Constants for Goldilocks & binary to generate them (#247)

* Constants for Goldilocks etc

* Fix typo

src/bin/generate_constants.rs

@@ -0,0 +1,38 @@
+//! Generates random constants using ChaCha20, seeded with zero.
+
+use plonky2::field::crandall_field::CrandallField;
+use plonky2::field::field_types::{Field, PrimeField};
+use plonky2::field::goldilocks_field::GoldilocksField;
+use rand::SeedableRng;
+use rand_chacha::ChaCha8Rng;
+
+// We will sample from CrandallField, which is slightly larger than GoldilocksField, then verify
+// that each constant also fits in GoldilocksField.
+type F = CrandallField;
+
+// const N: usize = 101; // For GMiMC
+// const N: usize = 8 * 30; // For Posiedon-8
+const N: usize = 12 * 30; // For Posiedon-12
+
+pub(crate) fn main() {
+    let mut rng = ChaCha8Rng::seed_from_u64(0);
+    let mut constants = [F::ZERO; N];
+    for i in 0..N {
+        constants[i] = F::rand_from_rng(&mut rng);
+        // Make sure the constant fits in the smaller field (Goldilocks) as well. If so, we also
+        // have random numbers in the smaller field. This may be viewed as rejection sampling,
+        // except that we never encounter a rejection in practice, so we don't bother handling it.
+        assert!(constants[i].to_canonical_u64() < GoldilocksField::ORDER);
+    }
+
+    // Print the constants in the format we prefer in our code.
+    for chunk in constants.chunks(4) {
+        for (i, c) in chunk.iter().enumerate() {
+            print!("{:#018x},", c.to_canonical_u64());
+            if i != chunk.len() - 1 {
+                print!(" ");
+            }
+        }
+        println!();
+    }
+}

src/hash/gmimc.rs

@@ -2,6 +2,7 @@ use unroll::unroll_for_loops;
 
 use crate::field::crandall_field::CrandallField;
 use crate::field::field_types::Field;
+use crate::field::goldilocks_field::GoldilocksField;
 
 pub(crate) const NUM_ROUNDS: usize = 101;
 
@@ -47,37 +48,43 @@ where
     }
 }
 
+/// See `generate_constants` about how these were generated.
+#[rustfmt::skip]
+const CRANDALL_AND_GOLDILOCKS_ROUND_CONSTANTS: [u64; NUM_ROUNDS] = [
+    0xb585f767417ee042, 0x7746a55f77c10331, 0xb2fb0d321d356f7a, 0x0f6760a486f1621f,
+    0xe10d6666b36abcdf, 0x8cae14cb455cc50b, 0xd438539cf2cee334, 0xef781c7d4c1fd8b4,
+    0xcdc4a23a0aca4b1f, 0x277fa208d07b52e3, 0xe17653a300493d38, 0xc54302f27c287dc1,
+    0x8628782231d47d10, 0x59cd1a8a690b49f2, 0xc3b919ad9efec0b0, 0xa484c4c637641d97,
+    0x308bbd23f191398b, 0x6e4a40c1bf713cf1, 0x9a2eedb7510414fb, 0xe360c6e111c2c63b,
+    0xd5c771901d4d89aa, 0xc35eae076e7d6b2f, 0x849c2656d0a09cad, 0xc0572c8c5cf1df2b,
+    0xe9fa634a883b8bf3, 0xf56f6d4900fb1fdd, 0xf7d713e872a72a1b, 0x8297132b6ba47612,
+    0xad6805e12ee8af1c, 0xac51d9f6485c22b9, 0x502ad7dc3bd56bf8, 0x57a1550c3761c577,
+    0x66bbd30e99d311da, 0x0da2abef5e948f87, 0xf0612750443f8e94, 0x28b8ec3afb937d8c,
+    0x92a756e6be54ca18, 0x70e741ec304e925d, 0x019d5ee2b037c59f, 0x6f6f2ed7a30707d1,
+    0x7cf416d01e8c169c, 0x61df517bb17617df, 0x85dc499b4c67dbaa, 0x4b959b48dad27b23,
+    0xe8be3e5e0dd779a0, 0xf5c0bc1e525ed8e6, 0x40b12cbf263cf853, 0xa637093f13e2ea3c,
+    0x3cc3f89232e3b0c8, 0x2e479dc16bfe86c0, 0x6f49de07d6d39469, 0x213ce7beecc232de,
+    0x5b043134851fc00a, 0xa2de45784a861506, 0x7103aaf97bed8dd5, 0x5326fc0dbb88a147,
+    0xa9ceb750364cb77a, 0x27f8ec88cc9e991f, 0xfceb4fda8c93fb83, 0xfac6ff13b45b260e,
+    0x7131aa455813380b, 0x93510360d5d68119, 0xad535b24fb96e3db, 0x4627f5c6b7efc045,
+    0x645cf794e4da78a9, 0x241c70ed1ac2877f, 0xacb8e076b009e825, 0x3737e9db6477bd9d,
+    0xe7ea5e344cd688ed, 0x90dee4a009214640, 0xd1b1edf7c77e74af, 0x0b65481bab42158e,
+    0x99ad1aab4b4fe3e7, 0x438a7c91f1a360cd, 0xb60de3bd159088bf, 0xc99cab6b47a3e3bb,
+    0x69a5ed92d5677cef, 0x5e7b329c482a9396, 0x5fc0ac0829f893c9, 0x32db82924fb757ea,
+    0x0ade699c5cf24145, 0x7cc5583b46d7b5bb, 0x85df9ed31bf8abcb, 0x6604df501ad4de64,
+    0xeb84f60941611aec, 0xda60883523989bd4, 0x8f97fe40bf3470bf, 0xa93f485ce0ff2b32,
+    0x6704e8eebc2afb4b, 0xcee3e9ac788ad755, 0x510d0e66062a270d, 0xf6323f48d74634a0,
+    0x0b508cdf04990c90, 0xf241708a4ef7ddf9, 0x60e75c28bb368f82, 0xa6217d8c3f0f9989,
+    0x7159cd30f5435b53, 0x839b4e8fe97ec79f, 0x0d3f3e5e885db625, 0x8f7d83be1daea54b,
+    0x780f22441e8dbc04,
+];
+
 impl GMiMC<12> for CrandallField {
-    /// This is the result of `gmimc_automatic_constants`; i.e. it's from ChaCha20 seeded with 0.
-    #[rustfmt::skip]
-    const ROUND_CONSTANTS: [u64; NUM_ROUNDS] = [
-        0xb585f767417ee042, 0x7746a55f77c10331, 0xb2fb0d321d356f7a, 0x0f6760a486f1621f,
-        0xe10d6666b36abcdf, 0x8cae14cb455cc50b, 0xd438539cf2cee334, 0xef781c7d4c1fd8b4,
-        0xcdc4a23a0aca4b1f, 0x277fa208d07b52e3, 0xe17653a300493d38, 0xc54302f27c287dc1,
-        0x8628782231d47d10, 0x59cd1a8a690b49f2, 0xc3b919ad9efec0b0, 0xa484c4c637641d97,
-        0x308bbd23f191398b, 0x6e4a40c1bf713cf1, 0x9a2eedb7510414fb, 0xe360c6e111c2c63b,
-        0xd5c771901d4d89aa, 0xc35eae076e7d6b2f, 0x849c2656d0a09cad, 0xc0572c8c5cf1df2b,
-        0xe9fa634a883b8bf3, 0xf56f6d4900fb1fdd, 0xf7d713e872a72a1b, 0x8297132b6ba47612,
-        0xad6805e12ee8af1c, 0xac51d9f6485c22b9, 0x502ad7dc3bd56bf8, 0x57a1550c3761c577,
-        0x66bbd30e99d311da, 0x0da2abef5e948f87, 0xf0612750443f8e94, 0x28b8ec3afb937d8c,
-        0x92a756e6be54ca18, 0x70e741ec304e925d, 0x019d5ee2b037c59f, 0x6f6f2ed7a30707d1,
-        0x7cf416d01e8c169c, 0x61df517bb17617df, 0x85dc499b4c67dbaa, 0x4b959b48dad27b23,
-        0xe8be3e5e0dd779a0, 0xf5c0bc1e525ed8e6, 0x40b12cbf263cf853, 0xa637093f13e2ea3c,
-        0x3cc3f89232e3b0c8, 0x2e479dc16bfe86c0, 0x6f49de07d6d39469, 0x213ce7beecc232de,
-        0x5b043134851fc00a, 0xa2de45784a861506, 0x7103aaf97bed8dd5, 0x5326fc0dbb88a147,
-        0xa9ceb750364cb77a, 0x27f8ec88cc9e991f, 0xfceb4fda8c93fb83, 0xfac6ff13b45b260e,
-        0x7131aa455813380b, 0x93510360d5d68119, 0xad535b24fb96e3db, 0x4627f5c6b7efc045,
-        0x645cf794e4da78a9, 0x241c70ed1ac2877f, 0xacb8e076b009e825, 0x3737e9db6477bd9d,
-        0xe7ea5e344cd688ed, 0x90dee4a009214640, 0xd1b1edf7c77e74af, 0x0b65481bab42158e,
-        0x99ad1aab4b4fe3e7, 0x438a7c91f1a360cd, 0xb60de3bd159088bf, 0xc99cab6b47a3e3bb,
-        0x69a5ed92d5677cef, 0x5e7b329c482a9396, 0x5fc0ac0829f893c9, 0x32db82924fb757ea,
-        0x0ade699c5cf24145, 0x7cc5583b46d7b5bb, 0x85df9ed31bf8abcb, 0x6604df501ad4de64,
-        0xeb84f60941611aec, 0xda60883523989bd4, 0x8f97fe40bf3470bf, 0xa93f485ce0ff2b32,
-        0x6704e8eebc2afb4b, 0xcee3e9ac788ad755, 0x510d0e66062a270d, 0xf6323f48d74634a0,
-        0x0b508cdf04990c90, 0xf241708a4ef7ddf9, 0x60e75c28bb368f82, 0xa6217d8c3f0f9989,
-        0x7159cd30f5435b53, 0x839b4e8fe97ec79f, 0x0d3f3e5e885db625, 0x8f7d83be1daea54b,
-        0x780f22441e8dbc04,
-    ];
+    const ROUND_CONSTANTS: [u64; NUM_ROUNDS] = CRANDALL_AND_GOLDILOCKS_ROUND_CONSTANTS;
+}
+
+impl GMiMC<12> for GoldilocksField {
+    const ROUND_CONSTANTS: [u64; NUM_ROUNDS] = CRANDALL_AND_GOLDILOCKS_ROUND_CONSTANTS;
 }
 
 #[cfg(test)]

src/hash/poseidon.rs

@@ -21,12 +21,9 @@ const N_PARTIAL_ROUNDS: usize = 22;
 const N_ROUNDS: usize = N_FULL_ROUNDS_TOTAL + N_PARTIAL_ROUNDS;
 const MAX_WIDTH: usize = 12; // we only have width 8 and 12, and 12 is bigger. :)
 
-// The round constants are the same as for GMiMC (hash.rs):
-// generated from ChaCha8 with a seed of 0. In this case we need
-// to generate more though. We include enough for a WIDTH of 12;
-// smaller widths just use a subset.
-// TODO: These are specific to CrandallField; for other fields they wouldn't represent uniformly
-// random numbers.
+/// Note that these work for the Crandall and Goldilocks fields, but not necessarily others. See
+/// `generate_constants` about how these were generated. We include enough for a WIDTH of 12;
+/// smaller widths just use a subset.
 #[rustfmt::skip]
 const ALL_ROUND_CONSTANTS: [u64; MAX_WIDTH * N_ROUNDS]  = [
     // WARNING: These must be in 0..CrandallField::ORDER (i.e. canonical form). If this condition is