poseidon2 parameters: external matrix

poseidon-parameters/src/v2.rs

@@ -5,6 +5,8 @@ pub use crate::arc_matrix::ArcMatrix;
 pub use crate::matrix::SquareMatrix;
 pub use crate::round_numbers::RoundNumbers;
 
+pub use crate::{matrix_ops::MatrixOperations, matrix_ops::SquareMatrixOperations};
+
 /// A set of Poseidon2 parameters for a given set of input parameters.
 #[derive(Clone, Debug)]
 pub struct PoseidonParameters<F: PrimeField> {

poseidon-paramgen/src/appendix_g.rs

@@ -8,11 +8,7 @@ mod tests {
     use num_bigint::BigUint;
     use poseidon_parameters::v1::{Alpha, PoseidonParameters};
 
-    use crate::{
-        input::{self, InputParameters},
-        rounds,
-        v1::generate,
-    };
+    use crate::{input::InputParameters, rounds, v1::generate};
 
     /// Represents a row in Table 7-9 in Appendix G of the paper.
     #[allow(dead_code)]

poseidon-paramgen/src/mds.rs

@@ -208,7 +208,7 @@ mod tests {
     use poseidon_parameters::v1::Alpha;
 
     use super::*;
-    use crate::{input, rounds};
+    use crate::rounds;
 
     #[test]
     fn convert_from_mds_to_vec_of_vecs() {

poseidon-paramgen/src/poseidon_build.rs

@@ -53,7 +53,7 @@ use poseidon_parameters::v2::{Alpha, ArcMatrix, RoundNumbers, SquareMatrix, Matr
 
 struct DisplayableV2PoseidonParameters<'a, F: PrimeField>(&'a V2PoseidonParameters<F>);
 impl<F: PrimeField> Display for DisplayableV2PoseidonParameters<'_, F> {
-    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+    fn fmt(&self, _f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         todo!()
     }
 }

poseidon-paramgen/src/rounds.rs

@@ -32,7 +32,7 @@ pub fn v1_generate<T: BigInteger>(input: &InputParameters<T>, alpha: &Alpha) ->
     choice.unwrap()
 }
 
-pub fn v2_generate<T: BigInteger>(input: &InputParameters<T>, alpha: &Alpha) -> RoundNumbers {
+pub fn v2_generate<T: BigInteger>(_input: &InputParameters<T>, _alpha: &Alpha) -> RoundNumbers {
     todo!()
 }
 

poseidon-paramgen/src/v2.rs

@@ -1,14 +1,17 @@
 use ark_ff::PrimeField;
 
+mod external;
+mod internal;
+
 use crate::{alpha, input::InputParameters, round_constants, rounds};
-use poseidon_parameters::v2::PoseidonParameters;
+use poseidon_parameters::v2::{PoseidonParameters, SquareMatrix};
 
 /// For generating parameters at build time.
 pub mod poseidon_build {
     pub use crate::poseidon_build::v2_compile as compile;
 }
 
-/// Generate a Poseidon instance mapped over Fp given a choice of:
+/// Generate a Poseidon2 instance mapped over Fp given a choice of:
 ///
 /// * M, the desired security level (in bits),
 /// * t, the width of the desired hash function, e.g. $t=3$ corresponds to 2-to-1 hash.
@@ -24,16 +27,29 @@ pub fn generate<F: PrimeField>(
     let alpha = alpha::generate::<F>(p, allow_inverse);
     let rounds = rounds::v2_generate(&input, &alpha);
     let arc = round_constants::v2_generate(&input, rounds, alpha);
-    let m_e = todo!();
-    let m_i = todo!();
+    let m_i: SquareMatrix<F> = internal::generate(t);
 
-    PoseidonParameters::<F> {
-        M: input.M,
-        t: input.t,
-        alpha,
-        rounds,
-        arc,
-        m_e,
-        m_i,
+    // We use the internal matrix also for the external rounds if t < 4.
+    if t < 4 {
+        PoseidonParameters::<F> {
+            M: input.M,
+            t: input.t,
+            alpha,
+            rounds,
+            arc,
+            m_i: m_i.clone(),
+            m_e: m_i,
+        }
+    } else {
+        let m_e = external::generate(t);
+        PoseidonParameters::<F> {
+            M: input.M,
+            t: input.t,
+            alpha,
+            rounds,
+            arc,
+            m_e,
+            m_i,
+        }
     }
 }

poseidon-paramgen/src/v2/external.rs

@@ -0,0 +1,192 @@
+use ark_ff::PrimeField;
+use poseidon_parameters::{
+    v2::MatrixOperations,
+    v2::{SquareMatrix, SquareMatrixOperations},
+};
+
+/// Generate external matrix
+pub fn generate<F: PrimeField>(t: usize) -> SquareMatrix<F> {
+    if t < 4 {
+        // For t=[2, 3], we don't need to generate an external matrix
+        // because we also use the internal matrix in the full rounds.
+        panic!("unexpected state size: should use internal matrix for t < 4")
+    } else if t % 4 != 0 {
+        // The internal matrix is only defined for t = 4t' where t' is an integer.
+        panic!("unexpected state size: internal matrix only defined for t % 4 != 0")
+    }
+
+    // For t>= 4, we use the following fixed matrix (Section 5.1, Poseidon2 paper).
+    let M4 = SquareMatrix::<F>::from_vec(vec![
+        F::from(5u64),
+        F::from(7u64),
+        F::one(),
+        F::from(3u64),
+        F::from(4u64),
+        F::from(6u64),
+        F::one(),
+        F::one(),
+        F::one(),
+        F::from(3u64),
+        F::from(5u64),
+        F::from(7u64),
+        F::one(),
+        F::one(),
+        F::from(4u64),
+        F::from(6u64),
+    ]);
+
+    if t == 4 {
+        M4
+    } else {
+        let mut matrix = SquareMatrix::identity(t);
+        let d = t / 4;
+        for i in 0..d {
+            for j in 0..d {
+                if i == j {
+                    for inner_row in 0..4 {
+                        for inner_col in 0..4 {
+                            matrix.set_element(
+                                i * 4 + inner_row,
+                                j * 4 + inner_col,
+                                F::from(2u64) * M4.get_element(inner_row, inner_col),
+                            )
+                        }
+                    }
+                } else {
+                    for inner_row in 0..4 {
+                        for inner_col in 0..4 {
+                            matrix.set_element(
+                                i * 4 + inner_row,
+                                j * 4 + inner_col,
+                                M4.get_element(inner_row, inner_col),
+                            )
+                        }
+                    }
+                }
+            }
+        }
+        matrix
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use ark_ed_on_bls12_377::Fq;
+
+    use super::*;
+
+    #[test]
+    fn external_matrix_t_equals_4() {
+        let matrix: SquareMatrix<Fq> = generate(4);
+        // If t=4, the matrix should simply be the fixed M4, unmodified.
+
+        // Row 0
+        assert_eq!(Fq::from(5u64), matrix.get_element(0, 0));
+        assert_eq!(Fq::from(7u64), matrix.get_element(0, 1));
+        assert_eq!(Fq::from(1u64), matrix.get_element(0, 2));
+        assert_eq!(Fq::from(3u64), matrix.get_element(0, 3));
+
+        // Row 1
+        assert_eq!(Fq::from(4u64), matrix.get_element(1, 0));
+        assert_eq!(Fq::from(6u64), matrix.get_element(1, 1));
+        assert_eq!(Fq::from(1u64), matrix.get_element(1, 2));
+        assert_eq!(Fq::from(1u64), matrix.get_element(1, 3));
+
+        // Row 2
+        assert_eq!(Fq::from(1u64), matrix.get_element(2, 0));
+        assert_eq!(Fq::from(3u64), matrix.get_element(2, 1));
+        assert_eq!(Fq::from(5u64), matrix.get_element(2, 2));
+        assert_eq!(Fq::from(7u64), matrix.get_element(2, 3));
+
+        // Row 3
+        assert_eq!(Fq::from(1u64), matrix.get_element(3, 0));
+        assert_eq!(Fq::from(1u64), matrix.get_element(3, 1));
+        assert_eq!(Fq::from(4u64), matrix.get_element(3, 2));
+        assert_eq!(Fq::from(6u64), matrix.get_element(3, 3));
+    }
+
+    #[test]
+    fn external_matrix_t_equals_8() {
+        let matrix: SquareMatrix<Fq> = generate(8);
+
+        // Row 0
+        assert_eq!(Fq::from(10u64), matrix.get_element(0, 0));
+        assert_eq!(Fq::from(14u64), matrix.get_element(0, 1));
+        assert_eq!(Fq::from(2u64), matrix.get_element(0, 2));
+        assert_eq!(Fq::from(6u64), matrix.get_element(0, 3));
+        assert_eq!(Fq::from(5u64), matrix.get_element(0, 4));
+        assert_eq!(Fq::from(7u64), matrix.get_element(0, 5));
+        assert_eq!(Fq::from(1u64), matrix.get_element(0, 6));
+        assert_eq!(Fq::from(3u64), matrix.get_element(0, 7));
+
+        // Row 1
+        assert_eq!(Fq::from(8u64), matrix.get_element(1, 0));
+        assert_eq!(Fq::from(12u64), matrix.get_element(1, 1));
+        assert_eq!(Fq::from(2u64), matrix.get_element(1, 2));
+        assert_eq!(Fq::from(2u64), matrix.get_element(1, 3));
+        assert_eq!(Fq::from(4u64), matrix.get_element(1, 4));
+        assert_eq!(Fq::from(6u64), matrix.get_element(1, 5));
+        assert_eq!(Fq::from(1u64), matrix.get_element(1, 6));
+        assert_eq!(Fq::from(1u64), matrix.get_element(1, 7));
+
+        // Row 2
+        assert_eq!(Fq::from(2u64), matrix.get_element(2, 0));
+        assert_eq!(Fq::from(6u64), matrix.get_element(2, 1));
+        assert_eq!(Fq::from(10u64), matrix.get_element(2, 2));
+        assert_eq!(Fq::from(14u64), matrix.get_element(2, 3));
+        assert_eq!(Fq::from(1u64), matrix.get_element(2, 4));
+        assert_eq!(Fq::from(3u64), matrix.get_element(2, 5));
+        assert_eq!(Fq::from(5u64), matrix.get_element(2, 6));
+        assert_eq!(Fq::from(7u64), matrix.get_element(2, 7));
+
+        // Row 3
+        assert_eq!(Fq::from(2u64), matrix.get_element(3, 0));
+        assert_eq!(Fq::from(2u64), matrix.get_element(3, 1));
+        assert_eq!(Fq::from(8u64), matrix.get_element(3, 2));
+        assert_eq!(Fq::from(12u64), matrix.get_element(3, 3));
+        assert_eq!(Fq::from(1u64), matrix.get_element(3, 4));
+        assert_eq!(Fq::from(1u64), matrix.get_element(3, 5));
+        assert_eq!(Fq::from(4u64), matrix.get_element(3, 6));
+        assert_eq!(Fq::from(6u64), matrix.get_element(3, 7));
+
+        // Row 4
+        assert_eq!(Fq::from(5u64), matrix.get_element(4, 0));
+        assert_eq!(Fq::from(7u64), matrix.get_element(4, 1));
+        assert_eq!(Fq::from(1u64), matrix.get_element(4, 2));
+        assert_eq!(Fq::from(3u64), matrix.get_element(4, 3));
+        assert_eq!(Fq::from(10u64), matrix.get_element(4, 4));
+        assert_eq!(Fq::from(14u64), matrix.get_element(4, 5));
+        assert_eq!(Fq::from(2u64), matrix.get_element(4, 6));
+        assert_eq!(Fq::from(6u64), matrix.get_element(4, 7));
+
+        // Row 5
+        assert_eq!(Fq::from(4u64), matrix.get_element(5, 0));
+        assert_eq!(Fq::from(6u64), matrix.get_element(5, 1));
+        assert_eq!(Fq::from(1u64), matrix.get_element(5, 2));
+        assert_eq!(Fq::from(1u64), matrix.get_element(5, 3));
+        assert_eq!(Fq::from(8u64), matrix.get_element(5, 4));
+        assert_eq!(Fq::from(12u64), matrix.get_element(5, 5));
+        assert_eq!(Fq::from(2u64), matrix.get_element(5, 6));
+        assert_eq!(Fq::from(2u64), matrix.get_element(5, 7));
+
+        // Row 6
+        assert_eq!(Fq::from(1u64), matrix.get_element(6, 0));
+        assert_eq!(Fq::from(3u64), matrix.get_element(6, 1));
+        assert_eq!(Fq::from(5u64), matrix.get_element(6, 2));
+        assert_eq!(Fq::from(7u64), matrix.get_element(6, 3));
+        assert_eq!(Fq::from(2u64), matrix.get_element(6, 4));
+        assert_eq!(Fq::from(6u64), matrix.get_element(6, 5));
+        assert_eq!(Fq::from(10u64), matrix.get_element(6, 6));
+        assert_eq!(Fq::from(14u64), matrix.get_element(6, 7));
+
+        // Row 7
+        assert_eq!(Fq::from(1u64), matrix.get_element(7, 0));
+        assert_eq!(Fq::from(1u64), matrix.get_element(7, 1));
+        assert_eq!(Fq::from(4u64), matrix.get_element(7, 2));
+        assert_eq!(Fq::from(6u64), matrix.get_element(7, 3));
+        assert_eq!(Fq::from(2u64), matrix.get_element(7, 4));
+        assert_eq!(Fq::from(2u64), matrix.get_element(7, 5));
+        assert_eq!(Fq::from(8u64), matrix.get_element(7, 6));
+        assert_eq!(Fq::from(12u64), matrix.get_element(7, 7));
+    }
+}

poseidon-paramgen/src/v2/internal.rs

@@ -0,0 +1,7 @@
+use ark_ff::PrimeField;
+use poseidon_parameters::v2::SquareMatrix;
+
+/// Generate internal matrix
+pub fn generate<F: PrimeField>(_t: usize) -> SquareMatrix<F> {
+    unimplemented!()
+}