feat(avm): poseidon2 in vm2

barretenberg/cpp/pil/vm2/execution.pil

@@ -9,6 +9,8 @@ include "bitwise.pil";
 include "precomputed.pil";
 include "sha256.pil";
 include "ecc.pil";
+include "poseidon2_hash.pil";
+include "poseidon2_perm.pil";
 
 namespace execution;
 

barretenberg/cpp/pil/vm2/poseidon2_hash.pil

@@ -0,0 +1,92 @@
+include "poseidon2_perm.pil";
+
+// Performs the poseidon2 full hash
+// It is **mostly** well-constrained
+namespace poseidon2_hash;
+
+    #[skippable_if]
+    sel = 0;
+
+    // These are the inputs to be hashed this round, we hash chunks of 3 field elements
+    pol commit input_0;
+    pol commit input_1;
+    pol commit input_2;
+
+    // Output of the hash it is matched with the result of the last permutation round
+    pol commit output;
+
+    pol commit sel;
+    sel * (1 - sel) = 0;
+    sel = execute_perm + end;
+    pol TWOPOW64 = 18446744073709551616;
+
+    pol commit input_len;
+    // Only used at the start of a new poseidon2 hash
+    pol IV = TWOPOW64 * input_len;
+
+
+    // Start of a poseidon2 computation
+    pol commit start;
+    start * (1 - start) = 0;
+    // When we end a poseidon, the next row must naturally have a start
+    sel' * (1 - precomputed.first_row) * (start' - end) = 0;
+
+    // We track the num of rounds remaining, excluding the first round that has to be performed by the start selector.
+    // We use the padded length to calculate the num of rounds to perform and the unpadded length is used in the IV.
+    pol commit num_perm_rounds_rem;
+    pol commit padding;
+    // Padding can either be 0, 1 or 2
+    padding * (padding - 1) * (padding - 2) = 0;
+    pol PADDED_LEN = input_len + padding;
+    start * ((num_perm_rounds_rem + 1) * 3 - PADDED_LEN) = 0;
+
+
+    // The row with the final result of the poseidon computation
+    pol commit end;
+    end * (1 - end) = 0;
+    // The final result of the output of the hash should match the output from the last permutation (b_0)
+    end * (output - b_0) = 0;
+    pol commit num_perm_rounds_rem_inv;
+    // end == 1 when the num_perm_rounds_rem == 0
+    sel * (num_perm_rounds_rem * (end * (1 - num_perm_rounds_rem_inv) + num_perm_rounds_rem_inv) - 1 + end) = 0;
+
+    // We perform the "squeeze" / perm operation until end
+    pol commit execute_perm;
+    execute_perm * (1 - execute_perm) = 0;
+    // The squeeze and end selector must be mutually exclusive
+    sel * (1 - end - execute_perm) = 0;
+    // Need an additional helper that holds the inverse of the num_perm_rounds_rem;
+    // If we still have rounds to perform, the num_perm_rounds_rem is decremented
+    execute_perm * (num_perm_rounds_rem' - num_perm_rounds_rem + 1) = 0;
+
+
+    // The input values are represented by a_0, a_1, a_2, a_3
+    // This most definitely could be simplified to a lower degree check
+    // the next perm input is constrained to be the previous perm output + the new values to be hashed.
+    // This occurs when we execute_perm = 1 and we are not the start or the end of the poseidon perm
+    pol NEXT_INPUT_IS_PREV_OUTPUT_SEL = execute_perm' * (1 - start) * execute_perm;
+    pol commit a_0;
+    start * (a_0 - input_0) = 0;
+    sel * NEXT_INPUT_IS_PREV_OUTPUT_SEL * (a_0' - b_0 - input_0') = 0;
+    pol commit a_1;
+    start * (a_1 - input_1) = 0;
+    sel * NEXT_INPUT_IS_PREV_OUTPUT_SEL * (a_1' - b_1 - input_1') = 0;
+    pol commit a_2;
+    start * (a_2 - input_2) = 0;
+    sel * NEXT_INPUT_IS_PREV_OUTPUT_SEL * (a_2' - b_2 - input_2') = 0;
+    pol commit a_3;
+    start * (a_3 - IV) = 0; // IV is placed in the last slot if this is the start
+    sel * NEXT_INPUT_IS_PREV_OUTPUT_SEL * (a_3' - b_3) = 0;
+
+    // Output value represented by b_0
+    pol commit b_0;
+    pol commit b_1;
+    pol commit b_2;
+    pol commit b_3;
+
+    #[LOOKUP_POS2_PERM]
+    sel { a_0, a_1, a_2, a_3, b_0, b_1, b_2, b_3}
+    in
+    poseidon2_perm.sel 
+        { poseidon2_perm.a_0, poseidon2_perm.a_1, poseidon2_perm.a_2, poseidon2_perm.a_3, 
+          poseidon2_perm.b_0, poseidon2_perm.b_1, poseidon2_perm.b_2, poseidon2_perm.b_3 };