#include <poseidon2_internal_relation.hpp>

Public Types
using	FF = FF_

Static Public Member Functions
template<typename AllEntities >
static bool	skip (const AllEntities &in)
	Returns true if the contribution from all subrelations for the provided inputs is identically zero.

template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >
static void	accumulate (ContainerOverSubrelations &evals, const AllEntities &in, const Parameters &, const FF &scaling_factor)
	Expression for the Poseidon2 internal round relation, based on I_i in Section 6 of https://eprint.iacr.org/2023/323.pdf.

Static Public Attributes
static constexpr std::array< size_t, 4 >	SUBRELATION_PARTIAL_LENGTHS

static constexpr fr	D1 = crypto::Poseidon2Bn254ScalarFieldParams::internal_matrix_diagonal[0]

static constexpr fr	D2 = crypto::Poseidon2Bn254ScalarFieldParams::internal_matrix_diagonal[1]

static constexpr fr	D3 = crypto::Poseidon2Bn254ScalarFieldParams::internal_matrix_diagonal[2]

static constexpr fr	D4 = crypto::Poseidon2Bn254ScalarFieldParams::internal_matrix_diagonal[3]

static constexpr fr	D1_plus_1 = fr{ 1 } + D1

Detailed Description

template<typename FF_>
class bb::Poseidon2InternalRelationImpl< FF_ >

Definition at line 13 of file poseidon2_internal_relation.hpp.

Member Typedef Documentation

◆ FF

template<typename FF_ >

using bb::Poseidon2InternalRelationImpl< FF_ >::FF = FF_

Definition at line 15 of file poseidon2_internal_relation.hpp.

Member Function Documentation

◆ accumulate()

template<typename FF_ >

template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >

static void bb::Poseidon2InternalRelationImpl< FF_ >::accumulate	(	ContainerOverSubrelations &	evals,
		const AllEntities &	in,
		const Parameters &	,
		const FF &	scaling_factor
	)

inlinestatic

Expression for the Poseidon2 internal round relation, based on I_i in Section 6 of https://eprint.iacr.org/2023/323.pdf.

Let the internal round matrix M_I be the 4×4 matrix

\[ M_I = \begin{bmatrix} D_1 + 1 & 1 & 1 & 1 \\ 1 & D_2 + 1 & 1 & 1 \\ 1 & 1 & D_3 + 1 & 1 \\ 1 & 1 & 1 & D_4 + 1 \end{bmatrix}, \quad \text{where } D_i \text{ are the diagonal entries of } M_I. \]

Define the state

\[ u_1 = \big(w_1 + \hat{c}_0^{(i)}\big)^{5},\qquad u_2 = w_2,\quad u_3 = w_3,\quad u_4 = w_4,\qquad \mathbf{u} = (u_1,u_2,u_3,u_4). \]

The internal round computes \( \mathbf{v} = M_I \cdot \mathbf{u}^{\top} \) and the relation enforces \( v_k = w_{k,\mathrm{shift}} \) for \( k \in \{1,2,3,4\} \):

\begin{align*} v_1 &= D_1\,u_1 + u_2 + u_3 + u_4,\\ v_2 &= u_1 + D_2\,u_2 + u_3 + u_4,\\ v_3 &= u_1 + u_2 + D_3\,u_3 + u_4,\\ v_4 &= u_1 + u_2 + u_3 + D_4\,u_4, \end{align*}

where \( \hat{c}_0^{(i)} \) is the internal round constant (provided via the \( q_l \) selector).

Concretely, the relation is encoded as four independent constraints multiplied by the \(\text{q_poseidon2_external}\) selector and the scaling factor \(\hat{g}\) arising from the GateSeparatorPolynomial. These contributions are added to the corresponding univariate accumulators \( A_k \) (one per subrelation):

\begin{align*} A_1 &\;\mathrel{+}= q_{\mathrm{poseidon2\_internal}}\cdot\big(v_1 - w_{1,\mathrm{shift}}\big)\cdot \hat{g},\\ A_2 &\;\mathrel{+}= q_{\mathrm{poseidon2\_internal}}\cdot\big(v_2 - w_{2,\mathrm{shift}}\big)\cdot \hat{g},\\ A_3 &\;\mathrel{+}= q_{\mathrm{poseidon2\_internal}}\cdot\big(v_3 - w_{3,\mathrm{shift}}\big)\cdot \hat{g},\\ A_4 &\;\mathrel{+}= q_{\mathrm{poseidon2\_internal}}\cdot\big(v_4 - w_{4,\mathrm{shift}}\big)\cdot \hat{g}. \end{align*}

At the end of each Sumcheck round, the subrelation accumulators are aggregated with independent challenges \( \alpha_i = \alpha_{i,\mathrm{Poseidon2Int}} \) (from the SubrelationSeparators)

\[ \alpha_{0}A_1 + \alpha_{1}A_2 + \alpha_{2}A_3 + \alpha_{3}A_4 \]

and multiplied by the linear factor of the GateSeparatorPolynomial.

Parameters

evals	A tuple of tuples of univariate accumulators; the subtuple for this relation is \([A_1,A_2,A_3,A_4]\), with \( \deg(A_k) = \text{SUBRELATION_PARTIAL_LENGTHS}[k] - 1 \).
in	In round \( k \) of Sumcheck at the point \( i_{>k} = (i_{k+1},\ldots,i_{d-1}) \) on the \( d-k-1 \) dimensional hypercube, an array of restrictions of the prover polynomials \( P_i(u_{<k}, X_k, i_{>k}) \).
parameters	Not used in this relation.
scaling_factor	Scaling term \( \hat{g} \) from the GateSeparatorPolynomial.

Definition at line 98 of file poseidon2_internal_relation.hpp.

◆ skip()

template<typename FF_ >

template<typename AllEntities >

static bool bb::Poseidon2InternalRelationImpl< FF_ >::skip ( const AllEntities & in )

template<typename FF_ >

constexpr std::array<size_t, 4> bb::Poseidon2InternalRelationImpl< FF_ >::SUBRELATION_PARTIAL_LENGTHS

staticconstexpr

Initial value:

Definition at line 17 of file poseidon2_internal_relation.hpp.

The documentation for this class was generated from the following file:

src/barretenberg/relations/poseidon2_internal_relation.hpp

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ FF

Member Function Documentation

◆ accumulate()

◆ skip()

Member Data Documentation

◆ D1

◆ D1_plus_1

◆ D2

◆ D3

◆ D4

◆ SUBRELATION_PARTIAL_LENGTHS