plonky2/evm/src/cpu/kernel/tests/bn254_field.rs
2022-12-20 00:22:59 -08:00

749 lines
20 KiB
Rust

use std::str::FromStr;
use anyhow::Result;
use ethereum_types::U256;
use rand::{thread_rng, Rng};
use crate::cpu::kernel::aggregator::KERNEL;
use crate::cpu::kernel::interpreter::{run_interpreter, BN_BASE};
type Fp = U256;
type Fp2 = [U256; 2];
type Fp6 = [Fp2; 3];
type Fp12 = [Fp6; 2];
const ZERO: Fp = U256([0, 0, 0, 0]);
fn embed_fp2(x: Fp) -> Fp2 {
[x, ZERO]
}
fn embed_fp2_fp6(a: Fp2) -> Fp6 {
[a, embed_fp2(ZERO), embed_fp2(ZERO)]
}
fn embed_fp6(x: Fp) -> Fp6 {
embed_fp2_fp6(embed_fp2(x))
}
fn embed_fp12(x: Fp) -> Fp12 {
[embed_fp6(x), embed_fp6(ZERO)]
}
fn gen_fp() -> Fp {
let mut rng = thread_rng();
let x64 = rng.gen::<u64>();
U256([x64, x64, x64, x64]) % BN_BASE
}
fn gen_fp6() -> Fp6 {
[
[gen_fp(), gen_fp()],
[gen_fp(), gen_fp()],
[gen_fp(), gen_fp()],
]
}
fn gen_fp12() -> Fp12 {
[gen_fp6(), gen_fp6()]
}
fn gen_fp12_sparse() -> Fp12 {
sparse_embed([gen_fp(), gen_fp(), gen_fp(), gen_fp(), gen_fp()])
}
fn add_fp(x: Fp, y: Fp) -> Fp {
(x + y) % BN_BASE
}
fn add3_fp(x: Fp, y: Fp, z: Fp) -> Fp {
(x + y + z) % BN_BASE
}
fn mul_fp(x: Fp, y: Fp) -> Fp {
U256::try_from(x.full_mul(y) % BN_BASE).unwrap()
}
fn sub_fp(x: Fp, y: Fp) -> Fp {
(BN_BASE + x - y) % BN_BASE
}
fn neg_fp(x: Fp) -> Fp {
(BN_BASE - x) % BN_BASE
}
fn conj_fp2(a: Fp2) -> Fp2 {
let [a, a_] = a;
[a, neg_fp(a_)]
}
fn add_fp2(a: Fp2, b: Fp2) -> Fp2 {
let [a, a_] = a;
let [b, b_] = b;
[add_fp(a, b), add_fp(a_, b_)]
}
fn add3_fp2(a: Fp2, b: Fp2, c: Fp2) -> Fp2 {
let [a, a_] = a;
let [b, b_] = b;
let [c, c_] = c;
[add3_fp(a, b, c), add3_fp(a_, b_, c_)]
}
fn sub_fp2(a: Fp2, b: Fp2) -> Fp2 {
let [a, a_] = a;
let [b, b_] = b;
[sub_fp(a, b), sub_fp(a_, b_)]
}
fn neg_fp2(a: Fp2) -> Fp2 {
sub_fp2(embed_fp2(ZERO), a)
}
fn mul_fp2(a: Fp2, b: Fp2) -> Fp2 {
let [a, a_] = a;
let [b, b_] = b;
[
sub_fp(mul_fp(a, b), mul_fp(a_, b_)),
add_fp(mul_fp(a, b_), mul_fp(a_, b)),
]
}
fn i9(a: Fp2) -> Fp2 {
let [a, a_] = a;
let nine = U256::from(9);
[sub_fp(mul_fp(nine, a), a_), add_fp(a, mul_fp(nine, a_))]
}
fn add_fp6(c: Fp6, d: Fp6) -> Fp6 {
let [c0, c1, c2] = c;
let [d0, d1, d2] = d;
let e0 = add_fp2(c0, d0);
let e1 = add_fp2(c1, d1);
let e2 = add_fp2(c2, d2);
[e0, e1, e2]
}
fn sub_fp6(c: Fp6, d: Fp6) -> Fp6 {
let [c0, c1, c2] = c;
let [d0, d1, d2] = d;
let e0 = sub_fp2(c0, d0);
let e1 = sub_fp2(c1, d1);
let e2 = sub_fp2(c2, d2);
[e0, e1, e2]
}
fn neg_fp6(a: Fp6) -> Fp6 {
sub_fp6(embed_fp6(ZERO), a)
}
fn mul_fp6(c: Fp6, d: Fp6) -> Fp6 {
let [c0, c1, c2] = c;
let [d0, d1, d2] = d;
let c0d0 = mul_fp2(c0, d0);
let c0d1 = mul_fp2(c0, d1);
let c0d2 = mul_fp2(c0, d2);
let c1d0 = mul_fp2(c1, d0);
let c1d1 = mul_fp2(c1, d1);
let c1d2 = mul_fp2(c1, d2);
let c2d0 = mul_fp2(c2, d0);
let c2d1 = mul_fp2(c2, d1);
let c2d2 = mul_fp2(c2, d2);
let cd12 = add_fp2(c1d2, c2d1);
[
add_fp2(c0d0, i9(cd12)),
add3_fp2(c0d1, c1d0, i9(c2d2)),
add3_fp2(c0d2, c1d1, c2d0),
]
}
fn sh(c: Fp6) -> Fp6 {
let [c0, c1, c2] = c;
[i9(c2), c0, c1]
}
fn sparse_embed(x: [U256; 5]) -> Fp12 {
let [g0, g1, g1_, g2, g2_] = x;
[
[embed_fp2(g0), [g1, g1_], embed_fp2(ZERO)],
[embed_fp2(ZERO), [g2, g2_], embed_fp2(ZERO)],
]
}
fn mul_fp12(f: Fp12, g: Fp12) -> Fp12 {
let [f0, f1] = f;
let [g0, g1] = g;
let h0 = mul_fp6(f0, g0);
let h1 = mul_fp6(f1, g1);
let h01 = mul_fp6(add_fp6(f0, f1), add_fp6(g0, g1));
[add_fp6(h0, sh(h1)), sub_fp6(h01, add_fp6(h0, h1))]
}
fn frob_t1(n: usize) -> Fp2 {
match n {
0 => [
U256::from_str("0x1").unwrap(),
U256::from_str("0x0").unwrap(),
],
1 => [
U256::from_str("0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d")
.unwrap(),
U256::from_str("0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2")
.unwrap(),
],
2 => [
U256::from_str("0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48")
.unwrap(),
U256::from_str("0x0").unwrap(),
],
3 => [
U256::from_str("0x856e078b755ef0abaff1c77959f25ac805ffd3d5d6942d37b746ee87bdcfb6d")
.unwrap(),
U256::from_str("0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de")
.unwrap(),
],
4 => [
U256::from_str("0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe").unwrap(),
U256::from_str("0x0").unwrap(),
],
5 => [
U256::from_str("0x28be74d4bb943f51699582b87809d9caf71614d4b0b71f3a62e913ee1dada9e4")
.unwrap(),
U256::from_str("0x14a88ae0cb747b99c2b86abcbe01477a54f40eb4c3f6068dedae0bcec9c7aac7")
.unwrap(),
],
_ => panic!(),
}
}
fn frob_t2(n: usize) -> Fp2 {
match n {
0 => [
U256::from_str("0x1").unwrap(),
U256::from_str("0x0").unwrap(),
],
1 => [
U256::from_str("0x5b54f5e64eea80180f3c0b75a181e84d33365f7be94ec72848a1f55921ea762")
.unwrap(),
U256::from_str("0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126")
.unwrap(),
],
2 => [
U256::from_str("0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe").unwrap(),
U256::from_str("0x0").unwrap(),
],
3 => [
U256::from_str("0xbc58c6611c08dab19bee0f7b5b2444ee633094575b06bcb0e1a92bc3ccbf066")
.unwrap(),
U256::from_str("0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f")
.unwrap(),
],
4 => [
U256::from_str("0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48")
.unwrap(),
U256::from_str("0x0").unwrap(),
],
5 => [
U256::from_str("0x1ee972ae6a826a7d1d9da40771b6f589de1afb54342c724fa97bda050992657f")
.unwrap(),
U256::from_str("0x10de546ff8d4ab51d2b513cdbb25772454326430418536d15721e37e70c255c9")
.unwrap(),
],
_ => panic!(),
}
}
fn frob_z(n: usize) -> Fp2 {
match n {
0 => [
U256::from_str("0x1").unwrap(),
U256::from_str("0x0").unwrap(),
],
1 => [
U256::from_str("0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470")
.unwrap(),
U256::from_str("0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac")
.unwrap(),
],
2 => [
U256::from_str("0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49")
.unwrap(),
U256::from_str("0x0").unwrap(),
],
3 => [
U256::from_str("0x19dc81cfcc82e4bbefe9608cd0acaa90894cb38dbe55d24ae86f7d391ed4a67f")
.unwrap(),
U256::from_str("0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101")
.unwrap(),
],
4 => [
U256::from_str("0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48")
.unwrap(),
U256::from_str("0x0").unwrap(),
],
5 => [
U256::from_str("0x757cab3a41d3cdc072fc0af59c61f302cfa95859526b0d41264475e420ac20f")
.unwrap(),
U256::from_str("0xca6b035381e35b618e9b79ba4e2606ca20b7dfd71573c93e85845e34c4a5b9c")
.unwrap(),
],
6 => [
U256::from_str("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46")
.unwrap(),
U256::from_str("0x0").unwrap(),
],
7 => [
U256::from_str("0x1ddf9756b8cbf849cf96a5d90a9accfd3b2f4c893f42a9166615563bfbb318d7")
.unwrap(),
U256::from_str("0xbfab77f2c36b843121dc8b86f6c4ccf2307d819d98302a771c39bb757899a9b")
.unwrap(),
],
8 => [
U256::from_str("0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe").unwrap(),
U256::from_str("0x0").unwrap(),
],
9 => [
U256::from_str("0x1687cca314aebb6dc866e529b0d4adcd0e34b703aa1bf84253b10eddb9a856c8")
.unwrap(),
U256::from_str("0x2fb855bcd54a22b6b18456d34c0b44c0187dc4add09d90a0c58be1eae3bc3c46")
.unwrap(),
],
10 => [
U256::from_str("0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff").unwrap(),
U256::from_str("0x0").unwrap(),
],
11 => [
U256::from_str("0x290c83bf3d14634db120850727bb392d6a86d50bd34b19b929bc44b896723b38")
.unwrap(),
U256::from_str("0x23bd9e3da9136a739f668e1adc9ef7f0f575ec93f71a8df953c846338c32a1ab")
.unwrap(),
],
_ => panic!(),
}
}
fn frob_fp6(n: usize, c: Fp6) -> Fp6 {
let [c0, c1, c2] = c;
let _c0 = conj_fp2(c0);
let _c1 = conj_fp2(c1);
let _c2 = conj_fp2(c2);
let n = n % 6;
let frob_t1 = frob_t1(n);
let frob_t2 = frob_t2(n);
if n % 2 != 0 {
[_c0, mul_fp2(frob_t1, _c1), mul_fp2(frob_t2, _c2)]
} else {
[c0, mul_fp2(frob_t1, c1), mul_fp2(frob_t2, c2)]
}
}
fn frob_fp12(n: usize, f: Fp12) -> Fp12 {
let [f0, f1] = f;
let scale = embed_fp2_fp6(frob_z(n));
[frob_fp6(n, f0), mul_fp6(scale, frob_fp6(n, f1))]
}
fn exp_fp(x: Fp, e: U256) -> Fp {
let mut current = x;
let mut product = U256::one();
for j in 0..256 {
if e.bit(j) {
product = U256::try_from(product.full_mul(current) % BN_BASE).unwrap();
}
current = U256::try_from(current.full_mul(current) % BN_BASE).unwrap();
}
product
}
fn inv_fp(x: Fp) -> Fp {
exp_fp(x, BN_BASE - 2)
}
fn inv_fp2(a: Fp2) -> Fp2 {
let [a0, a1] = a;
let norm = inv_fp(mul_fp(a0, a0) + mul_fp(a1, a1));
[mul_fp(norm, a0), neg_fp(mul_fp(norm, a1))]
}
fn inv_fp6(c: Fp6) -> Fp6 {
let b = mul_fp6(frob_fp6(1, c), frob_fp6(3, c));
let e = mul_fp6(b, frob_fp6(5, c))[0];
let n = mul_fp2(e, conj_fp2(e))[0];
let i = inv_fp(n);
let d = mul_fp2(embed_fp2(i), e);
let [f0, f1, f2] = frob_fp6(1, b);
[mul_fp2(d, f0), mul_fp2(d, f1), mul_fp2(d, f2)]
}
fn inv_fp12(f: Fp12) -> Fp12 {
let a = mul_fp12(frob_fp12(1, f), frob_fp12(7, f))[0];
let b = mul_fp6(a, frob_fp6(2, a));
let c = mul_fp6(b, frob_fp6(4, a))[0];
let n = mul_fp2(c, conj_fp2(c))[0];
let i = inv_fp(n);
let d = mul_fp2(embed_fp2(i), c);
let [g0, g1, g2] = frob_fp6(1, b);
let e = [mul_fp2(d, g0), mul_fp2(d, g1), mul_fp2(d, g2)];
[mul_fp6(e, f[0]), neg_fp6(mul_fp6(e, f[1]))]
}
const EXPS4: [(bool, bool, bool); 65] = [
(true, true, true),
(true, true, false),
(true, true, true),
(true, true, true),
(false, false, false),
(false, false, true),
(true, false, true),
(false, true, false),
(true, false, true),
(true, true, false),
(true, false, true),
(false, true, false),
(true, true, false),
(true, true, false),
(true, true, false),
(false, true, false),
(false, true, false),
(false, false, true),
(true, false, true),
(true, true, false),
(false, true, false),
(true, true, false),
(true, true, false),
(true, true, false),
(false, false, true),
(false, false, true),
(true, false, true),
(true, false, true),
(true, true, false),
(true, false, false),
(true, true, false),
(false, true, false),
(true, true, false),
(true, false, false),
(false, true, false),
(false, false, false),
(true, false, false),
(true, false, false),
(true, false, true),
(false, false, true),
(false, true, true),
(false, false, true),
(false, true, true),
(false, true, true),
(false, false, false),
(true, true, true),
(true, false, true),
(true, false, true),
(false, true, true),
(true, false, true),
(false, true, true),
(false, true, true),
(true, true, false),
(true, true, false),
(true, true, false),
(true, false, false),
(false, false, true),
(true, false, false),
(false, false, true),
(true, false, true),
(true, true, false),
(true, true, true),
(false, true, true),
(false, true, false),
(true, true, true),
];
const EXPS2: [(bool, bool); 62] = [
(true, false),
(true, true),
(false, false),
(true, false),
(true, false),
(true, true),
(true, false),
(true, true),
(true, false),
(false, true),
(false, true),
(true, true),
(true, true),
(false, false),
(true, true),
(false, false),
(false, false),
(false, true),
(false, true),
(true, true),
(true, true),
(true, true),
(false, true),
(true, true),
(false, false),
(true, true),
(true, false),
(true, true),
(false, false),
(true, true),
(true, true),
(true, false),
(false, false),
(false, true),
(false, false),
(true, true),
(false, true),
(false, false),
(true, false),
(false, true),
(false, true),
(true, false),
(false, true),
(false, false),
(false, false),
(false, false),
(false, true),
(true, false),
(true, true),
(false, true),
(true, true),
(true, false),
(false, true),
(false, false),
(true, false),
(false, true),
(true, false),
(true, true),
(true, false),
(true, true),
(false, true),
(true, true),
];
const EXPS0: [bool; 65] = [
false, false, true, false, false, true, true, false, true, false, true, true, true, false,
true, false, false, false, true, false, false, true, false, true, false, true, true, false,
false, false, false, false, true, false, true, false, true, true, true, false, false, true,
true, true, true, false, true, false, true, true, false, false, true, false, false, false,
true, true, true, true, false, false, true, true, false,
];
fn fast_exp(f: Fp12) -> Fp12 {
let mut sq: Fp12 = f;
let mut y0: Fp12 = embed_fp12(U256::from(1));
let mut y2: Fp12 = embed_fp12(U256::from(1));
let mut y4: Fp12 = embed_fp12(U256::from(1));
for (a, b, c) in EXPS4 {
if a {
y4 = mul_fp12(y4, sq);
}
if b {
y2 = mul_fp12(y2, sq);
}
if c {
y0 = mul_fp12(y0, sq);
}
sq = mul_fp12(sq, sq);
}
y4 = mul_fp12(y4, y4);
for (a, b) in EXPS2 {
if a {
y2 = mul_fp12(y2, sq);
}
if b {
y0 = mul_fp12(y0, sq);
}
sq = mul_fp12(sq, sq);
}
y2 = mul_fp12(y2, y2);
for a in EXPS0 {
if a {
y0 = mul_fp12(y0, sq);
}
sq = mul_fp12(sq, sq);
}
y0 = mul_fp12(y0, y0);
// TODO: y0 = inv_fp12(y0);
y4 = mul_fp12(y4, y2);
y4 = mul_fp12(y4, y2);
y4 = mul_fp12(y4, y0);
y4 = frob_fp12(1, y4);
y2 = frob_fp12(2, y2);
mul_fp12(mul_fp12(y4, y2), y0)
}
fn make_mul_stack(
in0: usize,
in1: usize,
out: usize,
f: Fp12,
g: Fp12,
mul_label: &str,
) -> Vec<U256> {
// stack: in0, f, f', in1, g, g', mul_dest, in0, in1, out, ret_stack, out
let in0 = U256::from(in0);
let in1 = U256::from(in1);
let out = U256::from(out);
let f: Vec<U256> = f.into_iter().flatten().flatten().collect();
let g: Vec<U256> = g.into_iter().flatten().flatten().collect();
let ret_stack = U256::from(KERNEL.global_labels["ret_stack"]);
let mul_dest = U256::from(KERNEL.global_labels[mul_label]);
let mut input = vec![in0];
input.extend(f);
input.extend(vec![in1]);
input.extend(g);
input.extend(vec![mul_dest, in0, in1, out, ret_stack, out]);
input.reverse();
input
}
fn make_mul_expected(f: Fp12, g: Fp12) -> Vec<U256> {
mul_fp12(f, g)
.into_iter()
.flatten()
.flatten()
.rev()
.collect()
}
#[test]
fn test_mul_fp12() -> Result<()> {
let in0 = 64;
let in1 = 76;
let out = 88;
let f: Fp12 = gen_fp12();
let g: Fp12 = gen_fp12();
let h: Fp12 = gen_fp12_sparse();
let test_mul = KERNEL.global_labels["test_mul_fp12"];
let normal: Vec<U256> = make_mul_stack(in0, in1, out, f, g, "mul_fp12");
let sparse: Vec<U256> = make_mul_stack(in0, in1, out, f, h, "mul_fp12_sparse");
let square: Vec<U256> = make_mul_stack(in0, in1, out, f, f, "square_fp12_test");
let out_normal: Vec<U256> = run_interpreter(test_mul, normal)?.stack().to_vec();
let out_sparse: Vec<U256> = run_interpreter(test_mul, sparse)?.stack().to_vec();
let out_square: Vec<U256> = run_interpreter(test_mul, square)?.stack().to_vec();
let exp_normal: Vec<U256> = make_mul_expected(f, g);
let exp_sparse: Vec<U256> = make_mul_expected(f, h);
let exp_square: Vec<U256> = make_mul_expected(f, f);
assert_eq!(out_normal, exp_normal);
assert_eq!(out_sparse, exp_sparse);
assert_eq!(out_square, exp_square);
Ok(())
}
#[test]
fn test_inv_fp12() -> Result<()> {
let ptr = U256::from(100);
let inv = U256::from(200);
let f: Fp12 = gen_fp12();
let flat_f: Vec<U256> = f.into_iter().flatten().flatten().collect();
let mut stack: Vec<U256> = flat_f.clone();
stack.extend(vec![ptr, inv]);
stack.reverse();
let g = inv_fp12(f);
let one = mul_fp12(f, g);
println!("ONE? {:#?}", one);
let mut expected: Vec<U256> = g.into_iter().flatten().flatten().collect();
expected.extend(vec![inv]);
expected.extend(flat_f);
expected.extend(vec![ptr, inv]);
expected.reverse();
let initial_offset = KERNEL.global_labels["inverse_fp12"];
let output: Vec<U256> = run_interpreter(initial_offset, stack)?.stack().to_vec();
assert_eq!(output, expected);
Ok(())
}
fn make_frob_stack(f: Fp12) -> Vec<U256> {
let ptr = U256::from(100);
let f: Vec<U256> = f.into_iter().flatten().flatten().collect();
let mut input = vec![ptr];
input.extend(f);
input.extend(vec![ptr]);
input.reverse();
input
}
fn make_frob_expected(n: usize, f: Fp12) -> Vec<U256> {
frob_fp12(n, f)
.into_iter()
.flatten()
.flatten()
.rev()
.collect()
}
#[test]
fn test_frob_fp12() -> Result<()> {
let f: Fp12 = gen_fp12();
let test_frob1 = KERNEL.global_labels["test_frob_fp12_1"];
let test_frob2 = KERNEL.global_labels["test_frob_fp12_2"];
let test_frob3 = KERNEL.global_labels["test_frob_fp12_3"];
let test_frob6 = KERNEL.global_labels["test_frob_fp12_6"];
let stack = make_frob_stack(f);
let out_frob1: Vec<U256> = run_interpreter(test_frob1, stack.clone())?.stack().to_vec();
let out_frob2: Vec<U256> = run_interpreter(test_frob2, stack.clone())?.stack().to_vec();
let out_frob3: Vec<U256> = run_interpreter(test_frob3, stack.clone())?.stack().to_vec();
let out_frob6: Vec<U256> = run_interpreter(test_frob6, stack)?.stack().to_vec();
let exp_frob1: Vec<U256> = make_frob_expected(1, f);
let exp_frob2: Vec<U256> = make_frob_expected(2, f);
let exp_frob3: Vec<U256> = make_frob_expected(3, f);
let exp_frob6: Vec<U256> = make_frob_expected(6, f);
assert_eq!(out_frob1, exp_frob1);
assert_eq!(out_frob2, exp_frob2);
assert_eq!(out_frob3, exp_frob3);
assert_eq!(out_frob6, exp_frob6);
Ok(())
}
fn make_power_stack(f: Fp12) -> Vec<U256> {
let sqr = U256::from(100);
let out = U256::from(300);
let f: Vec<U256> = f.into_iter().flatten().flatten().collect();
let ret_stack = U256::from(KERNEL.global_labels["ret_stack"]);
let mut input = vec![sqr];
input.extend(f);
input.extend(vec![sqr, out, ret_stack, out]);
input.reverse();
input
}