14a3_23b9_9b90_0331, + ]), + pallas::Base::from_raw([ + 0x347f_ef2c_00f0_953a, + 0x718b_7fbc_7788_af78, + 0xec01_ea79_642d_5760, + 0x1904_76b5_80cb_9277, + ]), + pallas::Base::from_raw([ + 0xff4e_7e6f_b268_dfd7, + 0x9660_902b_6008_7651, + 0xa424_63d3_0b44_2b6f, + 0x090a_3a9d_869d_2eef, + ]), + ], + [ + pallas::Base::from_raw([ + 0xf983_387e_a045_6203, + 0xe365_0013_04f9_a11e, + 0x0dbe_8fd2_270a_6795, + 0x3877_a955_8636_7567, + ]), + pallas::Base::from_raw([ + 0x39c0_af0f_e01f_4a06, + 0x6011_8c53_a218_1352, + 0x5df3_9a2c_c63d_dc0a, + 0x2d89_4691_240f_e953, + ]), + pallas::Base::from_raw([ + 0x1aca_9eaf_9bba_9850, + 0x5914_e855_eeb4_4aa1, + 0x7ef7_1780_2016_6189, + 0x21b9_c182_92bd_bc59, + ]), + ], + [ + pallas::Base::from_raw([ + 0x33f5_09a7_4ad9_d39b, + 0x272e_1cc6_c36a_2968, + 0x505a_05f2_a6ae_834c, + 0x2fe7_6be7_cff7_23e2, + ]), + pallas::Base::from_raw([ + 0x0df9_fa97_277f_a8b4, + 0xd15b_ff84_0dda_e8a5, + 0x9299_81d7_cfce_253b, + 0x187a_a448_f391_e3ca, + ]), + pallas::Base::from_raw([ + 0xf0c6_6af5_ffc7_3736, + 0x663c_cf7b_2ffe_4b5e, + 0x007a_b3aa_3617_f422, + 0x0b70_83ad_7517_07bf, + ]), + ], + [ + pallas::Base::from_raw([ + 0x2f9b_20f1_fbd4_9791, + 0x1975_b962_f6cb_8e0b, + 0x3bc4_ca99_02c5_2acb, + 0x030d_dbb4_7049_3f16, + ]), + pallas::Base::from_raw([ + 0x3a1c_62ca_8fbf_2525, + 0x8fb8_ab9d_60ea_17b2, + 0x950b_0ab1_8d35_46df, + 0x3130_fbaf_fb5a_a82a, + ]), + pallas::Base::from_raw([ + 0x43a8_7618_0dc3_82e0, + 0x15ce_2ead_2fcd_051e, + 0x4f74_d74b_ac2e_e457, + 0x337f_5447_07c4_30f0, + ]), + ], + [ + pallas::Base::from_raw([ + 0x26de_98a8_736d_1d11, + 0x7d8e_471a_9fb9_5fef, + 0xac9d_91b0_930d_ac75, + 0x3499_7991_9015_394f, + ]), + pallas::Base::from_raw([ + 0xccfc_b618_31d5_c775, + 0x3bf9_3da6_fff3_1d95, + 0x2305_cd7a_921e_c5f1, + 0x027c_c4ef_e3fb_35dd, + ]), + pallas::Base::from_raw([ + 0xc3fa_2629_635d_27de, + 0x67f1_c6b7_3147_64af, + 0x61b7_1a36_9868_2ad2, + 0x037f_9f23_6595_4c5b, + ]), + ], + [ + pallas::Base::from_raw([ + 0x77c5_b024_8483_71ae, + 0x6041_4abe_362d_01c9, + 0x10f1_cc6d_f8b4_bcd7, + 0x1f69_7cac_4d07_feb7, + ]), + pallas::Base::from_raw([ + 0x786a_dd24_4aa0_ef29, + 0x3145_c478_0631_09d6, + 0x26e6_c851_fbd5_72a6, + 0x267a_750f_e5d7_cfbc, + ]), + pallas::Base::from_raw([ + 0x180e_2b4d_3e75_6f65, + 0xaf28_5fa8_2ce4_fae5, + 0x678c_9996_d9a4_72c8, + 0x0c91_feab_4a43_193a, + ]), + ], + [ + pallas::Base::from_raw([ + 0x79c4_7c57_3ac4_10f7, + 0x7e3b_83af_4a4b_a3ba, + 0x2186_c303_8ea0_5e69, + 0x1745_569a_0a3e_3014, + ]), + pallas::Base::from_raw([ + 0x1e03_8852_2696_191f, + 0xfdff_66c6_f3b5_ffe1, + 0xeca5_1207_78a5_6711, + 0x2986_3d54_6e7e_7c0d, + ]), + pallas::Base::from_raw([ + 0x2f22_5e63_66bf_e390, + 0xa79a_03df_8339_94c6, + 0xbf06_bae4_9ef8_53f6, + 0x1148_d6ab_2bd0_0192, + ]), + ], + [ + pallas::Base::from_raw([ + 0xf4f6_331a_8b26_5d15, + 0xf745_f45d_350d_41d4, + 0xe18b_1499_060d_a366, + 0x02e0_e121_b0f3_dfef, + ]), + pallas::Base::from_raw([ + 0x078a_e6aa_1510_54b7, + 0x6904_0173_6d44_a653, + 0xb89e_f73a_40a2_b274, + 0x0d0a_a46e_76a6_a278, + ]), + pallas::Base::from_raw([ + 0x9a4d_532c_7b6e_0958, + 0x392d_de71_0f1f_06db, + 0xeee5_45f3_fa6d_3d08, + 0x1394_3675_b04a_a986, + ]), + ], + [ + pallas::Base::from_raw([ + 0x961f_c818_dcbb_66b5, + 0xc9f2_b325_7530_dafe, + 0xd97a_11d6_3088_f5d9, + 0x2901_ec61_942d_34aa, + ]), + pallas::Base::from_raw([ + 0xfdf5_44b9_63d1_fdc7, + 0x22ff_a2a2_af9f_a3e3, + 0xf431_d544_34a3_e0cf, + 0x2020_4a21_05d2_2e7e, + ]), + pallas::Base::from_raw([ + 0x1211_b9e2_190d_6852, + 0xa004_abe8_e015_28c4, + 0x5c1e_3e9e_27a5_71c3, + 0x3a8a_6282_9512_1d5c, + ]), + ], +]; +// Secure MDS: 0 +// n: 255 +// t: 3 +// N: 765 +// Result Algorithm 1: +// [True, 0] +// Result Algorithm 2: +// [True, None] +// Result Algorithm 3: +// [True, None] +// Prime number: 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001 +// MDS matrix: +const MDS: [[pallas::Base; 3]; 3] = [ + [ + pallas::Base::from_raw([ + 0x323f_2486_d7e1_1b63, + 0x97d7_a0ab_2385_0b56, + 0xb3d5_9fbd_c8c9_ead4, + 0x0ab5_e5b8_74a6_8de7, + ]), + pallas::Base::from_raw([ + 0x8eca_5596_e996_ab5e, + 0x240d_4a7c_bf73_5736, + 0x293f_0f0d_886c_7954, + 0x3191_6628_e58a_5abb, + ]), + pallas::Base::from_raw([ + 0x19d1_cf25_d8e8_345d, + 0xa0a3_b71a_5fb1_5735, + 0xd803_952b_bb36_4fdf, + 0x07c0_45d5_f5e9_e5a6, + ]), + ], + [ + pallas::Base::from_raw([ + 0xd049_cdc8_d085_167c, + 0x3a0a_4640_48bd_770a, + 0xf8e2_4f66_822c_2d9f, + 0x2331_6263_0ebf_9ed7, + ]), + pallas::Base::from_raw([ + 0x4022_7011_3e04_7a2e, + 0x78f8_365c_85bb_ab07, + 0xb366_6454_8d60_957d, + 0x25ca_e259_9892_a8b0, + ]), + pallas::Base::from_raw([ + 0xf84d_806f_685f_747a, + 0x9aad_3d82_62ef_d83f, + 0x7493_8717_989a_1957, + 0x22f5_b5e1_e608_1c97, + ]), + ], + [ + pallas::Base::from_raw([ + 0xfee7_a994_4f84_dbe4, + 0x2168_0eab_c56b_c15d, + 0xf333_aa91_c383_3464, + 0x2e29_dd59_c64b_1037, + ]), + pallas::Base::from_raw([ + 0xc771_effa_4326_3664, + 0xcbea_f48b_3a06_24c3, + 0x92d1_5e7d_ceef_1665, + 0x1d1a_ab4e_c1cd_6788, + ]), + pallas::Base::from_raw([ + 0x1563_9415_f6e8_5ef1, + 0x7587_2c39_b59a_31f6, + 0x51e0_cbea_d655_16b9, + 0x3bf7_6308_6a18_9364, + ]), + ], +]; + +const MDS_INV: [[pallas::Base; 3]; 3] = [ + [ + pallas::Base::from_raw([ + 0xc6de_463c_d140_4e6b, + 0x4543_705f_35e9_8ab5, + 0xcc59_ffd0_0de8_6443, + 0x2cc0_57f3_fa14_687a, + ]), + pallas::Base::from_raw([ + 0x1718_4041_7cab_7576, + 0xfadb_f8ae_7ae2_4796, + 0x5fd7_2b55_df20_8385, + 0x32e7_c439_f2f9_67e5, + ]), + pallas::Base::from_raw([ + 0x9426_45bd_7d44_64e0, + 0x1403_db6f_5030_2040, + 0xf461_778a_bf6c_91fa, + 0x2eae_5df8_c311_5969, + ]), + ], + [ + pallas::Base::from_raw([ + 0xa1ca_1516_a4a1_a6a0, + 0x13f0_74fd_e9a1_8b29, + 0xdb18_b4ae_fe68_d26d, + 0x07bf_3684_8106_7199, + ]), + pallas::Base::from_raw([ + 0xe824_25bc_1b23_a059, + 0xbb1d_6504_0c85_c1bf, + 0x018a_918b_9dac_5dad, + 0x2aec_6906_c63f_3cf1, + ]), + pallas::Base::from_raw([ + 0xe054_1adf_238e_0781, + 0x76b2_a713_9db7_1b36, + 0x1215_944a_64a2_46b2, + 0x0952_e024_3aec_2af0, + ]), + ], + [ + pallas::Base::from_raw([ + 0x2a41_8d8d_73a7_c908, + 0xaef9_112e_952f_dbb5, + 0x723a_63a0_c09d_ab26, + 0x2fcb_ba6f_9159_a219, + ]), + pallas::Base::from_raw([ + 0x76ef_ab42_d4fb_a90b, + 0xc5e4_960d_7424_cd37, + 0xb4dd_d4b4_d645_2256, + 0x1ec7_3725_74f3_851b, + ]), + pallas::Base::from_raw([ + 0xadc8_933c_6f3c_72ee, + 0x87a7_435d_30f8_be81, + 0x3c26_fa4b_7d25_b1e4, + 0x0d0c_2efd_6472_f12a, + ]), + ], +]; + +#[cfg(test)] +mod tests { + use std::marker::PhantomData; + + use ff::PrimeField; + use halo2::arithmetic::FieldExt; + use pasta_curves::pallas; + + use crate::primitives::poseidon::{permute, ConstantLength, Hash, Spec}; + + use super::{OrchardNullifier, MDS, MDS_INV, ROUND_CONSTANTS}; + + /// The same Poseidon specification as poseidon::OrchardNullifier, but constructed + /// such that its constants will be generated at runtime. + #[derive(Debug)] + pub struct P128Pow5T3 { + secure_mds: usize, + _field: PhantomData, + } + + impl P128Pow5T3 { + pub fn new(secure_mds: usize) -> Self { + P128Pow5T3 { + secure_mds, + _field: PhantomData::default(), + } + } + } + + impl Spec for P128Pow5T3 { + fn full_rounds() -> usize { + 8 + } + + fn partial_rounds() -> usize { + 56 + } + + fn sbox(val: F) -> F { + val.pow_vartime(&[5]) + } + + fn secure_mds(&self) -> usize { + self.secure_mds + } + } + + #[test] + fn verify_constants() { + let poseidon = P128Pow5T3::::new(0); + let (round_constants, mds, mds_inv) = poseidon.constants(); + + for (actual, expected) in round_constants + .iter() + .flatten() + .zip(ROUND_CONSTANTS.iter().flatten()) + { + assert_eq!(actual, expected); + } + + for (actual, expected) in mds.iter().flatten().zip(MDS.iter().flatten()) { + assert_eq!(actual, expected); + } + + for (actual, expected) in mds_inv.iter().flatten().zip(MDS_INV.iter().flatten()) { + assert_eq!(actual, expected); + } + } + + #[test] + fn test_against_reference() { + // This is the test vector output by the reference code at + // , using parameters from + // `generate_parameters_grain.sage 1 0 255 3 8 56 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001`. + + let mut input = [ + pallas::Base::from_raw([ + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + ]), + pallas::Base::from_raw([ + 0x0000_0000_0000_0001, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + ]), + pallas::Base::from_raw([ + 0x0000_0000_0000_0002, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + ]), + ]; + + let expected_output = [ + pallas::Base::from_raw([ + 0xaeb1_bc02_4aec_a456, + 0xf7e6_9a71_d0b6_42a0, + 0x94ef_b364_f966_240f, + 0x2a52_6acd_0b64_b453, + ]), + pallas::Base::from_raw([ + 0x012a_3e96_28e5_b82a, + 0xdcd4_2e7f_bed9_dafe, + 0x76ff_7dae_343d_5512, + 0x13c5_d156_8b4a_a430, + ]), + pallas::Base::from_raw([ + 0x3590_29a1_d34e_9ddd, + 0xf7cf_dfe1_bda4_2c7b, + 0x256f_cd59_7984_561a, + 0x0a49_c868_c697_6544, + ]), + ]; + + permute::, 3, 2>(&mut input, &MDS, &ROUND_CONSTANTS); + assert_eq!(input, expected_output); + } + + #[test] + fn permute_test_vectors() { + let (round_constants, mds, _) = OrchardNullifier.constants(); + + for tv in crate::primitives::poseidon::test_vectors::permute() { + let mut state = [ + pallas::Base::from_repr(tv.initial_state[0]).unwrap(), + pallas::Base::from_repr(tv.initial_state[1]).unwrap(), + pallas::Base::from_repr(tv.initial_state[2]).unwrap(), + ]; + + permute::(&mut state, &mds, &round_constants); + + for (expected, actual) in tv.final_state.iter().zip(state.iter()) { + assert_eq!(&actual.to_repr(), expected); + } + } + } + + #[test] + fn hash_test_vectors() { + for tv in crate::primitives::poseidon::test_vectors::hash() { + let message = [ + pallas::Base::from_repr(tv.input[0]).unwrap(), + pallas::Base::from_repr(tv.input[1]).unwrap(), + ]; + + let result = Hash::init(OrchardNullifier, ConstantLength).hash(message); + + assert_eq!(result.to_repr(), tv.output); + } + } +} diff --git a/examples/halo2/src/primitives/poseidon/test_vectors.rs b/examples/halo2/src/primitives/poseidon/test_vectors.rs new file mode 100644 index 000000000..97b9bcfea --- /dev/null +++ b/examples/halo2/src/primitives/poseidon/test_vectors.rs @@ -0,0 +1,632 @@ +//! Test vectors for [`OrchardNullifier`]. + +pub(crate) struct PermuteTestVector { + pub(crate) initial_state: [[u8; 32]; 3], + pub(crate) final_state: [[u8; 32]; 3], +} + +pub(crate) struct HashTestVector { + pub(crate) input: [[u8; 32]; 2], + pub(crate) output: [u8; 32], +} + +pub(crate) fn permute() -> Vec { + use PermuteTestVector as TestVector; + + // From https://github.com/zcash-hackworks/zcash-test-vectors/blob/master/orchard_poseidon.py + vec![ + TestVector { + initial_state: [ + [ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + ], + [ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + ], + [ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + ], + ], + final_state: [ + [ + 0x56, 0xa4, 0xec, 0x4a, 0x02, 0xbc, 0xb1, 0xae, 0xa0, 0x42, 0xb6, 0xd0, 0x71, + 0x9a, 0xe6, 0xf7, 0x0f, 0x24, 0x66, 0xf9, 0x64, 0xb3, 0xef, 0x94, 0x53, 0xb4, + 0x64, 0x0b, 0xcd, 0x6a, 0x52, 0x2a, + ], + [ + 0x2a, 0xb8, 0xe5, 0x28, 0x96, 0x3e, 0x2a, 0x01, 0xfe, 0xda, 0xd9, 0xbe, 0x7f, + 0x2e, 0xd4, 0xdc, 0x12, 0x55, 0x3d, 0x34, 0xae, 0x7d, 0xff, 0x76, 0x30, 0xa4, + 0x4a, 0x8b, 0x56, 0xd1, 0xc5, 0x13, + ], + [ + 0xdd, 0x9d, 0x4e, 0xd3, 0xa1, 0x29, 0x90, 0x35, 0x7b, 0x2c, 0xa4, 0xbd, 0xe1, + 0xdf, 0xcf, 0xf7, 0x1a, 0x56, 0x84, 0x79, 0x59, 0xcd, 0x6f, 0x25, 0x44, 0x65, + 0x97, 0xc6, 0x68, 0xc8, 0x49, 0x0a, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0x5c, 0x7a, 0x8f, 0x73, 0xad, 0xfc, 0x70, 0xfb, 0x3f, 0x13, 0x94, 0x49, 0xac, + 0x6b, 0x57, 0x07, 0x4c, 0x4d, 0x6e, 0x66, 0xb1, 0x64, 0x93, 0x9d, 0xaf, 0xfa, + 0x2e, 0xf6, 0xee, 0x69, 0x21, 0x08, + ], + [ + 0x1a, 0xdd, 0x86, 0xb3, 0xf2, 0xe1, 0xbd, 0xa6, 0x2a, 0x5d, 0x2e, 0x0e, 0x98, + 0x2b, 0x77, 0xe6, 0xb0, 0xef, 0x9c, 0xa3, 0xf2, 0x49, 0x88, 0xc7, 0xb3, 0x53, + 0x42, 0x01, 0xcf, 0xb1, 0xcd, 0x0d, + ], + [ + 0xbd, 0x69, 0xb8, 0x25, 0x32, 0xb6, 0x94, 0x0f, 0xf2, 0x59, 0x0f, 0x67, 0x9b, + 0xa9, 0xc7, 0x27, 0x1f, 0xe0, 0x1f, 0x7e, 0x9c, 0x8e, 0x36, 0xd6, 0xa5, 0xe2, + 0x9d, 0x4e, 0x30, 0xa7, 0x35, 0x14, + ], + ], + final_state: [ + [ + 0xd0, 0x6e, 0x2f, 0x83, 0x38, 0x92, 0x8a, 0x7e, 0xe7, 0x38, 0x0c, 0x77, 0x92, + 0x80, 0x87, 0xcd, 0xa2, 0xfd, 0x29, 0x61, 0xa1, 0x52, 0x69, 0x03, 0x7a, 0x22, + 0xd6, 0xd1, 0x20, 0xae, 0xdd, 0x21, + ], + [ + 0x29, 0x55, 0xa4, 0x5f, 0x41, 0x6f, 0x10, 0xd6, 0xbc, 0x79, 0xac, 0x94, 0xd0, + 0xc0, 0x69, 0xc9, 0x49, 0xe5, 0xf4, 0xbd, 0x09, 0x48, 0x1e, 0x1f, 0x36, 0x8c, + 0xb9, 0xb8, 0xee, 0x51, 0x14, 0x0d, + ], + [ + 0x0d, 0x83, 0x76, 0xbb, 0xe9, 0xd6, 0x5d, 0x2b, 0x1e, 0x13, 0x6f, 0xb7, 0xd9, + 0x82, 0xab, 0x87, 0xc5, 0x1c, 0x40, 0x30, 0x44, 0xbe, 0x5c, 0x79, 0x9d, 0x56, + 0xbb, 0x68, 0xac, 0xf9, 0x5b, 0x10, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0xbc, 0x50, 0x98, 0x42, 0x55, 0xd6, 0xaf, 0xbe, 0x9e, 0xf9, 0x28, 0x48, 0xed, + 0x5a, 0xc0, 0x08, 0x62, 0xc2, 0xfa, 0x7b, 0x2f, 0xec, 0xbc, 0xb6, 0x4b, 0x69, + 0x68, 0x91, 0x2a, 0x63, 0x81, 0x0e, + ], + [ + 0x3d, 0xc1, 0x66, 0xd5, 0x6a, 0x1d, 0x62, 0xf5, 0xa8, 0xd7, 0x55, 0x1d, 0xb5, + 0xfd, 0x93, 0x13, 0xe8, 0xc7, 0x20, 0x3d, 0x99, 0x6a, 0xf7, 0xd4, 0x77, 0x08, + 0x37, 0x56, 0xd5, 0x9a, 0xf8, 0x0d, + ], + [ + 0x05, 0xa7, 0x45, 0xf4, 0x5d, 0x7f, 0xf6, 0xdb, 0x10, 0xbc, 0x67, 0xfd, 0xf0, + 0xf0, 0x3e, 0xbf, 0x81, 0x30, 0xab, 0x33, 0x36, 0x26, 0x97, 0xb0, 0xe4, 0xe4, + 0xc7, 0x63, 0xcc, 0xb8, 0xf6, 0x36, + ], + ], + final_state: [ + [ + 0x0b, 0x77, 0xec, 0x53, 0x07, 0x14, 0x5a, 0x0c, 0x05, 0x2d, 0xc7, 0xa9, 0xd6, + 0xf9, 0x6a, 0xc3, 0x41, 0xae, 0x72, 0x64, 0x08, 0x32, 0xd5, 0x8e, 0x51, 0xeb, + 0x92, 0xa4, 0x17, 0x80, 0x17, 0x12, + ], + [ + 0x3b, 0x52, 0x3f, 0x44, 0xf0, 0x0e, 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0x94, 0x8d, 0x32, 0x0d, 0xad, 0x16, + ], + ], + final_state: [ + [ + 0x67, 0x80, 0x08, 0x3f, 0x7f, 0x82, 0xcb, 0x42, 0x54, 0xe7, 0xb6, 0x6f, 0x4b, + 0x83, 0x84, 0x6a, 0xc9, 0x77, 0x3f, 0xb9, 0xc3, 0x9c, 0x6e, 0xc9, 0x81, 0x8b, + 0x06, 0x22, 0x23, 0x09, 0x55, 0x2a, + ], + [ + 0xa5, 0xf9, 0xa5, 0x7e, 0x2c, 0x40, 0xb1, 0x58, 0xd8, 0x16, 0x53, 0x43, 0xe6, + 0x02, 0x65, 0x2c, 0x3e, 0xfc, 0x0b, 0x64, 0xdd, 0xca, 0xee, 0xe5, 0xce, 0x3d, + 0x95, 0x1f, 0xd5, 0x9f, 0x50, 0x08, + ], + [ + 0xdc, 0xa4, 0x64, 0x36, 0x12, 0x7c, 0x47, 0x7e, 0x83, 0x95, 0x0f, 0xa0, 0x7c, + 0xc6, 0x8a, 0x56, 0x6e, 0x54, 0x18, 0x55, 0xad, 0xc2, 0x68, 0x52, 0x97, 0x87, + 0x35, 0x24, 0x88, 0x92, 0x1e, 0x3b, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0x4d, 0x54, 0x31, 0xe6, 0x43, 0x7d, 0x0b, 0x5b, 0xed, 0xbb, 0xcd, 0xaf, 0x34, + 0x5b, 0x86, 0xc4, 0x12, 0x1f, 0xc0, 0x0f, 0xe7, 0xf2, 0x35, 0x73, 0x42, 0x76, + 0xd3, 0x8d, 0x47, 0xf1, 0xe1, 0x11, + ], + [ + 0xdd, 0x0c, 0x7a, 0x1d, 0x81, 0x1c, 0x7d, 0x9c, 0xd4, 0x6d, 0x37, 0x7b, 0x3f, + 0xde, 0xab, 0x3f, 0xb6, 0x79, 0xf3, 0xdc, 0x60, 0x1d, 0x00, 0x82, 0x85, 0xed, + 0xcb, 0xda, 0xe6, 0x9c, 0xe8, 0x3c, + ], + [ + 0x19, 0xe4, 0xaa, 0xc0, 0x35, 0x90, 0x17, 0xec, 0x85, 0xa1, 0x83, 0xd2, 0x20, + 0x53, 0xdb, 0x33, 0xf7, 0x34, 0x76, 0xf2, 0x1a, 0x48, 0x2e, 0xc9, 0x37, 0x83, + 0x65, 0xc8, 0xf7, 0x39, 0x3c, 0x14, + ], + ], + final_state: [ + [ + 0x89, 0x99, 0x8e, 0x5e, 0x0f, 0xa1, 0x95, 0x2a, 0x40, 0xb8, 0xb5, 0x2b, 0x62, + 0xd9, 0x45, 0x70, 0xa4, 0x9a, 0x7d, 0x91, 0xdd, 0x22, 0x6d, 0x69, 0x2b, 0xc9, + 0xb1, 0xa6, 0x13, 0xc9, 0x08, 0x30, + ], + [ + 0xd0, 0xee, 0x44, 0xd9, 0xa9, 0x0d, 0x90, 0x79, 0xef, 0xfb, 0x24, 0x86, 0xd3, + 0xd8, 0x4d, 0x1a, 0x18, 0x4e, 0xdf, 0x14, 0x97, 0x0b, 0xac, 0x36, 0xc7, 0x48, + 0x04, 0xc7, 0xff, 0xbe, 0xe5, 0x0b, + ], + [ + 0x04, 0x81, 0x45, 0xa6, 0x61, 0xce, 0x78, 0x7c, 0x7e, 0x12, 0x2a, 0xc6, 0x44, + 0x7e, 0x9b, 0xa3, 0x93, 0xd3, 0x67, 0xac, 0x05, 0x4f, 0xaa, 0xc5, 0xb7, 0xb5, + 0xf7, 0x19, 0x2b, 0x2f, 0xde, 0x21, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0xe2, 0x88, 0x53, 0x15, 0xeb, 0x46, 0x71, 0x09, 0x8b, 0x79, 0x53, 0x5e, 0x79, + 0x0f, 0xe5, 0x3e, 0x29, 0xfe, 0xf2, 0xb3, 0x76, 0x66, 0x97, 0xac, 0x32, 0xb4, + 0xf4, 0x73, 0xf4, 0x68, 0xa0, 0x08, + ], + [ + 0xe6, 0x23, 0x89, 0xfc, 0x16, 0x57, 0xe0, 0xde, 0xf0, 0xb6, 0x32, 0xc6, 0xae, + 0x25, 0xf9, 0xf7, 0x83, 0xb2, 0x7d, 0xb5, 0x9a, 0x4a, 0x15, 0x3d, 0x88, 0x2d, + 0x2b, 0x21, 0x03, 0x59, 0x65, 0x15, + ], + [ + 0xeb, 0x94, 0x94, 0xc6, 0xd2, 0x27, 0xe2, 0x16, 0x3b, 0x46, 0x99, 0xd9, 0x91, + 0xf4, 0x33, 0xbf, 0x94, 0x86, 0xa7, 0xaf, 0xcf, 0x4a, 0x0d, 0x9c, 0x73, 0x1e, + 0x98, 0x5d, 0x99, 0x58, 0x9c, 0x0b, + ], + ], + final_state: [ + [ + 0xce, 0x2d, 0x1f, 0x8d, 0x67, 0x7f, 0xfb, 0xfd, 0x73, 0xb2, 0x35, 0xe8, 0xc6, + 0x87, 0xfb, 0x42, 0x18, 0x7f, 0x78, 0x81, 0xc3, 0xce, 0x9c, 0x79, 0x4f, 0x2b, + 0xd4, 0x61, 0x40, 0xf7, 0xcc, 0x2a, + ], + [ + 0xaf, 0x82, 0x92, 0x39, 0xb6, 0xd5, 0x5d, 0x5f, 0x43, 0xec, 0x6f, 0x32, 0xb8, + 0x4a, 0x2a, 0x01, 0x1e, 0x64, 0xc5, 0x74, 0x73, 0x9f, 0x87, 0xcb, 0x47, 0xdc, + 0x70, 0x23, 0x83, 0xfa, 0x5a, 0x34, + ], + [ + 0x03, 0xd1, 0x08, 0x5b, 0x21, 0x4c, 0x69, 0xb8, 0xbf, 0xe8, 0x91, 0x02, 0xbd, + 0x61, 0x7e, 0xce, 0x0c, 0x54, 0x00, 0x17, 0x96, 0x40, 0x41, 0x05, 0xc5, 0x33, + 0x30, 0xd2, 0x49, 0x58, 0x1d, 0x0f, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0xb7, 0x38, 0xe8, 0xaa, 0x0a, 0x15, 0x26, 0xa5, 0xbd, 0xef, 0x61, 0x31, 0x20, + 0x37, 0x2e, 0x83, 0x1a, 0x20, 0xda, 0x8a, 0xba, 0x18, 0xd1, 0xdb, 0xeb, 0xbc, + 0x86, 0x2d, 0xed, 0x42, 0x43, 0x1e, + ], + [ + 0x91, 0x47, 0x69, 0x30, 0xe3, 0x38, 0x5c, 0xd3, 0xe3, 0x37, 0x9e, 0x38, 0x53, + 0xd9, 0x34, 0x67, 0xe0, 0x01, 0xaf, 0xa2, 0xfb, 0x8d, 0xc3, 0x43, 0x6d, 0x75, + 0xa4, 0xa6, 0xf2, 0x65, 0x72, 0x10, + ], + [ + 0x4b, 0x19, 0x22, 0x32, 0xec, 0xb9, 0xf0, 0xc0, 0x24, 0x11, 0xe5, 0x25, 0x96, + 0xbc, 0x5e, 0x90, 0x45, 0x7e, 0x74, 0x59, 0x39, 0xff, 0xed, 0xbd, 0x12, 0x86, + 0x3c, 0xe7, 0x1a, 0x02, 0xaf, 0x11, + ], + ], + final_state: [ + [ + 0x5f, 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0xa2, 0x70, 0x57, 0x26, 0x70, 0xdc, 0x82, 0xd3, + 0x90, 0x26, 0xc6, 0xcb, 0x4c, 0xd4, 0xb0, 0xf7, 0xf5, 0xaa, 0x2a, 0x4f, 0x5a, + 0x53, 0x41, 0xec, 0x5d, 0xd7, 0x15, + ], + [ + 0x40, 0x6f, 0x2f, 0xdd, 0x2a, 0xfa, 0x73, 0x3f, 0x5f, 0x64, 0x1c, 0x8c, 0x21, + 0x86, 0x2a, 0x1b, 0xaf, 0xce, 0x26, 0x09, 0xd9, 0xee, 0xcf, 0xa1, 0x58, 0xcf, + 0xb5, 0xcd, 0x79, 0xf8, 0x80, 0x08, + ], + [ + 0xe2, 0x15, 0xdc, 0x7d, 0x96, 0x57, 0xba, 0xd3, 0xfb, 0x88, 0xb0, 0x1e, 0x99, + 0x38, 0x44, 0x54, 0x36, 0x24, 0xc2, 0x5f, 0xa9, 0x59, 0xcc, 0x97, 0x48, 0x9c, + 0xe7, 0x57, 0x45, 0x82, 0x4b, 0x37, + ], + ], + final_state: [ + [ + 0x63, 0x09, 0x15, 0xd7, 0xd8, 0x25, 0xeb, 0x74, 0x37, 0xb0, 0xe4, 0x6e, 0x37, + 0x28, 0x6a, 0x88, 0xb3, 0x89, 0xdc, 0x69, 0x85, 0x93, 0x07, 0x11, 0x6d, 0x34, + 0x7b, 0x98, 0xca, 0x14, 0x5c, 0x31, + ], + [ + 0xaa, 0x58, 0x1b, 0xae, 0xe9, 0x4f, 0xb5, 0x46, 0xa7, 0x61, 0xf1, 0x7a, 0x5d, + 0x6e, 0xaa, 0x70, 0x29, 0x52, 0x78, 0x42, 0xf3, 0x1c, 0x39, 0x87, 0xb8, 0x68, + 0xed, 0x7d, 0xaf, 0xfd, 0xb5, 0x34, + ], + [ + 0x7d, 0xc1, 0x17, 0xb3, 0x39, 0x1a, 0xab, 0x85, 0xde, 0x9f, 0x42, 0x4d, 0xb6, + 0x65, 0x1e, 0x00, 0x45, 0xab, 0x79, 0x98, 0xf2, 0x8e, 0x54, 0x10, 0x15, 0x35, + 0x90, 0x61, 0x99, 0xce, 0x1f, 0x1a, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0x86, 0x8c, 0x53, 0x23, 0x9c, 0xfb, 0xdf, 0x73, 0xca, 0xec, 0x65, 0x60, 0x40, + 0x37, 0x31, 0x4f, 0xaa, 0xce, 0xb5, 0x62, 0x18, 0xc6, 0xbd, 0x30, 0xf8, 0x37, + 0x4a, 0xc1, 0x33, 0x86, 0x79, 0x3f, + ], + [ + 0x21, 0xa9, 0xfb, 0x80, 0xad, 0x03, 0xbc, 0x0c, 0xda, 0x4a, 0x44, 0x94, 0x6c, + 0x00, 0xe1, 0xb1, 0xa1, 0xdf, 0x0e, 0x5b, 0x87, 0xb5, 0xbe, 0xce, 0x47, 0x7a, + 0x70, 0x96, 0x49, 0xe9, 0x50, 0x06, + ], + [ + 0x04, 0x91, 0x39, 0x48, 0x25, 0x64, 0xf1, 0x85, 0xc7, 0x90, 0x0e, 0x83, 0xc7, + 0x38, 0x07, 0x0a, 0xf6, 0x55, 0x6d, 0xf6, 0xed, 0x4b, 0x4d, 0xdd, 0x3d, 0x9a, + 0x69, 0xf5, 0x33, 0x57, 0xd7, 0x36, + ], + ], + final_state: [ + [ + 0x6a, 0x5a, 0x19, 0x19, 0xa4, 0x49, 0xa5, 0xe0, 0x29, 0x71, 0x1f, 0x48, 0x8a, + 0xdb, 0xd6, 0xb0, 0x3e, 0x5c, 0x92, 0x7b, 0x6f, 0x9d, 0x9d, 0x35, 0xc5, 0xb3, + 0xcc, 0xeb, 0x76, 0x60, 0x52, 0x03, + ], + [ + 0x80, 0x47, 0x5b, 0x46, 0x89, 0x59, 0x61, 0x47, 0xab, 0x2a, 0xdf, 0x01, 0x73, + 0xdb, 0x28, 0x9b, 0x3a, 0x26, 0xa1, 0x04, 0x84, 0x21, 0x73, 0xe8, 0x8b, 0xdb, + 0xfe, 0xc0, 0x4a, 0x28, 0x67, 0x1b, + ], + [ + 0x1e, 0xf3, 0xc8, 0xd0, 0xf5, 0x44, 0x44, 0xf5, 0x55, 0xb1, 0x5f, 0x7b, 0xc9, + 0xfa, 0x4f, 0xfa, 0x0f, 0x56, 0x7c, 0x0f, 0x19, 0xac, 0x7d, 0x0f, 0xf9, 0x44, + 0xfd, 0x36, 0x42, 0x6e, 0x32, 0x3a, + ], + ], + }, + TestVector { + initial_state: [ + [ + 0x7d, 0x4f, 0x5c, 0xcb, 0x01, 0x64, 0x3c, 0x31, 0xdb, 0x84, 0x5e, 0xec, 0xd5, + 0xd6, 0x3d, 0xc1, 0x6a, 0x95, 0xe3, 0x02, 0x5b, 0x97, 0x92, 0xff, 0xf7, 0xf2, + 0x44, 0xfc, 0x71, 0x62, 0x69, 0x39, + ], + [ + 0x26, 0xd6, 0x2e, 0x95, 0x96, 0xfa, 0x82, 0x5c, 0x6b, 0xf2, 0x1a, 0xff, 0x9e, + 0x68, 0x62, 0x5a, 0x19, 0x24, 0x40, 0xea, 0x06, 0x82, 0x81, 0x23, 0xd9, 0x78, + 0x84, 0x80, 0x6f, 0x15, 0xfa, 0x08, + ], + [ + 0xd9, 0x52, 0x75, 0x4a, 0x23, 0x64, 0xb6, 0x66, 0xff, 0xc3, 0x0f, 0xdb, 0x01, + 0x47, 0x86, 0xda, 0x3a, 0x61, 0x28, 0xae, 0xf7, 0x84, 0xa6, 0x46, 0x10, 0xa8, + 0x9d, 0x1a, 0x70, 0x99, 0x21, 0x2d, + ], + ], + final_state: [ + [ + 0x1b, 0x4a, 0xc9, 0xbe, 0xf5, 0x6b, 0xdb, 0x6f, 0xb4, 0x2d, 0x3e, 0x3c, 0xd3, + 0xa2, 0xac, 0x70, 0xa4, 0xc4, 0x0c, 0x42, 0x5b, 0x0b, 0xd6, 0x67, 0x9c, 0xa5, + 0x7b, 0x30, 0x7e, 0xf1, 0xd4, 0x2f, + ], + [ + 0x1a, 0x2e, 0xf4, 0x11, 0x94, 0xaa, 0xa2, 0x34, 0x32, 0xe0, 0x86, 0xed, 0x8a, + 0xdb, 0xd1, 0xde, 0xec, 0x3c, 0x7c, 0xb3, 0x96, 0xde, 0x35, 0xba, 0xe9, 0x5a, + 0xaf, 0x5a, 0x08, 0xa0, 0xec, 0x36, + ], + [ + 0x68, 0xeb, 0x80, 0xc7, 0x3e, 0x2c, 0xcb, 0xde, 0xe1, 0xba, 0x71, 0x24, 0x77, + 0x61, 0xd5, 0xb5, 0xec, 0xc6, 0x20, 0xe6, 0xe4, 0x8e, 0x00, 0x3b, 0x02, 0x3d, + 0x9f, 0x55, 0x61, 0x66, 0x2f, 0x20, + ], + ], + }, + ] +} + +pub(crate) fn hash() -> Vec { + use HashTestVector as TestVector; + + // From https://github.com/zcash-hackworks/zcash-test-vectors/blob/master/orchard_poseidon_hash.py + vec![ + TestVector { + input: [ + [ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + ], + [ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + ], + ], + output: [ + 0x83, 0x58, 0xd7, 0x11, 0xa0, 0x32, 0x9d, 0x38, 0xbe, 0xcd, 0x54, 0xfb, 0xa7, 0xc2, + 0x83, 0xed, 0x3e, 0x08, 0x9a, 0x39, 0xc9, 0x1b, 0x6a, 0x9d, 0x10, 0xef, 0xb0, 0x2b, + 0xc3, 0xf1, 0x2f, 0x06, + ], + }, + TestVector { + input: [ + [ + 0x5c, 0x7a, 0x8f, 0x73, 0xad, 0xfc, 0x70, 0xfb, 0x3f, 0x13, 0x94, 0x49, 0xac, + 0x6b, 0x57, 0x07, 0x4c, 0x4d, 0x6e, 0x66, 0xb1, 0x64, 0x93, 0x9d, 0xaf, 0xfa, + 0x2e, 0xf6, 0xee, 0x69, 0x21, 0x08, + ], + [ + 0x1a, 0xdd, 0x86, 0xb3, 0xf2, 0xe1, 0xbd, 0xa6, 0x2a, 0x5d, 0x2e, 0x0e, 0x98, + 0x2b, 0x77, 0xe6, 0xb0, 0xef, 0x9c, 0xa3, 0xf2, 0x49, 0x88, 0xc7, 0xb3, 0x53, + 0x42, 0x01, 0xcf, 0xb1, 0xcd, 0x0d, + ], + ], + output: [ + 0xdb, 0x26, 0x75, 0xff, 0x3e, 0xf8, 0xfe, 0x30, 0xc4, 0xd5, 0xde, 0x61, 0xca, 0xc0, + 0x2a, 0x8e, 0xf1, 0xa0, 0x85, 0x23, 0xbe, 0x92, 0x39, 0x4b, 0x79, 0xd2, 0x67, 0x26, + 0x30, 0x3b, 0xe6, 0x03, + ], + }, + TestVector { + input: [ + [ + 0xbd, 0x69, 0xb8, 0x25, 0x32, 0xb6, 0x94, 0x0f, 0xf2, 0x59, 0x0f, 0x67, 0x9b, + 0xa9, 0xc7, 0x27, 0x1f, 0xe0, 0x1f, 0x7e, 0x9c, 0x8e, 0x36, 0xd6, 0xa5, 0xe2, + 0x9d, 0x4e, 0x30, 0xa7, 0x35, 0x14, + ], + [ + 0xbc, 0x50, 0x98, 0x42, 0x55, 0xd6, 0xaf, 0xbe, 0x9e, 0xf9, 0x28, 0x48, 0xed, + 0x5a, 0xc0, 0x08, 0x62, 0xc2, 0xfa, 0x7b, 0x2f, 0xec, 0xbc, 0xb6, 0x4b, 0x69, + 0x68, 0x91, 0x2a, 0x63, 0x81, 0x0e, + ], + ], + output: [ + 0xf5, 0x12, 0x1d, 0x1e, 0x1d, 0x5c, 0xfe, 0x8d, 0xa8, 0x96, 0xac, 0x0f, 0x9c, 0x18, + 0x3d, 0x76, 0x00, 0x31, 0xf6, 0xef, 0x8c, 0x7a, 0x41, 0xe6, 0x5e, 0xb0, 0x07, 0xcd, + 0xdc, 0x1d, 0x14, 0x3d, + ], + }, + TestVector { + input: [ + [ + 0x3d, 0xc1, 0x66, 0xd5, 0x6a, 0x1d, 0x62, 0xf5, 0xa8, 0xd7, 0x55, 0x1d, 0xb5, + 0xfd, 0x93, 0x13, 0xe8, 0xc7, 0x20, 0x3d, 0x99, 0x6a, 0xf7, 0xd4, 0x77, 0x08, + 0x37, 0x56, 0xd5, 0x9a, 0xf8, 0x0d, + ], + [ + 0x05, 0xa7, 0x45, 0xf4, 0x5d, 0x7f, 0xf6, 0xdb, 0x10, 0xbc, 0x67, 0xfd, 0xf0, + 0xf0, 0x3e, 0xbf, 0x81, 0x30, 0xab, 0x33, 0x36, 0x26, 0x97, 0xb0, 0xe4, 0xe4, + 0xc7, 0x63, 0xcc, 0xb8, 0xf6, 0x36, + ], + ], + output: [ + 0xa4, 0x16, 0xa5, 0xe7, 0x13, 0x51, 0x36, 0xa0, 0x50, 0x56, 0x90, 0x00, 0x58, 0xfa, + 0x50, 0xbf, 0x18, 0x6a, 0xd7, 0x33, 0x90, 0xac, 0xe6, 0x32, 0x3d, 0x8d, 0x81, 0xaa, + 0x8a, 0xdb, 0xd4, 0x11, + ], + }, + TestVector { + input: [ + [ + 0x49, 0x5c, 0x22, 0x2f, 0x7f, 0xba, 0x1e, 0x31, 0xde, 0xfa, 0x3d, 0x5a, 0x57, + 0xef, 0xc2, 0xe1, 0xe9, 0xb0, 0x1a, 0x03, 0x55, 0x87, 0xd5, 0xfb, 0x1a, 0x38, + 0xe0, 0x1d, 0x94, 0x90, 0x3d, 0x3c, + ], + [ + 0x3d, 0x0a, 0xd3, 0x36, 0x1f, 0xec, 0x09, 0x77, 0x90, 0xd9, 0xbe, 0x0e, 0x42, + 0x98, 0x8d, 0x7d, 0x25, 0xc9, 0xa1, 0x38, 0xf4, 0x9b, 0x1a, 0x53, 0x7e, 0xdc, + 0xf0, 0x4b, 0xe3, 0x4a, 0x98, 0x11, + ], + ], + output: [ + 0x1a, 0xba, 0xf3, 0x06, 0xfe, 0xd0, 0x5f, 0xa8, 0x92, 0x84, 0x8c, 0x49, 0xf6, 0xba, + 0x10, 0x41, 0x63, 0x43, 0x3f, 0x3f, 0x63, 0x31, 0x08, 0xa1, 0x3b, 0xc1, 0x5b, 0x2a, + 0x1d, 0x55, 0xd4, 0x0c, + ], + }, + TestVector { + input: [ + [ + 0xa4, 0xaf, 0x9d, 0xb6, 0xd2, 0x7b, 0x50, 0x72, 0x83, 0x5f, 0x0c, 0x3e, 0x88, + 0x39, 0x5e, 0xd7, 0xa4, 0x1b, 0x00, 0x52, 0xad, 0x80, 0x84, 0xa8, 0xb9, 0xda, + 0x94, 0x8d, 0x32, 0x0d, 0xad, 0x16, + ], + [ + 0x4d, 0x54, 0x31, 0xe6, 0x43, 0x7d, 0x0b, 0x5b, 0xed, 0xbb, 0xcd, 0xaf, 0x34, + 0x5b, 0x86, 0xc4, 0x12, 0x1f, 0xc0, 0x0f, 0xe7, 0xf2, 0x35, 0x73, 0x42, 0x76, + 0xd3, 0x8d, 0x47, 0xf1, 0xe1, 0x11, + ], + ], + output: [ + 0x04, 0xa1, 0x8a, 0xeb, 0x59, 0x3f, 0x79, 0x0b, 0x76, 0xa3, 0x99, 0xb7, 0xc1, 0x52, + 0x8a, 0xcd, 0xed, 0xe9, 0x3b, 0x3b, 0x2c, 0x49, 0x6b, 0xd7, 0x1b, 0xd5, 0x87, 0xcb, + 0xd7, 0xcf, 0xdf, 0x35, + ], + }, + TestVector { + input: [ + [ + 0xdd, 0x0c, 0x7a, 0x1d, 0x81, 0x1c, 0x7d, 0x9c, 0xd4, 0x6d, 0x37, 0x7b, 0x3f, + 0xde, 0xab, 0x3f, 0xb6, 0x79, 0xf3, 0xdc, 0x60, 0x1d, 0x00, 0x82, 0x85, 0xed, + 0xcb, 0xda, 0xe6, 0x9c, 0xe8, 0x3c, + ], + [ + 0x19, 0xe4, 0xaa, 0xc0, 0x35, 0x90, 0x17, 0xec, 0x85, 0xa1, 0x83, 0xd2, 0x20, + 0x53, 0xdb, 0x33, 0xf7, 0x34, 0x76, 0xf2, 0x1a, 0x48, 0x2e, 0xc9, 0x37, 0x83, + 0x65, 0xc8, 0xf7, 0x39, 0x3c, 0x14, + ], + ], + output: [ + 0x11, 0x03, 0xcc, 0xdc, 0x00, 0xd0, 0xf3, 0x5f, 0x65, 0x83, 0x14, 0x11, 0x6b, 0xc2, + 0xbc, 0xd9, 0x43, 0x74, 0xa9, 0x1f, 0xf9, 0x87, 0x7e, 0x70, 0x66, 0x33, 0x29, 0x04, + 0x2b, 0xd2, 0xf6, 0x1f, + ], + }, + TestVector { + input: [ + [ + 0xe2, 0x88, 0x53, 0x15, 0xeb, 0x46, 0x71, 0x09, 0x8b, 0x79, 0x53, 0x5e, 0x79, + 0x0f, 0xe5, 0x3e, 0x29, 0xfe, 0xf2, 0xb3, 0x76, 0x66, 0x97, 0xac, 0x32, 0xb4, + 0xf4, 0x73, 0xf4, 0x68, 0xa0, 0x08, + ], + [ + 0xe6, 0x23, 0x89, 0xfc, 0x16, 0x57, 0xe0, 0xde, 0xf0, 0xb6, 0x32, 0xc6, 0xae, + 0x25, 0xf9, 0xf7, 0x83, 0xb2, 0x7d, 0xb5, 0x9a, 0x4a, 0x15, 0x3d, 0x88, 0x2d, + 0x2b, 0x21, 0x03, 0x59, 0x65, 0x15, + ], + ], + output: [ + 0xf8, 0xf8, 0xc6, 0x5f, 0x43, 0x7c, 0x45, 0xbe, 0xac, 0x11, 0xeb, 0x7d, 0x9e, 0x47, + 0x58, 0x6d, 0x87, 0x9a, 0xfd, 0x6f, 0x93, 0x04, 0x35, 0xbe, 0x0c, 0x01, 0xd1, 0x9c, + 0x89, 0x5b, 0x8d, 0x10, + ], + }, + TestVector { + input: [ + [ + 0xeb, 0x94, 0x94, 0xc6, 0xd2, 0x27, 0xe2, 0x16, 0x3b, 0x46, 0x99, 0xd9, 0x91, + 0xf4, 0x33, 0xbf, 0x94, 0x86, 0xa7, 0xaf, 0xcf, 0x4a, 0x0d, 0x9c, 0x73, 0x1e, + 0x98, 0x5d, 0x99, 0x58, 0x9c, 0x0b, + ], + [ + 0xb7, 0x38, 0xe8, 0xaa, 0x0a, 0x15, 0x26, 0xa5, 0xbd, 0xef, 0x61, 0x31, 0x20, + 0x37, 0x2e, 0x83, 0x1a, 0x20, 0xda, 0x8a, 0xba, 0x18, 0xd1, 0xdb, 0xeb, 0xbc, + 0x86, 0x2d, 0xed, 0x42, 0x43, 0x1e, + ], + ], + output: [ + 0x5a, 0xeb, 0x48, 0x96, 0x21, 0xb0, 0x2e, 0x8e, 0x69, 0x27, 0xb9, 0x4f, 0xd2, 0x9a, + 0x61, 0x01, 0x83, 0xdf, 0x7f, 0x42, 0x87, 0xe9, 0xcb, 0xf1, 0xcc, 0xc8, 0x81, 0xd7, + 0xd0, 0xb7, 0x38, 0x27, + ], + }, + TestVector { + input: [ + [ + 0x91, 0x47, 0x69, 0x30, 0xe3, 0x38, 0x5c, 0xd3, 0xe3, 0x37, 0x9e, 0x38, 0x53, + 0xd9, 0x34, 0x67, 0xe0, 0x01, 0xaf, 0xa2, 0xfb, 0x8d, 0xc3, 0x43, 0x6d, 0x75, + 0xa4, 0xa6, 0xf2, 0x65, 0x72, 0x10, + ], + [ + 0x4b, 0x19, 0x22, 0x32, 0xec, 0xb9, 0xf0, 0xc0, 0x24, 0x11, 0xe5, 0x25, 0x96, + 0xbc, 0x5e, 0x90, 0x45, 0x7e, 0x74, 0x59, 0x39, 0xff, 0xed, 0xbd, 0x12, 0x86, + 0x3c, 0xe7, 0x1a, 0x02, 0xaf, 0x11, + ], + ], + output: [ + 0xb0, 0x14, 0x47, 0x20, 0xf5, 0xf2, 0xa2, 0x5d, 0x49, 0x2a, 0x50, 0x4e, 0xc0, 0x73, + 0x7f, 0x09, 0x7e, 0xd8, 0x52, 0x17, 0x4f, 0x55, 0xf5, 0x86, 0x30, 0x91, 0x30, 0x6c, + 0x1a, 0xf2, 0x00, 0x35, + ], + }, + TestVector { + input: [ + [ + 0x7b, 0x41, 0x7a, 0xdb, 0x63, 0xb3, 0x71, 0x22, 0xa5, 0xbf, 0x62, 0xd2, 0x6f, + 0x1e, 0x7f, 0x26, 0x8f, 0xb8, 0x6b, 0x12, 0xb5, 0x6d, 0xa9, 0xc3, 0x82, 0x85, + 0x7d, 0xee, 0xcc, 0x40, 0xa9, 0x0d, + ], + [ + 0x5e, 0x29, 0x35, 0x39, 0x71, 0xb3, 0x49, 0x94, 0xb6, 0x21, 0xb0, 0xb2, 0x61, + 0xae, 0xb3, 0x78, 0x6d, 0xd9, 0x84, 0xd5, 0x67, 0xdb, 0x28, 0x57, 0xb9, 0x27, + 0xb7, 0xfa, 0xe2, 0xdb, 0x58, 0x31, + ], + ], + output: [ + 0xbb, 0xbe, 0xb7, 0x42, 0xd6, 0xe7, 0xc0, 0x1a, 0xdb, 0xf4, 0xd3, 0x85, 0x5e, 0x35, + 0xfe, 0xc4, 0x62, 0x04, 0x30, 0x89, 0xc1, 0x8b, 0xa8, 0x02, 0x90, 0x64, 0x7b, 0xb0, + 0xe5, 0x81, 0xad, 0x11, + ], + }, + ] +}