From a9b34dc8b4ed6f79fe20ae6c7649ddf1a9b339e0 Mon Sep 17 00:00:00 2001 From: enitrat Date: Fri, 8 Nov 2024 00:06:10 +0700 Subject: [PATCH 1/2] feat: ec-pairing (felt) --- cairo/kakarot-ssj/Scarb.lock | 2 +- cairo/kakarot-ssj/crates/evm/Scarb.toml | 2 +- .../crates/evm/src/precompiles.cairo | 6 +- .../evm/src/precompiles/ec_operations.cairo | 1 + .../ec_operations/ec_pairing.cairo | 135 +++ .../evm/src/precompiles/p256verify.cairo | 38 +- .../crates/utils/src/constants.cairo | 7 + pyproject.toml | 2 +- uv.lock | 977 +----------------- 9 files changed, 153 insertions(+), 1017 deletions(-) create mode 100644 cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo diff --git a/cairo/kakarot-ssj/Scarb.lock b/cairo/kakarot-ssj/Scarb.lock index 8a345708d..1a6bd64d2 100644 --- a/cairo/kakarot-ssj/Scarb.lock +++ b/cairo/kakarot-ssj/Scarb.lock @@ -34,7 +34,7 @@ dependencies = [ [[package]] name = "garaga" version = "0.1.0" -source = "git+https://github.com/keep-starknet-strange/garaga.git#933784eee3811334cf1a5b83d9ffcc9cfda3be8c" +source = "git+https://github.com/keep-starknet-strange/garaga.git?rev=c741f55#c741f558f8275f278b34a7c47751cf26acab3da9" [[package]] name = "openzeppelin" diff --git a/cairo/kakarot-ssj/crates/evm/Scarb.toml b/cairo/kakarot-ssj/crates/evm/Scarb.toml index 1180c54a4..ac64ac9d3 100644 --- a/cairo/kakarot-ssj/crates/evm/Scarb.toml +++ b/cairo/kakarot-ssj/crates/evm/Scarb.toml @@ -10,7 +10,7 @@ starknet.workspace = true utils = { path = "../utils" } contracts = { path = "../contracts" } openzeppelin = { path = "../openzeppelin" } -garaga = { git = "https://github.com/keep-starknet-strange/garaga.git" } +garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", rev = "c741f55" } [dev-dependencies] snforge_std = { git = "https://github.com/foundry-rs/starknet-foundry.git", tag = "v0.31.0" } diff --git a/cairo/kakarot-ssj/crates/evm/src/precompiles.cairo b/cairo/kakarot-ssj/crates/evm/src/precompiles.cairo index ff8dd9386..d7929155c 100644 --- a/cairo/kakarot-ssj/crates/evm/src/precompiles.cairo +++ b/cairo/kakarot-ssj/crates/evm/src/precompiles.cairo @@ -9,6 +9,7 @@ mod sha256; pub use blake2f::Blake2f; pub use ec_operations::ec_add::EcAdd; pub use ec_operations::ec_mul::EcMul; +pub use ec_operations::ec_pairing::EcPairing; pub use ec_recover::EcRecover; pub use identity::Identity; pub use modexp::ModExp; @@ -104,10 +105,7 @@ pub impl PrecompilesImpl of Precompiles { 0x05 => { ModExp::exec(input)? }, 0x06 => { EcAdd::exec(input)? }, 0x07 => { EcMul::exec(input)? }, - 0x08 => { - // we should never reach this branch! - panic!("pre-compile at address {:?} isn't implemented yet", precompile_address) - }, + 0x08 => { EcPairing::exec(input)? }, 0x09 => { Blake2f::exec(input)? }, 0x0a => { // Point Evaluation diff --git a/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations.cairo b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations.cairo index d696d0fee..1aa488172 100644 --- a/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations.cairo +++ b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations.cairo @@ -1,5 +1,6 @@ pub(crate) mod ec_add; pub(crate) mod ec_mul; +pub(crate) mod ec_pairing; use core::circuit::CircuitElement as CE; use core::circuit::CircuitInput as CI; use core::circuit::{ diff --git a/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo new file mode 100644 index 000000000..6c3694d75 --- /dev/null +++ b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo @@ -0,0 +1,135 @@ +use core::starknet::{EthAddress}; +use crate::errors::EVMError; +use crate::precompiles::Precompile; +use crate::precompiles::ec_operations::{is_on_curve, BN254_PRIME}; +use garaga::circuits::tower_circuits::run_BN254_E12T_MUL_circuit; +use garaga::definitions::G1G2Pair; +use garaga::ec_ops::{G1PointImpl}; +use garaga::ec_ops_g2::{G2PointImpl}; + +use garaga::single_pairing_tower::{ + E12TOne, G1Point, G2Point, miller_loop_bn254_tower, final_exp_bn254_tower, u384 +}; +use utils::traits::bytes::FromBytes; +use utils::constants::{ONE_32_BYTES, ZERO_32_BYTES}; + +const BASE_COST: u64 = 45000; +const PAIRING_COST: u64 = 34000; +const U256_BYTES_LEN: usize = 32; +const GARAGA_BN254_CURVE_INDEX: u32 = 0; + +pub impl EcPairing of Precompile { + fn address() -> EthAddress { + 0x8.try_into().unwrap() + } + + fn exec(mut input: Span) -> Result<(u64, Span), EVMError> { + let (n, rem) = DivRem::div_rem(input.len(), 192); + + let gas = PAIRING_COST * n.into() + BASE_COST; + + // "The input must always be a multiple of 6 32-byte values. 0 inputs is valid and returns + // 1" + // https://www.evm.codes/precompiled?fork=cancun#0x08 + + if rem != 0 || n == 1 { + // rem != 0: input length must be a multiple of 196 + // n == 1: single pairing is non-degerative by definition, can't be 1. + return Result::Err(EVMError::InvalidParameter('invalid ec_pairing input')); + } + if n == 0 { + return Result::Ok((BASE_COST, ONE_32_BYTES.span())); + } + + let mut pairs: Array = array![]; + let mut offset = 0; + let mut everything_ok = true; + for _ in 0_usize + ..n { + let x: u256 = input.slice(offset, U256_BYTES_LEN).from_be_bytes().unwrap(); + let y: u256 = input.slice(offset + 32, U256_BYTES_LEN).from_be_bytes().unwrap(); + let x1: u256 = input.slice(offset + 64, U256_BYTES_LEN).from_be_bytes().unwrap(); + let x0: u256 = input.slice(offset + 96, U256_BYTES_LEN).from_be_bytes().unwrap(); + let y1: u256 = input.slice(offset + 128, U256_BYTES_LEN).from_be_bytes().unwrap(); + let y0: u256 = input.slice(offset + 160, U256_BYTES_LEN).from_be_bytes().unwrap(); + let x_384: u384 = x.into(); + let y_384: u384 = y.into(); + let p = G1Point { x: x_384, y: y_384 }; + let q = G2Point { x0: x0.into(), x1: x1.into(), y0: y0.into(), y1: y1.into() }; + + if !is_on_curve(x_384, y_384) + || !q.is_on_curve(GARAGA_BN254_CURVE_INDEX) + || x >= BN254_PRIME + || y >= BN254_PRIME + || x0 >= BN254_PRIME + || x1 >= BN254_PRIME + || y0 >= BN254_PRIME + || y1 >= BN254_PRIME { + everything_ok = false; + } + pairs.append(G1G2Pair { p: p, q: q }); + offset += 192; + }; + + if !everything_ok { + return Result::Err(EVMError::InvalidParameter('invalid ec_pairing input')); + } + + let res = ec_pairing(pairs.span()); + + let result_bytes = match res { + true => { ONE_32_BYTES.span() }, + false => { ZERO_32_BYTES.span() }, + }; + + return Result::Ok((gas, result_bytes)); + } +} + +// Assumes len is >= 2. +// Assumes pairs are on curve. +// Returns true if Π e(Pi,Qi) = 1 where e is the optimal ate pairing on BN254 +fn ec_pairing(pairs: Span) -> bool { + let pair_0 = pairs.at(0); + let (mut m) = miller_loop_bn254_tower(*pair_0.p, *pair_0.q); + + for i in 1_usize + ..pairs + .len() { + let pair_i = pairs.at(i); + let (__m) = miller_loop_bn254_tower(*pair_i.p, *pair_i.q); + let (_m) = run_BN254_E12T_MUL_circuit(m, __m); + m = _m; + }; + + let f = final_exp_bn254_tower(m); + return f.is_one(); +} +#[cfg(test)] +mod tests { + use super::EcPairing; + use utils::constants::ONE_32_BYTES; + + #[test] + fn test_ec_pairing() { + #[cairofmt::skip] + let bytes_input: Array = array![ + 0x2c, 0xf4, 0x44, 0x99, 0xd5, 0xd2, 0x7b, 0xb1, 0x86, 0x30, 0x8b, 0x7a, 0xf7, 0xaf, 0x2, 0xac, 0x5b, 0xc9, 0xee, 0xb6, 0xa3, 0xd1, 0x47, 0xc1, 0x86, 0xb2, 0x1f, 0xb1, 0xb7, 0x6e, 0x18, 0xda, 0x2c, + 0xf, 0x0, 0x1f, 0x52, 0x11, 0xc, 0xcf, 0xe6, 0x91, 0x8, 0x92, 0x49, 0x26, 0xe4, 0x5f, 0xb, 0xc, 0x86, 0x8d, 0xf0, 0xe7, 0xbd, 0xe1, 0xfe, 0x16, 0xd3, 0x24, 0x2d, 0xc7, 0x15, 0xf6, 0x1f, 0xb1, + 0x9b, 0xb4, 0x76, 0xf6, 0xb9, 0xe4, 0x4e, 0x2a, 0x32, 0x23, 0x4d, 0xa8, 0x21, 0x2f, 0x61, 0xcd, 0x63, 0x91, 0x93, 0x54, 0xbc, 0x6, 0xae, 0xf3, 0x1e, 0x3c, 0xfa, 0xff, 0x3e, 0xbc, 0x22, 0x60, 0x68, + 0x45, 0xff, 0x18, 0x67, 0x93, 0x91, 0x4e, 0x3, 0xe2, 0x1d, 0xf5, 0x44, 0xc3, 0x4f, 0xfe, 0x2f, 0x2f, 0x35, 0x4, 0xde, 0x8a, 0x79, 0xd9, 0x15, 0x9e, 0xca, 0x2d, 0x98, 0xd9, 0x2b, 0xd3, 0x68, 0xe2, 0x83, 0x81, 0xe8, 0xec, 0xcb, 0x5f, 0xa8, 0x1f, 0xc2, 0x6c, + 0xf3, 0xf0, 0x48, 0xee, 0xa9, 0xab, 0xfd, 0xd8, 0x5d, 0x7e, 0xd3, 0xab, 0x36, 0x98, 0xd6, 0x3e, 0x4f, 0x90, 0x2f, 0xe0, 0x2e, 0x47, 0x88, 0x75, 0x7, 0xad, 0xf0, 0xff, 0x17, 0x43, 0xcb, 0xac, 0x6b, + 0xa2, 0x91, 0xe6, 0x6f, 0x59, 0xbe, 0x6b, 0xd7, 0x63, 0x95, 0xb, 0xb1, 0x60, 0x41, 0xa0, 0xa8, 0x5e, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x30, 0x64, 0x4e, 0x72, 0xe1, 0x31, 0xa0, 0x29, 0xb8, 0x50, 0x45, 0xb6, 0x81, 0x81, 0x58, 0x5d, 0x97, + 0x81, 0x6a, 0x91, 0x68, 0x71, 0xca, 0x8d, 0x3c, 0x20, 0x8c, 0x16, 0xd8, 0x7c, 0xfd, 0x45, 0x19, 0x71, 0xff, 0x4, 0x71, 0xb0, 0x9f, 0xa9, 0x3c, 0xaa, 0xf1, 0x3c, 0xbf, 0x44, 0x3c, 0x1a, 0xed, 0xe0, + 0x9c, 0xc4, 0x32, 0x8f, 0x5a, 0x62, 0xaa, 0xd4, 0x5f, 0x40, 0xec, 0x13, 0x3e, 0xb4, 0x9, 0x10, 0x58, 0xa3, 0x14, 0x18, 0x22, 0x98, 0x57, 0x33, 0xcb, 0xdd, 0xdf, 0xed, 0xf, 0xd8, 0xd6, 0xc1, 0x4, + 0xe9, 0xe9, 0xef, 0xf4, 0xb, 0xf5, 0xab, 0xfe, 0xf9, 0xab, 0x16, 0x3b, 0xc7, 0x2a, 0x23, 0xaf, 0x9a, 0x5c, 0xe2, 0xba, 0x27, 0x96, 0xc1, 0xf4, 0xe4, 0x53, 0xa3, 0x70, 0xeb, 0xa, 0xf8, 0xc2, 0x12, + 0xd9, 0xdc, 0x9a, 0xcd, 0x8f, 0xc0, 0x2c, 0x2e, 0x90, 0x7b, 0xae, 0xa2, 0x23, 0xa8, 0xeb, 0xb, 0x9, 0x96, 0x25, 0x2c, 0xb5, 0x48, 0xa4, 0x48, 0x7d, 0xa9, 0x7b, 0x2, 0x42, 0x2e, 0xbc, 0xe, + 0x83, 0x46, 0x13, 0xf9, 0x54, 0xde, 0x6c, 0x7e, 0xa, 0xfd, 0xc1, 0xfc + ]; + + let result = EcPairing::exec(bytes_input.span()); + let (_gas, return_data) = result.unwrap(); + assert_eq!(return_data, ONE_32_BYTES.span()); + } +} diff --git a/cairo/kakarot-ssj/crates/evm/src/precompiles/p256verify.cairo b/cairo/kakarot-ssj/crates/evm/src/precompiles/p256verify.cairo index f0bbc4948..680eb215a 100644 --- a/cairo/kakarot-ssj/crates/evm/src/precompiles/p256verify.cairo +++ b/cairo/kakarot-ssj/crates/evm/src/precompiles/p256verify.cairo @@ -4,46 +4,10 @@ use core::starknet::{EthAddress, secp256r1::{Secp256r1Point}, secp256_trait::is_ use crate::errors::{EVMError}; use crate::precompiles::Precompile; use utils::traits::bytes::FromBytes; +use utils::constants::ONE_32_BYTES; const P256VERIFY_PRECOMPILE_GAS_COST: u64 = 3450; -const ONE_32_BYTES: [ - u8 - ; 32] = [ - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x00, - 0x01 -]; - pub impl P256Verify of Precompile { #[inline(always)] fn address() -> EthAddress { diff --git a/cairo/kakarot-ssj/crates/utils/src/constants.cairo b/cairo/kakarot-ssj/crates/utils/src/constants.cairo index 5f9b52a8b..977ede8a3 100644 --- a/cairo/kakarot-ssj/crates/utils/src/constants.cairo +++ b/cairo/kakarot-ssj/crates/utils/src/constants.cairo @@ -493,3 +493,10 @@ pub const POW_2_120: u128 = 0x1000000000000000000000000000000; pub const POW_2_127: u128 = 0x80000000000000000000000000000000; pub const MAX_ADDRESS: u256 = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff; + + +#[cairofmt::skip] +pub const ONE_32_BYTES: [ u8 ; 32] = [ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 ]; + +#[cairofmt::skip] +pub const ZERO_32_BYTES: [ u8 ; 32] = [ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ]; diff --git a/pyproject.toml b/pyproject.toml index c3206be6f..0df5fc9e6 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -35,7 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+source = "git+https://github.com/keep-starknet-strange/garaga.git?branch=g2#7b1b9168347063d26b791c88a30440f9fc723c86" [[package]] name = "openzeppelin" diff --git a/cairo/kakarot-ssj/crates/evm/Scarb.toml b/cairo/kakarot-ssj/crates/evm/Scarb.toml index ac64ac9d3..432fdcfd3 100644 --- a/cairo/kakarot-ssj/crates/evm/Scarb.toml +++ b/cairo/kakarot-ssj/crates/evm/Scarb.toml @@ -10,7 +10,7 @@ starknet.workspace = true utils = { path = "../utils" } contracts = { path = "../contracts" } openzeppelin = { path = "../openzeppelin" } -garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", rev = "c741f55" } +garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", branch = "g2" } [dev-dependencies] snforge_std = { git = "https://github.com/foundry-rs/starknet-foundry.git", tag = "v0.31.0" } diff --git a/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo index 6c3694d75..07b125fb9 100644 --- a/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo +++ b/cairo/kakarot-ssj/crates/evm/src/precompiles/ec_operations/ec_pairing.cairo @@ -1,22 +1,24 @@ +use core::num::traits::Zero; use core::starknet::{EthAddress}; use crate::errors::EVMError; use crate::precompiles::Precompile; use crate::precompiles::ec_operations::{is_on_curve, BN254_PRIME}; use garaga::circuits::tower_circuits::run_BN254_E12T_MUL_circuit; use garaga::definitions::G1G2Pair; -use garaga::ec_ops::{G1PointImpl}; -use garaga::ec_ops_g2::{G2PointImpl}; +use garaga::ec_ops_g2::{G2PointTrait, ec_mul as ec_mul_g2}; use garaga::single_pairing_tower::{ E12TOne, G1Point, G2Point, miller_loop_bn254_tower, final_exp_bn254_tower, u384 }; -use utils::traits::bytes::FromBytes; use utils::constants::{ONE_32_BYTES, ZERO_32_BYTES}; +use utils::traits::bytes::FromBytes; const BASE_COST: u64 = 45000; const PAIRING_COST: u64 = 34000; const U256_BYTES_LEN: usize = 32; const GARAGA_BN254_CURVE_INDEX: u32 = 0; +const BN254_CURVE_ORDER: u256 = + 21888242871839275222246405745257275088548364400416034343698204186575808495617; pub impl EcPairing of Precompile { fn address() -> EthAddress { @@ -28,14 +30,9 @@ pub impl EcPairing of Precompile { let gas = PAIRING_COST * n.into() + BASE_COST; - // "The input must always be a multiple of 6 32-byte values. 0 inputs is valid and returns - // 1" - // https://www.evm.codes/precompiled?fork=cancun#0x08 - - if rem != 0 || n == 1 { + if rem != 0 { // rem != 0: input length must be a multiple of 196 - // n == 1: single pairing is non-degerative by definition, can't be 1. - return Result::Err(EVMError::InvalidParameter('invalid ec_pairing input')); + return Result::Err(EVMError::InvalidParameter('invalid ec_pairing input length')); } if n == 0 { return Result::Ok((BASE_COST, ONE_32_BYTES.span())); @@ -52,21 +49,46 @@ pub impl EcPairing of Precompile { let x0: u256 = input.slice(offset + 96, U256_BYTES_LEN).from_be_bytes().unwrap(); let y1: u256 = input.slice(offset + 128, U256_BYTES_LEN).from_be_bytes().unwrap(); let y0: u256 = input.slice(offset + 160, U256_BYTES_LEN).from_be_bytes().unwrap(); - let x_384: u384 = x.into(); - let y_384: u384 = y.into(); - let p = G1Point { x: x_384, y: y_384 }; - let q = G2Point { x0: x0.into(), x1: x1.into(), y0: y0.into(), y1: y1.into() }; - if !is_on_curve(x_384, y_384) - || !q.is_on_curve(GARAGA_BN254_CURVE_INDEX) - || x >= BN254_PRIME + if x >= BN254_PRIME || y >= BN254_PRIME || x0 >= BN254_PRIME || x1 >= BN254_PRIME || y0 >= BN254_PRIME || y1 >= BN254_PRIME { everything_ok = false; + break; + } + + // If p and q are not the point at infinity, check that it's they're on the curve. + let x_384: u384 = x.into(); + let y_384: u384 = y.into(); + let p = G1Point { x: x_384, y: y_384 }; + let p_infinity = p.is_zero(); + if (!p_infinity) { + if (!is_on_curve(x_384, y_384)) { + everything_ok = false; + break; + } + } + + let q = G2Point { x0: x0.into(), x1: x1.into(), y0: y0.into(), y1: y1.into() }; + let q_infinity = q.is_zero(); + if (!q_infinity) { + if (!q.is_on_curve(GARAGA_BN254_CURVE_INDEX)) { + everything_ok = false; + break; + } + } + + // Subgroup check + // Cofactor for G1 group is 1, so we don't need to check for `p` + let q_mul_r = ec_mul_g2(q, BN254_CURVE_ORDER, GARAGA_BN254_CURVE_INDEX).unwrap(); + if (!q_mul_r.is_zero()) { + everything_ok = false; + break; } + pairs.append(G1G2Pair { p: p, q: q }); offset += 192; }; @@ -86,21 +108,35 @@ pub impl EcPairing of Precompile { } } -// Assumes len is >= 2. +// Assumes len is >= 1. // Assumes pairs are on curve. // Returns true if Π e(Pi,Qi) = 1 where e is the optimal ate pairing on BN254 -fn ec_pairing(pairs: Span) -> bool { - let pair_0 = pairs.at(0); - let (mut m) = miller_loop_bn254_tower(*pair_0.p, *pair_0.q); - - for i in 1_usize - ..pairs - .len() { - let pair_i = pairs.at(i); - let (__m) = miller_loop_bn254_tower(*pair_i.p, *pair_i.q); - let (_m) = run_BN254_E12T_MUL_circuit(m, __m); - m = _m; - }; +fn ec_pairing(mut pairs: Span) -> bool { + let n_pairs = pairs.len(); + let pair_0 = pairs.pop_front().unwrap(); + let (mut m,) = match pair_0.p.is_zero() || pair_0.q.is_zero() { + true => { + if n_pairs == 1 { + return true; + } + (E12TOne::one(),) + }, + false => { miller_loop_bn254_tower(*pair_0.p, *pair_0.q) } + }; + + // The original input had only one pair + if n_pairs == 1 { + return final_exp_bn254_tower(m).is_one(); + }; + + for pair_i in pairs { + let (__m,) = match pair_i.p.is_zero() || pair_i.q.is_zero() { + true => { (E12TOne::one(),) }, + false => { miller_loop_bn254_tower(*pair_i.p, *pair_i.q) } + }; + let (_m) = run_BN254_E12T_MUL_circuit(m, __m); + m = _m; + }; let f = final_exp_bn254_tower(m); return f.is_one();