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Copy pathposeidon2.pil
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poseidon2.pil
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// Implementation based on https://eprint.iacr.org/2023/323.pdf
include "poseidon2_params.pil";
namespace poseidon2(256);
pol commit clk;
// Selector for poseidon2 operation
pol commit sel_poseidon_perm;
// Selector is boolean
sel_poseidon_perm * (1 - sel_poseidon_perm) = 0;
// No relations will be checked if this identity is satisfied.
#[skippable_if]
sel_poseidon_perm = 0;
// The initial mem address for inputs or output
pol commit input_addr;
pol commit output_addr;
// Address that is loaded by the gadget memory operations
pol commit mem_addr_read_a;
pol commit mem_addr_read_b;
pol commit mem_addr_read_c;
pol commit mem_addr_read_d;
// Address that is written by the gadget memory operations
pol commit mem_addr_write_a;
pol commit mem_addr_write_b;
pol commit mem_addr_write_c;
pol commit mem_addr_write_d;
// Space Id
pol commit space_id;
// Accessed read / write addresses are contiguous blocks
sel_poseidon_perm * (mem_addr_read_a - input_addr) = 0;
sel_poseidon_perm * (mem_addr_read_b - (input_addr + 1)) = 0;
sel_poseidon_perm * (mem_addr_read_c - (input_addr + 2)) = 0;
sel_poseidon_perm * (mem_addr_read_d - (input_addr + 3)) = 0;
sel_poseidon_perm * (mem_addr_write_a - output_addr) = 0;
sel_poseidon_perm * (mem_addr_write_b - (output_addr + 1)) = 0;
sel_poseidon_perm * (mem_addr_write_c - (output_addr + 2)) = 0;
sel_poseidon_perm * (mem_addr_write_d - (output_addr + 3)) = 0;
// The input values are represented by a_0, a_1, a_2, a_3
pol commit a_0;
pol commit a_1;
pol commit a_2;
pol commit a_3;
// Output values represented by b_0, b_1, b_2, b_3
pol commit b_0;
pol commit b_1;
pol commit b_2;
pol commit b_3;
// ==== READ MEM OPS =====
#[PERM_POS_MEM_READ_A]
sel_poseidon_perm {clk, space_id, mem_addr_read_a, a_0, main.zeroes}
is
mem.sel_op_poseidon_read_a {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_READ_B]
sel_poseidon_perm {clk, space_id, mem_addr_read_b, a_1, main.zeroes}
is
mem.sel_op_poseidon_read_b {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_READ_C]
sel_poseidon_perm {clk, space_id, mem_addr_read_c, a_2, main.zeroes}
is
mem.sel_op_poseidon_read_c {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_READ_D]
sel_poseidon_perm {clk, space_id, mem_addr_read_d, a_3, main.zeroes}
is
mem.sel_op_poseidon_read_d {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
//// ==== WRITE MEM OPS =====
#[PERM_POS_MEM_WRITE_A]
sel_poseidon_perm {clk, space_id, mem_addr_write_a, b_0, sel_poseidon_perm}
is
mem.sel_op_poseidon_write_a {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_WRITE_B]
sel_poseidon_perm {clk, space_id, mem_addr_write_b, b_1, sel_poseidon_perm}
is
mem.sel_op_poseidon_write_b {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_WRITE_C]
sel_poseidon_perm {clk, space_id, mem_addr_write_c, b_2, sel_poseidon_perm}
is
mem.sel_op_poseidon_write_c {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
#[PERM_POS_MEM_WRITE_D]
sel_poseidon_perm {clk, space_id, mem_addr_write_d, b_3, sel_poseidon_perm}
is
mem.sel_op_poseidon_write_d {mem.clk, mem.space_id, mem.addr, mem.val, mem.rw};
// Intermediate helper values denoted by T_{id} - based on Appendix B of https://eprint.iacr.org/2023/323.pdf;
// T_0 = a_0 + a_1;
// T_1 = a_2 + a_3;
// T_2 = 2 * a_1 + T_0;
// T_3 = 2 * a_3 + T_0;
// T_4 = 4 * T_1 + T_3;
// T_5 = 4 * T_0 + T_2;
// T_6 = T_3 + T_5;
// T_7 = T_2 + T_4;
// We additionally include the round identifier in the naming
// <STEP>_<ROUND>_<INPUT>
// e.g. ARK_0_2 -> Add Round Constant, round 0, input 2
// FIRST EXTERNAL MATRIX LAYER
pol commit EXT_LAYER_4;
pol commit EXT_LAYER_5;
pol commit EXT_LAYER_6;
pol commit EXT_LAYER_7;
pol EXT_LAYER_0 = a_0 + a_1;
pol EXT_LAYER_1 = a_2 + a_3;
pol EXT_LAYER_2 = 2 * a_1 + EXT_LAYER_1;
pol EXT_LAYER_3 = 2 * a_3 + EXT_LAYER_0;
sel_poseidon_perm * (EXT_LAYER_4 - (4 * EXT_LAYER_1 + EXT_LAYER_3)) = 0;
sel_poseidon_perm * (EXT_LAYER_5 - (4 * EXT_LAYER_0 + EXT_LAYER_2)) = 0;
sel_poseidon_perm * (EXT_LAYER_6 - (EXT_LAYER_3 + EXT_LAYER_5)) = 0;
sel_poseidon_perm * (EXT_LAYER_7 - (EXT_LAYER_2 + EXT_LAYER_4)) = 0;
/////////////////////////////////////////////////////
// START FULL ROUNDS (4 ROUNDS)
/////////////////////////////////////////////////////
// Round 1 (Full Round)
// ARK (Add Round Constant)
pol ARK_0_0 = EXT_LAYER_6 + poseidon2_params.C_0_0;
pol ARK_0_1 = EXT_LAYER_5 + poseidon2_params.C_0_1;
pol ARK_0_2 = EXT_LAYER_7 + poseidon2_params.C_0_2;
pol ARK_0_3 = EXT_LAYER_4 + poseidon2_params.C_0_3;
// S-BOX (In full round all inputs are exponentiated)
pol A_0_0 = ARK_0_0 * ARK_0_0 * ARK_0_0 * ARK_0_0 * ARK_0_0;
pol A_0_1 = ARK_0_1 * ARK_0_1 * ARK_0_1 * ARK_0_1 * ARK_0_1;
pol A_0_2 = ARK_0_2 * ARK_0_2 * ARK_0_2 * ARK_0_2 * ARK_0_2;
pol A_0_3 = ARK_0_3 * ARK_0_3 * ARK_0_3 * ARK_0_3 * ARK_0_3;
// MATRIX (Full round uses the external matrix)
pol commit T_0_4;
pol commit T_0_5;
pol commit T_0_6;
pol commit T_0_7;
pol T_0_0 = A_0_0 + A_0_1;
pol T_0_1 = A_0_2 + A_0_3;
pol T_0_2 = 2 * A_0_1 + T_0_1;
pol T_0_3 = 2 * A_0_3 + T_0_0;
sel_poseidon_perm * (T_0_4 - (4 * T_0_1 + T_0_3)) = 0;
sel_poseidon_perm * (T_0_5 - (4 * T_0_0 + T_0_2)) = 0;
sel_poseidon_perm * (T_0_6 - (T_0_3 + T_0_5)) = 0;
sel_poseidon_perm * (T_0_7 - (T_0_2 + T_0_4)) = 0;
// Round 2 (Full Round)
// ARK (Add Round Constant)
pol ARK_1_0 = T_0_6 + poseidon2_params.C_1_0;
pol ARK_1_1 = T_0_5 + poseidon2_params.C_1_1;
pol ARK_1_2 = T_0_7 + poseidon2_params.C_1_2;
pol ARK_1_3 = T_0_4 + poseidon2_params.C_1_3;
// S-BOX (In full round all inputs are exponentiated)
pol A_1_0 = ARK_1_0 * ARK_1_0 * ARK_1_0 * ARK_1_0 * ARK_1_0;
pol A_1_1 = ARK_1_1 * ARK_1_1 * ARK_1_1 * ARK_1_1 * ARK_1_1;
pol A_1_2 = ARK_1_2 * ARK_1_2 * ARK_1_2 * ARK_1_2 * ARK_1_2;
pol A_1_3 = ARK_1_3 * ARK_1_3 * ARK_1_3 * ARK_1_3 * ARK_1_3;
// MATRIX (Full round uses the external matrix)
pol commit T_1_4;
pol commit T_1_5;
pol commit T_1_6;
pol commit T_1_7;
pol T_1_0 = A_1_0 + A_1_1;
pol T_1_1 = A_1_2 + A_1_3;
pol T_1_2 = 2 * A_1_1 + T_1_1;
pol T_1_3 = 2 * A_1_3 + T_1_0;
sel_poseidon_perm * (T_1_4 - (4 * T_1_1 + T_1_3)) = 0;
sel_poseidon_perm * (T_1_5 - (4 * T_1_0 + T_1_2)) = 0;
sel_poseidon_perm * (T_1_6 - (T_1_3 + T_1_5)) = 0;
sel_poseidon_perm * (T_1_7 - (T_1_2 + T_1_4)) = 0;
// Round 3 (Full Round)
// ARK (Add Round Constant)
pol ARK_2_0 = T_1_6 + poseidon2_params.C_2_0;
pol ARK_2_1 = T_1_5 + poseidon2_params.C_2_1;
pol ARK_2_2 = T_1_7 + poseidon2_params.C_2_2;
pol ARK_2_3 = T_1_4 + poseidon2_params.C_2_3;
// S-BOX (In full round all inputs are exponentiated)
pol A_2_0 = ARK_2_0 * ARK_2_0 * ARK_2_0 * ARK_2_0 * ARK_2_0;
pol A_2_1 = ARK_2_1 * ARK_2_1 * ARK_2_1 * ARK_2_1 * ARK_2_1;
pol A_2_2 = ARK_2_2 * ARK_2_2 * ARK_2_2 * ARK_2_2 * ARK_2_2;
pol A_2_3 = ARK_2_3 * ARK_2_3 * ARK_2_3 * ARK_2_3 * ARK_2_3;
// MATRIX (Full round uses the external matrix)
pol commit T_2_4;
pol commit T_2_5;
pol commit T_2_6;
pol commit T_2_7;
pol T_2_0 = A_2_0 + A_2_1;
pol T_2_1 = A_2_2 + A_2_3;
pol T_2_2 = 2 * A_2_1 + T_2_1;
pol T_2_3 = 2 * A_2_3 + T_2_0;
sel_poseidon_perm * (T_2_4 - (4 * T_2_1 + T_2_3)) = 0;
sel_poseidon_perm * (T_2_5 - (4 * T_2_0 + T_2_2)) = 0;
sel_poseidon_perm * (T_2_6 - (T_2_3 + T_2_5)) = 0;
sel_poseidon_perm * (T_2_7 - (T_2_2 + T_2_4)) = 0;
// Round 4 (Full Round)
// ARK (Add Round Constant)
pol ARK_3_0 = T_2_6 + poseidon2_params.C_3_0;
pol ARK_3_1 = T_2_5 + poseidon2_params.C_3_1;
pol ARK_3_2 = T_2_7 + poseidon2_params.C_3_2;
pol ARK_3_3 = T_2_4 + poseidon2_params.C_3_3;
// S-BOX (In full round all inputs are exponentiated)
pol A_3_0 = ARK_3_0 * ARK_3_0 * ARK_3_0 * ARK_3_0 * ARK_3_0;
pol A_3_1 = ARK_3_1 * ARK_3_1 * ARK_3_1 * ARK_3_1 * ARK_3_1;
pol A_3_2 = ARK_3_2 * ARK_3_2 * ARK_3_2 * ARK_3_2 * ARK_3_2;
pol A_3_3 = ARK_3_3 * ARK_3_3 * ARK_3_3 * ARK_3_3 * ARK_3_3;
// MATRIX (Full round uses the external matrix)
pol commit T_3_4;
pol commit T_3_5;
pol commit T_3_6;
pol commit T_3_7;
pol T_3_0 = A_3_0 + A_3_1;
pol T_3_1 = A_3_2 + A_3_3;
pol T_3_2 = 2 * A_3_1 + T_3_1;
pol T_3_3 = 2 * A_3_3 + T_3_0;
sel_poseidon_perm * (T_3_4 - (4 * T_3_1 + T_3_3)) = 0;
sel_poseidon_perm * (T_3_5 - (4 * T_3_0 + T_3_2)) = 0;
sel_poseidon_perm * (T_3_6 - (T_3_3 + T_3_5)) = 0;
sel_poseidon_perm * (T_3_7 - (T_3_2 + T_3_4)) = 0;
/////////////////////////////////////////////////////
// PARTIAL ROUNDS (56 ROUNDS)
/////////////////////////////////////////////////////
// Round 5 (Partial Round)
// ARK (Add Round Constant)
pol ARK_4_0 = T_3_6 + poseidon2_params.C_4_0;
pol ARK_4_1 = T_3_5 + poseidon2_params.C_4_1;
pol ARK_4_2 = T_3_7 + poseidon2_params.C_4_2;
pol ARK_4_3 = T_3_4 + poseidon2_params.C_4_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_4_0 = ARK_4_0 * ARK_4_0 * ARK_4_0 * ARK_4_0 * ARK_4_0;
pol A_4_1 = ARK_4_1;
pol A_4_2 = ARK_4_2;
pol A_4_3 = ARK_4_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_4_0;
pol commit B_4_1;
pol commit B_4_2;
pol commit B_4_3;
pol SUM_4 = A_4_0 + A_4_1 + A_4_2 + A_4_3;
sel_poseidon_perm * (B_4_0 - (poseidon2_params.MU_0 * A_4_0 + SUM_4)) = 0;
sel_poseidon_perm * (B_4_1 - (poseidon2_params.MU_1 * A_4_1 + SUM_4)) = 0;
sel_poseidon_perm * (B_4_2 - (poseidon2_params.MU_2 * A_4_2 + SUM_4)) = 0;
sel_poseidon_perm * (B_4_3 - (poseidon2_params.MU_3 * A_4_3 + SUM_4)) = 0;
// Round 6 (Partial Round)
// ARK (Add Round Constant)
pol ARK_5_0 = B_4_0 + poseidon2_params.C_5_0;
pol ARK_5_1 = B_4_1 + poseidon2_params.C_5_1;
pol ARK_5_2 = B_4_2 + poseidon2_params.C_5_2;
pol ARK_5_3 = B_4_3 + poseidon2_params.C_5_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_5_0 = ARK_5_0 * ARK_5_0 * ARK_5_0 * ARK_5_0 * ARK_5_0;
pol A_5_1 = ARK_5_1;
pol A_5_2 = ARK_5_2;
pol A_5_3 = ARK_5_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_5_0;
pol commit B_5_1;
pol commit B_5_2;
pol commit B_5_3;
pol SUM_5 = A_5_0 + A_5_1 + A_5_2 + A_5_3;
sel_poseidon_perm * (B_5_0 - (poseidon2_params.MU_0 * A_5_0 + SUM_5)) = 0;
sel_poseidon_perm * (B_5_1 - (poseidon2_params.MU_1 * A_5_1 + SUM_5)) = 0;
sel_poseidon_perm * (B_5_2 - (poseidon2_params.MU_2 * A_5_2 + SUM_5)) = 0;
sel_poseidon_perm * (B_5_3 - (poseidon2_params.MU_3 * A_5_3 + SUM_5)) = 0;
// Round 7 (Partial Round)
// ARK (Add Round Constant)
pol ARK_6_0 = B_5_0 + poseidon2_params.C_6_0;
pol ARK_6_1 = B_5_1 + poseidon2_params.C_6_1;
pol ARK_6_2 = B_5_2 + poseidon2_params.C_6_2;
pol ARK_6_3 = B_5_3 + poseidon2_params.C_6_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_6_0 = ARK_6_0 * ARK_6_0 * ARK_6_0 * ARK_6_0 * ARK_6_0;
pol A_6_1 = ARK_6_1;
pol A_6_2 = ARK_6_2;
pol A_6_3 = ARK_6_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_6_0;
pol commit B_6_1;
pol commit B_6_2;
pol commit B_6_3;
pol SUM_6 = A_6_0 + A_6_1 + A_6_2 + A_6_3;
sel_poseidon_perm * (B_6_0 - (poseidon2_params.MU_0 * A_6_0 + SUM_6)) = 0;
sel_poseidon_perm * (B_6_1 - (poseidon2_params.MU_1 * A_6_1 + SUM_6)) = 0;
sel_poseidon_perm * (B_6_2 - (poseidon2_params.MU_2 * A_6_2 + SUM_6)) = 0;
sel_poseidon_perm * (B_6_3 - (poseidon2_params.MU_3 * A_6_3 + SUM_6)) = 0;
// Round 8 (Partial Round)
// ARK (Add Round Constant)
pol ARK_7_0 = B_6_0 + poseidon2_params.C_7_0;
pol ARK_7_1 = B_6_1 + poseidon2_params.C_7_1;
pol ARK_7_2 = B_6_2 + poseidon2_params.C_7_2;
pol ARK_7_3 = B_6_3 + poseidon2_params.C_7_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_7_0 = ARK_7_0 * ARK_7_0 * ARK_7_0 * ARK_7_0 * ARK_7_0;
pol A_7_1 = ARK_7_1;
pol A_7_2 = ARK_7_2;
pol A_7_3 = ARK_7_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_7_0;
pol commit B_7_1;
pol commit B_7_2;
pol commit B_7_3;
pol SUM_7 = A_7_0 + A_7_1 + A_7_2 + A_7_3;
sel_poseidon_perm * (B_7_0 - (poseidon2_params.MU_0 * A_7_0 + SUM_7)) = 0;
sel_poseidon_perm * (B_7_1 - (poseidon2_params.MU_1 * A_7_1 + SUM_7)) = 0;
sel_poseidon_perm * (B_7_2 - (poseidon2_params.MU_2 * A_7_2 + SUM_7)) = 0;
sel_poseidon_perm * (B_7_3 - (poseidon2_params.MU_3 * A_7_3 + SUM_7)) = 0;
// Round 9 (Partial Round)
// ARK (Add Round Constant)
pol ARK_8_0 = B_7_0 + poseidon2_params.C_8_0;
pol ARK_8_1 = B_7_1 + poseidon2_params.C_8_1;
pol ARK_8_2 = B_7_2 + poseidon2_params.C_8_2;
pol ARK_8_3 = B_7_3 + poseidon2_params.C_8_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_8_0 = ARK_8_0 * ARK_8_0 * ARK_8_0 * ARK_8_0 * ARK_8_0;
pol A_8_1 = ARK_8_1;
pol A_8_2 = ARK_8_2;
pol A_8_3 = ARK_8_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_8_0;
pol commit B_8_1;
pol commit B_8_2;
pol commit B_8_3;
pol SUM_8 = A_8_0 + A_8_1 + A_8_2 + A_8_3;
sel_poseidon_perm * (B_8_0 - (poseidon2_params.MU_0 * A_8_0 + SUM_8)) = 0;
sel_poseidon_perm * (B_8_1 - (poseidon2_params.MU_1 * A_8_1 + SUM_8)) = 0;
sel_poseidon_perm * (B_8_2 - (poseidon2_params.MU_2 * A_8_2 + SUM_8)) = 0;
sel_poseidon_perm * (B_8_3 - (poseidon2_params.MU_3 * A_8_3 + SUM_8)) = 0;
// Round 10 (Partial Round)
// ARK (Add Round Constant)
pol ARK_9_0 = B_8_0 + poseidon2_params.C_9_0;
pol ARK_9_1 = B_8_1 + poseidon2_params.C_9_1;
pol ARK_9_2 = B_8_2 + poseidon2_params.C_9_2;
pol ARK_9_3 = B_8_3 + poseidon2_params.C_9_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_9_0 = ARK_9_0 * ARK_9_0 * ARK_9_0 * ARK_9_0 * ARK_9_0;
pol A_9_1 = ARK_9_1;
pol A_9_2 = ARK_9_2;
pol A_9_3 = ARK_9_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_9_0;
pol commit B_9_1;
pol commit B_9_2;
pol commit B_9_3;
pol SUM_9 = A_9_0 + A_9_1 + A_9_2 + A_9_3;
sel_poseidon_perm * (B_9_0 - (poseidon2_params.MU_0 * A_9_0 + SUM_9)) = 0;
sel_poseidon_perm * (B_9_1 - (poseidon2_params.MU_1 * A_9_1 + SUM_9)) = 0;
sel_poseidon_perm * (B_9_2 - (poseidon2_params.MU_2 * A_9_2 + SUM_9)) = 0;
sel_poseidon_perm * (B_9_3 - (poseidon2_params.MU_3 * A_9_3 + SUM_9)) = 0;
// Round 11 (Partial Round)
// ARK (Add Round Constant)
pol ARK_10_0 = B_9_0 + poseidon2_params.C_10_0;
pol ARK_10_1 = B_9_1 + poseidon2_params.C_10_1;
pol ARK_10_2 = B_9_2 + poseidon2_params.C_10_2;
pol ARK_10_3 = B_9_3 + poseidon2_params.C_10_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_10_0 = ARK_10_0 * ARK_10_0 * ARK_10_0 * ARK_10_0 * ARK_10_0;
pol A_10_1 = ARK_10_1;
pol A_10_2 = ARK_10_2;
pol A_10_3 = ARK_10_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_10_0;
pol commit B_10_1;
pol commit B_10_2;
pol commit B_10_3;
pol SUM_10 = A_10_0 + A_10_1 + A_10_2 + A_10_3;
sel_poseidon_perm * (B_10_0 - (poseidon2_params.MU_0 * A_10_0 + SUM_10)) = 0;
sel_poseidon_perm * (B_10_1 - (poseidon2_params.MU_1 * A_10_1 + SUM_10)) = 0;
sel_poseidon_perm * (B_10_2 - (poseidon2_params.MU_2 * A_10_2 + SUM_10)) = 0;
sel_poseidon_perm * (B_10_3 - (poseidon2_params.MU_3 * A_10_3 + SUM_10)) = 0;
// Round 12 (Partial Round)
// ARK (Add Round Constant)
pol ARK_11_0 = B_10_0 + poseidon2_params.C_11_0;
pol ARK_11_1 = B_10_1 + poseidon2_params.C_11_1;
pol ARK_11_2 = B_10_2 + poseidon2_params.C_11_2;
pol ARK_11_3 = B_10_3 + poseidon2_params.C_11_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_11_0 = ARK_11_0 * ARK_11_0 * ARK_11_0 * ARK_11_0 * ARK_11_0;
pol A_11_1 = ARK_11_1;
pol A_11_2 = ARK_11_2;
pol A_11_3 = ARK_11_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_11_0;
pol commit B_11_1;
pol commit B_11_2;
pol commit B_11_3;
pol SUM_11 = A_11_0 + A_11_1 + A_11_2 + A_11_3;
sel_poseidon_perm * (B_11_0 - (poseidon2_params.MU_0 * A_11_0 + SUM_11)) = 0;
sel_poseidon_perm * (B_11_1 - (poseidon2_params.MU_1 * A_11_1 + SUM_11)) = 0;
sel_poseidon_perm * (B_11_2 - (poseidon2_params.MU_2 * A_11_2 + SUM_11)) = 0;
sel_poseidon_perm * (B_11_3 - (poseidon2_params.MU_3 * A_11_3 + SUM_11)) = 0;
// Round 13 (Partial Round)
// ARK (Add Round Constant)
pol ARK_12_0 = B_11_0 + poseidon2_params.C_12_0;
pol ARK_12_1 = B_11_1 + poseidon2_params.C_12_1;
pol ARK_12_2 = B_11_2 + poseidon2_params.C_12_2;
pol ARK_12_3 = B_11_3 + poseidon2_params.C_12_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_12_0 = ARK_12_0 * ARK_12_0 * ARK_12_0 * ARK_12_0 * ARK_12_0;
pol A_12_1 = ARK_12_1;
pol A_12_2 = ARK_12_2;
pol A_12_3 = ARK_12_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_12_0;
pol commit B_12_1;
pol commit B_12_2;
pol commit B_12_3;
pol SUM_12 = A_12_0 + A_12_1 + A_12_2 + A_12_3;
sel_poseidon_perm * (B_12_0 - (poseidon2_params.MU_0 * A_12_0 + SUM_12)) = 0;
sel_poseidon_perm * (B_12_1 - (poseidon2_params.MU_1 * A_12_1 + SUM_12)) = 0;
sel_poseidon_perm * (B_12_2 - (poseidon2_params.MU_2 * A_12_2 + SUM_12)) = 0;
sel_poseidon_perm * (B_12_3 - (poseidon2_params.MU_3 * A_12_3 + SUM_12)) = 0;
// Round 14 (Partial Round)
// ARK (Add Round Constant)
pol ARK_13_0 = B_12_0 + poseidon2_params.C_13_0;
pol ARK_13_1 = B_12_1 + poseidon2_params.C_13_1;
pol ARK_13_2 = B_12_2 + poseidon2_params.C_13_2;
pol ARK_13_3 = B_12_3 + poseidon2_params.C_13_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_13_0 = ARK_13_0 * ARK_13_0 * ARK_13_0 * ARK_13_0 * ARK_13_0;
pol A_13_1 = ARK_13_1;
pol A_13_2 = ARK_13_2;
pol A_13_3 = ARK_13_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_13_0;
pol commit B_13_1;
pol commit B_13_2;
pol commit B_13_3;
pol SUM_13 = A_13_0 + A_13_1 + A_13_2 + A_13_3;
sel_poseidon_perm * (B_13_0 - (poseidon2_params.MU_0 * A_13_0 + SUM_13)) = 0;
sel_poseidon_perm * (B_13_1 - (poseidon2_params.MU_1 * A_13_1 + SUM_13)) = 0;
sel_poseidon_perm * (B_13_2 - (poseidon2_params.MU_2 * A_13_2 + SUM_13)) = 0;
sel_poseidon_perm * (B_13_3 - (poseidon2_params.MU_3 * A_13_3 + SUM_13)) = 0;
// Round 15 (Partial Round)
// ARK (Add Round Constant)
pol ARK_14_0 = B_13_0 + poseidon2_params.C_14_0;
pol ARK_14_1 = B_13_1 + poseidon2_params.C_14_1;
pol ARK_14_2 = B_13_2 + poseidon2_params.C_14_2;
pol ARK_14_3 = B_13_3 + poseidon2_params.C_14_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_14_0 = ARK_14_0 * ARK_14_0 * ARK_14_0 * ARK_14_0 * ARK_14_0;
pol A_14_1 = ARK_14_1;
pol A_14_2 = ARK_14_2;
pol A_14_3 = ARK_14_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_14_0;
pol commit B_14_1;
pol commit B_14_2;
pol commit B_14_3;
pol SUM_14 = A_14_0 + A_14_1 + A_14_2 + A_14_3;
sel_poseidon_perm * (B_14_0 - (poseidon2_params.MU_0 * A_14_0 + SUM_14)) = 0;
sel_poseidon_perm * (B_14_1 - (poseidon2_params.MU_1 * A_14_1 + SUM_14)) = 0;
sel_poseidon_perm * (B_14_2 - (poseidon2_params.MU_2 * A_14_2 + SUM_14)) = 0;
sel_poseidon_perm * (B_14_3 - (poseidon2_params.MU_3 * A_14_3 + SUM_14)) = 0;
// Round 16 (Partial Round)
// ARK (Add Round Constant)
pol ARK_15_0 = B_14_0 + poseidon2_params.C_15_0;
pol ARK_15_1 = B_14_1 + poseidon2_params.C_15_1;
pol ARK_15_2 = B_14_2 + poseidon2_params.C_15_2;
pol ARK_15_3 = B_14_3 + poseidon2_params.C_15_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_15_0 = ARK_15_0 * ARK_15_0 * ARK_15_0 * ARK_15_0 * ARK_15_0;
pol A_15_1 = ARK_15_1;
pol A_15_2 = ARK_15_2;
pol A_15_3 = ARK_15_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_15_0;
pol commit B_15_1;
pol commit B_15_2;
pol commit B_15_3;
pol SUM_15 = A_15_0 + A_15_1 + A_15_2 + A_15_3;
sel_poseidon_perm * (B_15_0 - (poseidon2_params.MU_0 * A_15_0 + SUM_15)) = 0;
sel_poseidon_perm * (B_15_1 - (poseidon2_params.MU_1 * A_15_1 + SUM_15)) = 0;
sel_poseidon_perm * (B_15_2 - (poseidon2_params.MU_2 * A_15_2 + SUM_15)) = 0;
sel_poseidon_perm * (B_15_3 - (poseidon2_params.MU_3 * A_15_3 + SUM_15)) = 0;
// Round 17 (Partial Round)
// ARK (Add Round Constant)
pol ARK_16_0 = B_15_0 + poseidon2_params.C_16_0;
pol ARK_16_1 = B_15_1 + poseidon2_params.C_16_1;
pol ARK_16_2 = B_15_2 + poseidon2_params.C_16_2;
pol ARK_16_3 = B_15_3 + poseidon2_params.C_16_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_16_0 = ARK_16_0 * ARK_16_0 * ARK_16_0 * ARK_16_0 * ARK_16_0;
pol A_16_1 = ARK_16_1;
pol A_16_2 = ARK_16_2;
pol A_16_3 = ARK_16_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_16_0;
pol commit B_16_1;
pol commit B_16_2;
pol commit B_16_3;
pol SUM_16 = A_16_0 + A_16_1 + A_16_2 + A_16_3;
sel_poseidon_perm * (B_16_0 - (poseidon2_params.MU_0 * A_16_0 + SUM_16)) = 0;
sel_poseidon_perm * (B_16_1 - (poseidon2_params.MU_1 * A_16_1 + SUM_16)) = 0;
sel_poseidon_perm * (B_16_2 - (poseidon2_params.MU_2 * A_16_2 + SUM_16)) = 0;
sel_poseidon_perm * (B_16_3 - (poseidon2_params.MU_3 * A_16_3 + SUM_16)) = 0;
// Round 18 (Partial Round)
// ARK (Add Round Constant)
pol ARK_17_0 = B_16_0 + poseidon2_params.C_17_0;
pol ARK_17_1 = B_16_1 + poseidon2_params.C_17_1;
pol ARK_17_2 = B_16_2 + poseidon2_params.C_17_2;
pol ARK_17_3 = B_16_3 + poseidon2_params.C_17_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_17_0 = ARK_17_0 * ARK_17_0 * ARK_17_0 * ARK_17_0 * ARK_17_0;
pol A_17_1 = ARK_17_1;
pol A_17_2 = ARK_17_2;
pol A_17_3 = ARK_17_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_17_0;
pol commit B_17_1;
pol commit B_17_2;
pol commit B_17_3;
pol SUM_17 = A_17_0 + A_17_1 + A_17_2 + A_17_3;
sel_poseidon_perm * (B_17_0 - (poseidon2_params.MU_0 * A_17_0 + SUM_17)) = 0;
sel_poseidon_perm * (B_17_1 - (poseidon2_params.MU_1 * A_17_1 + SUM_17)) = 0;
sel_poseidon_perm * (B_17_2 - (poseidon2_params.MU_2 * A_17_2 + SUM_17)) = 0;
sel_poseidon_perm * (B_17_3 - (poseidon2_params.MU_3 * A_17_3 + SUM_17)) = 0;
// Round 19 (Partial Round)
// ARK (Add Round Constant)
pol ARK_18_0 = B_17_0 + poseidon2_params.C_18_0;
pol ARK_18_1 = B_17_1 + poseidon2_params.C_18_1;
pol ARK_18_2 = B_17_2 + poseidon2_params.C_18_2;
pol ARK_18_3 = B_17_3 + poseidon2_params.C_18_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_18_0 = ARK_18_0 * ARK_18_0 * ARK_18_0 * ARK_18_0 * ARK_18_0;
pol A_18_1 = ARK_18_1;
pol A_18_2 = ARK_18_2;
pol A_18_3 = ARK_18_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_18_0;
pol commit B_18_1;
pol commit B_18_2;
pol commit B_18_3;
pol SUM_18 = A_18_0 + A_18_1 + A_18_2 + A_18_3;
sel_poseidon_perm * (B_18_0 - (poseidon2_params.MU_0 * A_18_0 + SUM_18)) = 0;
sel_poseidon_perm * (B_18_1 - (poseidon2_params.MU_1 * A_18_1 + SUM_18)) = 0;
sel_poseidon_perm * (B_18_2 - (poseidon2_params.MU_2 * A_18_2 + SUM_18)) = 0;
sel_poseidon_perm * (B_18_3 - (poseidon2_params.MU_3 * A_18_3 + SUM_18)) = 0;
// Round 20 (Partial Round)
// ARK (Add Round Constant)
pol ARK_19_0 = B_18_0 + poseidon2_params.C_19_0;
pol ARK_19_1 = B_18_1 + poseidon2_params.C_19_1;
pol ARK_19_2 = B_18_2 + poseidon2_params.C_19_2;
pol ARK_19_3 = B_18_3 + poseidon2_params.C_19_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_19_0 = ARK_19_0 * ARK_19_0 * ARK_19_0 * ARK_19_0 * ARK_19_0;
pol A_19_1 = ARK_19_1;
pol A_19_2 = ARK_19_2;
pol A_19_3 = ARK_19_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_19_0;
pol commit B_19_1;
pol commit B_19_2;
pol commit B_19_3;
pol SUM_19 = A_19_0 + A_19_1 + A_19_2 + A_19_3;
sel_poseidon_perm * (B_19_0 - (poseidon2_params.MU_0 * A_19_0 + SUM_19)) = 0;
sel_poseidon_perm * (B_19_1 - (poseidon2_params.MU_1 * A_19_1 + SUM_19)) = 0;
sel_poseidon_perm * (B_19_2 - (poseidon2_params.MU_2 * A_19_2 + SUM_19)) = 0;
sel_poseidon_perm * (B_19_3 - (poseidon2_params.MU_3 * A_19_3 + SUM_19)) = 0;
// Round 21 (Partial Round)
// ARK (Add Round Constant)
pol ARK_20_0 = B_19_0 + poseidon2_params.C_20_0;
pol ARK_20_1 = B_19_1 + poseidon2_params.C_20_1;
pol ARK_20_2 = B_19_2 + poseidon2_params.C_20_2;
pol ARK_20_3 = B_19_3 + poseidon2_params.C_20_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_20_0 = ARK_20_0 * ARK_20_0 * ARK_20_0 * ARK_20_0 * ARK_20_0;
pol A_20_1 = ARK_20_1;
pol A_20_2 = ARK_20_2;
pol A_20_3 = ARK_20_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_20_0;
pol commit B_20_1;
pol commit B_20_2;
pol commit B_20_3;
pol SUM_20 = A_20_0 + A_20_1 + A_20_2 + A_20_3;
sel_poseidon_perm * (B_20_0 - (poseidon2_params.MU_0 * A_20_0 + SUM_20)) = 0;
sel_poseidon_perm * (B_20_1 - (poseidon2_params.MU_1 * A_20_1 + SUM_20)) = 0;
sel_poseidon_perm * (B_20_2 - (poseidon2_params.MU_2 * A_20_2 + SUM_20)) = 0;
sel_poseidon_perm * (B_20_3 - (poseidon2_params.MU_3 * A_20_3 + SUM_20)) = 0;
// Round 22 (Partial Round)
// ARK (Add Round Constant)
pol ARK_21_0 = B_20_0 + poseidon2_params.C_21_0;
pol ARK_21_1 = B_20_1 + poseidon2_params.C_21_1;
pol ARK_21_2 = B_20_2 + poseidon2_params.C_21_2;
pol ARK_21_3 = B_20_3 + poseidon2_params.C_21_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_21_0 = ARK_21_0 * ARK_21_0 * ARK_21_0 * ARK_21_0 * ARK_21_0;
pol A_21_1 = ARK_21_1;
pol A_21_2 = ARK_21_2;
pol A_21_3 = ARK_21_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_21_0;
pol commit B_21_1;
pol commit B_21_2;
pol commit B_21_3;
pol SUM_21 = A_21_0 + A_21_1 + A_21_2 + A_21_3;
sel_poseidon_perm * (B_21_0 - (poseidon2_params.MU_0 * A_21_0 + SUM_21)) = 0;
sel_poseidon_perm * (B_21_1 - (poseidon2_params.MU_1 * A_21_1 + SUM_21)) = 0;
sel_poseidon_perm * (B_21_2 - (poseidon2_params.MU_2 * A_21_2 + SUM_21)) = 0;
sel_poseidon_perm * (B_21_3 - (poseidon2_params.MU_3 * A_21_3 + SUM_21)) = 0;
// Round 23 (Partial Round)
// ARK (Add Round Constant)
pol ARK_22_0 = B_21_0 + poseidon2_params.C_22_0;
pol ARK_22_1 = B_21_1 + poseidon2_params.C_22_1;
pol ARK_22_2 = B_21_2 + poseidon2_params.C_22_2;
pol ARK_22_3 = B_21_3 + poseidon2_params.C_22_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_22_0 = ARK_22_0 * ARK_22_0 * ARK_22_0 * ARK_22_0 * ARK_22_0;
pol A_22_1 = ARK_22_1;
pol A_22_2 = ARK_22_2;
pol A_22_3 = ARK_22_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_22_0;
pol commit B_22_1;
pol commit B_22_2;
pol commit B_22_3;
pol SUM_22 = A_22_0 + A_22_1 + A_22_2 + A_22_3;
sel_poseidon_perm * (B_22_0 - (poseidon2_params.MU_0 * A_22_0 + SUM_22)) = 0;
sel_poseidon_perm * (B_22_1 - (poseidon2_params.MU_1 * A_22_1 + SUM_22)) = 0;
sel_poseidon_perm * (B_22_2 - (poseidon2_params.MU_2 * A_22_2 + SUM_22)) = 0;
sel_poseidon_perm * (B_22_3 - (poseidon2_params.MU_3 * A_22_3 + SUM_22)) = 0;
// Round 24 (Partial Round)
// ARK (Add Round Constant)
pol ARK_23_0 = B_22_0 + poseidon2_params.C_23_0;
pol ARK_23_1 = B_22_1 + poseidon2_params.C_23_1;
pol ARK_23_2 = B_22_2 + poseidon2_params.C_23_2;
pol ARK_23_3 = B_22_3 + poseidon2_params.C_23_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_23_0 = ARK_23_0 * ARK_23_0 * ARK_23_0 * ARK_23_0 * ARK_23_0;
pol A_23_1 = ARK_23_1;
pol A_23_2 = ARK_23_2;
pol A_23_3 = ARK_23_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_23_0;
pol commit B_23_1;
pol commit B_23_2;
pol commit B_23_3;
pol SUM_23 = A_23_0 + A_23_1 + A_23_2 + A_23_3;
sel_poseidon_perm * (B_23_0 - (poseidon2_params.MU_0 * A_23_0 + SUM_23)) = 0;
sel_poseidon_perm * (B_23_1 - (poseidon2_params.MU_1 * A_23_1 + SUM_23)) = 0;
sel_poseidon_perm * (B_23_2 - (poseidon2_params.MU_2 * A_23_2 + SUM_23)) = 0;
sel_poseidon_perm * (B_23_3 - (poseidon2_params.MU_3 * A_23_3 + SUM_23)) = 0;
// Round 25 (Partial Round)
// ARK (Add Round Constant)
pol ARK_24_0 = B_23_0 + poseidon2_params.C_24_0;
pol ARK_24_1 = B_23_1 + poseidon2_params.C_24_1;
pol ARK_24_2 = B_23_2 + poseidon2_params.C_24_2;
pol ARK_24_3 = B_23_3 + poseidon2_params.C_24_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_24_0 = ARK_24_0 * ARK_24_0 * ARK_24_0 * ARK_24_0 * ARK_24_0;
pol A_24_1 = ARK_24_1;
pol A_24_2 = ARK_24_2;
pol A_24_3 = ARK_24_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_24_0;
pol commit B_24_1;
pol commit B_24_2;
pol commit B_24_3;
pol SUM_24 = A_24_0 + A_24_1 + A_24_2 + A_24_3;
sel_poseidon_perm * (B_24_0 - (poseidon2_params.MU_0 * A_24_0 + SUM_24)) = 0;
sel_poseidon_perm * (B_24_1 - (poseidon2_params.MU_1 * A_24_1 + SUM_24)) = 0;
sel_poseidon_perm * (B_24_2 - (poseidon2_params.MU_2 * A_24_2 + SUM_24)) = 0;
sel_poseidon_perm * (B_24_3 - (poseidon2_params.MU_3 * A_24_3 + SUM_24)) = 0;
// Round 26 (Partial Round)
// ARK (Add Round Constant)
pol ARK_25_0 = B_24_0 + poseidon2_params.C_25_0;
pol ARK_25_1 = B_24_1 + poseidon2_params.C_25_1;
pol ARK_25_2 = B_24_2 + poseidon2_params.C_25_2;
pol ARK_25_3 = B_24_3 + poseidon2_params.C_25_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_25_0 = ARK_25_0 * ARK_25_0 * ARK_25_0 * ARK_25_0 * ARK_25_0;
pol A_25_1 = ARK_25_1;
pol A_25_2 = ARK_25_2;
pol A_25_3 = ARK_25_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_25_0;
pol commit B_25_1;
pol commit B_25_2;
pol commit B_25_3;
pol SUM_25 = A_25_0 + A_25_1 + A_25_2 + A_25_3;
sel_poseidon_perm * (B_25_0 - (poseidon2_params.MU_0 * A_25_0 + SUM_25)) = 0;
sel_poseidon_perm * (B_25_1 - (poseidon2_params.MU_1 * A_25_1 + SUM_25)) = 0;
sel_poseidon_perm * (B_25_2 - (poseidon2_params.MU_2 * A_25_2 + SUM_25)) = 0;
sel_poseidon_perm * (B_25_3 - (poseidon2_params.MU_3 * A_25_3 + SUM_25)) = 0;
// Round 27 (Partial Round)
// ARK (Add Round Constant)
pol ARK_26_0 = B_25_0 + poseidon2_params.C_26_0;
pol ARK_26_1 = B_25_1 + poseidon2_params.C_26_1;
pol ARK_26_2 = B_25_2 + poseidon2_params.C_26_2;
pol ARK_26_3 = B_25_3 + poseidon2_params.C_26_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_26_0 = ARK_26_0 * ARK_26_0 * ARK_26_0 * ARK_26_0 * ARK_26_0;
pol A_26_1 = ARK_26_1;
pol A_26_2 = ARK_26_2;
pol A_26_3 = ARK_26_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_26_0;
pol commit B_26_1;
pol commit B_26_2;
pol commit B_26_3;
pol SUM_26 = A_26_0 + A_26_1 + A_26_2 + A_26_3;
sel_poseidon_perm * (B_26_0 - (poseidon2_params.MU_0 * A_26_0 + SUM_26)) = 0;
sel_poseidon_perm * (B_26_1 - (poseidon2_params.MU_1 * A_26_1 + SUM_26)) = 0;
sel_poseidon_perm * (B_26_2 - (poseidon2_params.MU_2 * A_26_2 + SUM_26)) = 0;
sel_poseidon_perm * (B_26_3 - (poseidon2_params.MU_3 * A_26_3 + SUM_26)) = 0;
// Round 28 (Partial Round)
// ARK (Add Round Constant)
pol ARK_27_0 = B_26_0 + poseidon2_params.C_27_0;
pol ARK_27_1 = B_26_1 + poseidon2_params.C_27_1;
pol ARK_27_2 = B_26_2 + poseidon2_params.C_27_2;
pol ARK_27_3 = B_26_3 + poseidon2_params.C_27_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_27_0 = ARK_27_0 * ARK_27_0 * ARK_27_0 * ARK_27_0 * ARK_27_0;
pol A_27_1 = ARK_27_1;
pol A_27_2 = ARK_27_2;
pol A_27_3 = ARK_27_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_27_0;
pol commit B_27_1;
pol commit B_27_2;
pol commit B_27_3;
pol SUM_27 = A_27_0 + A_27_1 + A_27_2 + A_27_3;
sel_poseidon_perm * (B_27_0 - (poseidon2_params.MU_0 * A_27_0 + SUM_27)) = 0;
sel_poseidon_perm * (B_27_1 - (poseidon2_params.MU_1 * A_27_1 + SUM_27)) = 0;
sel_poseidon_perm * (B_27_2 - (poseidon2_params.MU_2 * A_27_2 + SUM_27)) = 0;
sel_poseidon_perm * (B_27_3 - (poseidon2_params.MU_3 * A_27_3 + SUM_27)) = 0;
// Round 29 (Partial Round)
// ARK (Add Round Constant)
pol ARK_28_0 = B_27_0 + poseidon2_params.C_28_0;
pol ARK_28_1 = B_27_1 + poseidon2_params.C_28_1;
pol ARK_28_2 = B_27_2 + poseidon2_params.C_28_2;
pol ARK_28_3 = B_27_3 + poseidon2_params.C_28_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_28_0 = ARK_28_0 * ARK_28_0 * ARK_28_0 * ARK_28_0 * ARK_28_0;
pol A_28_1 = ARK_28_1;
pol A_28_2 = ARK_28_2;
pol A_28_3 = ARK_28_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_28_0;
pol commit B_28_1;
pol commit B_28_2;
pol commit B_28_3;
pol SUM_28 = A_28_0 + A_28_1 + A_28_2 + A_28_3;
sel_poseidon_perm * (B_28_0 - (poseidon2_params.MU_0 * A_28_0 + SUM_28)) = 0;
sel_poseidon_perm * (B_28_1 - (poseidon2_params.MU_1 * A_28_1 + SUM_28)) = 0;
sel_poseidon_perm * (B_28_2 - (poseidon2_params.MU_2 * A_28_2 + SUM_28)) = 0;
sel_poseidon_perm * (B_28_3 - (poseidon2_params.MU_3 * A_28_3 + SUM_28)) = 0;
// Round 30 (Partial Round)
// ARK (Add Round Constant)
pol ARK_29_0 = B_28_0 + poseidon2_params.C_29_0;
pol ARK_29_1 = B_28_1 + poseidon2_params.C_29_1;
pol ARK_29_2 = B_28_2 + poseidon2_params.C_29_2;
pol ARK_29_3 = B_28_3 + poseidon2_params.C_29_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_29_0 = ARK_29_0 * ARK_29_0 * ARK_29_0 * ARK_29_0 * ARK_29_0;
pol A_29_1 = ARK_29_1;
pol A_29_2 = ARK_29_2;
pol A_29_3 = ARK_29_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_29_0;
pol commit B_29_1;
pol commit B_29_2;
pol commit B_29_3;
pol SUM_29 = A_29_0 + A_29_1 + A_29_2 + A_29_3;
sel_poseidon_perm * (B_29_0 - (poseidon2_params.MU_0 * A_29_0 + SUM_29)) = 0;
sel_poseidon_perm * (B_29_1 - (poseidon2_params.MU_1 * A_29_1 + SUM_29)) = 0;
sel_poseidon_perm * (B_29_2 - (poseidon2_params.MU_2 * A_29_2 + SUM_29)) = 0;
sel_poseidon_perm * (B_29_3 - (poseidon2_params.MU_3 * A_29_3 + SUM_29)) = 0;
// Round 31 (Partial Round)
// ARK (Add Round Constant)
pol ARK_30_0 = B_29_0 + poseidon2_params.C_30_0;
pol ARK_30_1 = B_29_1 + poseidon2_params.C_30_1;
pol ARK_30_2 = B_29_2 + poseidon2_params.C_30_2;
pol ARK_30_3 = B_29_3 + poseidon2_params.C_30_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_30_0 = ARK_30_0 * ARK_30_0 * ARK_30_0 * ARK_30_0 * ARK_30_0;
pol A_30_1 = ARK_30_1;
pol A_30_2 = ARK_30_2;
pol A_30_3 = ARK_30_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_30_0;
pol commit B_30_1;
pol commit B_30_2;
pol commit B_30_3;
pol SUM_30 = A_30_0 + A_30_1 + A_30_2 + A_30_3;
sel_poseidon_perm * (B_30_0 - (poseidon2_params.MU_0 * A_30_0 + SUM_30)) = 0;
sel_poseidon_perm * (B_30_1 - (poseidon2_params.MU_1 * A_30_1 + SUM_30)) = 0;
sel_poseidon_perm * (B_30_2 - (poseidon2_params.MU_2 * A_30_2 + SUM_30)) = 0;
sel_poseidon_perm * (B_30_3 - (poseidon2_params.MU_3 * A_30_3 + SUM_30)) = 0;
// Round 32 (Partial Round)
// ARK (Add Round Constant)
pol ARK_31_0 = B_30_0 + poseidon2_params.C_31_0;
pol ARK_31_1 = B_30_1 + poseidon2_params.C_31_1;
pol ARK_31_2 = B_30_2 + poseidon2_params.C_31_2;
pol ARK_31_3 = B_30_3 + poseidon2_params.C_31_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_31_0 = ARK_31_0 * ARK_31_0 * ARK_31_0 * ARK_31_0 * ARK_31_0;
pol A_31_1 = ARK_31_1;
pol A_31_2 = ARK_31_2;
pol A_31_3 = ARK_31_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_31_0;
pol commit B_31_1;
pol commit B_31_2;
pol commit B_31_3;
pol SUM_31 = A_31_0 + A_31_1 + A_31_2 + A_31_3;
sel_poseidon_perm * (B_31_0 - (poseidon2_params.MU_0 * A_31_0 + SUM_31)) = 0;
sel_poseidon_perm * (B_31_1 - (poseidon2_params.MU_1 * A_31_1 + SUM_31)) = 0;
sel_poseidon_perm * (B_31_2 - (poseidon2_params.MU_2 * A_31_2 + SUM_31)) = 0;
sel_poseidon_perm * (B_31_3 - (poseidon2_params.MU_3 * A_31_3 + SUM_31)) = 0;
// Round 33 (Partial Round)
// ARK (Add Round Constant)
pol ARK_32_0 = B_31_0 + poseidon2_params.C_32_0;
pol ARK_32_1 = B_31_1 + poseidon2_params.C_32_1;
pol ARK_32_2 = B_31_2 + poseidon2_params.C_32_2;
pol ARK_32_3 = B_31_3 + poseidon2_params.C_32_3;
// S-BOX (In partial round only first input is exponentiated)
pol A_32_0 = ARK_32_0 * ARK_32_0 * ARK_32_0 * ARK_32_0 * ARK_32_0;
pol A_32_1 = ARK_32_1;
pol A_32_2 = ARK_32_2;
pol A_32_3 = ARK_32_3;
// MATRIX (Partial round uses the external matrix)
pol commit B_32_0;
pol commit B_32_1;
pol commit B_32_2;
pol commit B_32_3;
pol SUM_32 = A_32_0 + A_32_1 + A_32_2 + A_32_3;
sel_poseidon_perm * (B_32_0 - (poseidon2_params.MU_0 * A_32_0 + SUM_32)) = 0;
sel_poseidon_perm * (B_32_1 - (poseidon2_params.MU_1 * A_32_1 + SUM_32)) = 0;
sel_poseidon_perm * (B_32_2 - (poseidon2_params.MU_2 * A_32_2 + SUM_32)) = 0;
sel_poseidon_perm * (B_32_3 - (poseidon2_params.MU_3 * A_32_3 + SUM_32)) = 0;