openvm_keccak256_circuit/air.rs
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use std::{array::from_fn, borrow::Borrow, iter::zip};
use itertools::{izip, Itertools};
use openvm_circuit::{
arch::{ExecutionBridge, ExecutionState},
system::memory::{
offline_checker::{MemoryBridge, MemoryReadAuxCols, MemoryWriteAuxCols},
MemoryAddress,
},
};
use openvm_circuit_primitives::{
bitwise_op_lookup::BitwiseOperationLookupBus,
utils::{assert_array_eq, not, select},
};
use openvm_instructions::riscv::{RV32_CELL_BITS, RV32_REGISTER_NUM_LIMBS};
use openvm_keccak256_transpiler::Rv32KeccakOpcode;
use openvm_rv32im_circuit::adapters::abstract_compose;
use openvm_stark_backend::{
air_builders::sub::SubAirBuilder,
interaction::InteractionBuilder,
p3_air::{Air, AirBuilder, BaseAir},
p3_field::AbstractField,
p3_matrix::Matrix,
rap::{BaseAirWithPublicValues, PartitionedBaseAir},
};
use p3_keccak_air::{KeccakAir, NUM_KECCAK_COLS as NUM_KECCAK_PERM_COLS, U64_LIMBS};
use super::{
columns::{KeccakVmCols, NUM_KECCAK_VM_COLS},
KECCAK_ABSORB_READS, KECCAK_DIGEST_BYTES, KECCAK_DIGEST_WRITES, KECCAK_RATE_BYTES,
KECCAK_RATE_U16S, KECCAK_REGISTER_READS, KECCAK_WIDTH_U16S, KECCAK_WORD_SIZE,
NUM_ABSORB_ROUNDS,
};
#[derive(Clone, Copy, Debug, derive_new::new)]
pub struct KeccakVmAir {
pub execution_bridge: ExecutionBridge,
pub memory_bridge: MemoryBridge,
/// Bus to send 8-bit XOR requests to.
pub bitwise_lookup_bus: BitwiseOperationLookupBus,
/// Maximum number of bits allowed for an address pointer
pub ptr_max_bits: usize,
pub(super) offset: usize,
}
impl<F> BaseAirWithPublicValues<F> for KeccakVmAir {}
impl<F> PartitionedBaseAir<F> for KeccakVmAir {}
impl<F> BaseAir<F> for KeccakVmAir {
fn width(&self) -> usize {
NUM_KECCAK_VM_COLS
}
}
impl<AB: InteractionBuilder> Air<AB> for KeccakVmAir {
fn eval(&self, builder: &mut AB) {
let main = builder.main();
let (local, next) = (main.row_slice(0), main.row_slice(1));
let local: &KeccakVmCols<AB::Var> = (*local).borrow();
let next: &KeccakVmCols<AB::Var> = (*next).borrow();
builder.assert_bool(local.sponge.is_new_start);
builder.assert_eq(
local.sponge.is_new_start,
local.sponge.is_new_start * local.is_first_round(),
);
builder.assert_eq(
local.instruction.is_enabled_first_round,
local.instruction.is_enabled * local.is_first_round(),
);
// Not strictly necessary:
builder
.when_first_row()
.assert_one(local.sponge.is_new_start);
self.eval_keccak_f(builder);
self.constrain_padding(builder, local, next);
self.constrain_consistency_across_rounds(builder, local, next);
let mem = &local.mem_oc;
// Interactions:
self.constrain_absorb(builder, local, next);
let start_read_timestamp = self.eval_instruction(builder, local, &mem.register_aux);
let start_write_timestamp =
self.constrain_input_read(builder, local, start_read_timestamp, &mem.absorb_reads);
self.constrain_output_write(
builder,
local,
start_write_timestamp.clone(),
&mem.digest_writes,
);
self.constrain_block_transition(builder, local, next, start_write_timestamp);
}
}
impl KeccakVmAir {
/// Evaluate the keccak-f permutation constraints.
///
/// WARNING: The keccak-f AIR columns **must** be the first columns in the main AIR.
#[inline]
pub fn eval_keccak_f<AB: AirBuilder>(&self, builder: &mut AB) {
let keccak_f_air = KeccakAir {};
let mut sub_builder =
SubAirBuilder::<AB, KeccakAir, AB::Var>::new(builder, 0..NUM_KECCAK_PERM_COLS);
keccak_f_air.eval(&mut sub_builder);
}
/// Many columns are expected to be the same between rounds and only change per-block.
pub fn constrain_consistency_across_rounds<AB: AirBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
next: &KeccakVmCols<AB::Var>,
) {
let mut transition_builder = builder.when_transition();
let mut round_builder = transition_builder.when(not(local.is_last_round()));
// Instruction columns
local
.instruction
.assert_eq(&mut round_builder, next.instruction);
}
pub fn constrain_block_transition<AB: AirBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
next: &KeccakVmCols<AB::Var>,
start_write_timestamp: AB::Expr,
) {
// When we transition between blocks, if the next block isn't a new block
// (this means it's not receiving a new opcode or starting a dummy block)
// then we want _parts_ of opcode instruction to stay the same
// between blocks.
let mut block_transition = builder.when(local.is_last_round() * not(next.is_new_start()));
block_transition.assert_eq(local.instruction.is_enabled, next.instruction.is_enabled);
// dst is only going to be used for writes in the last input block
assert_array_eq(
&mut block_transition,
local.instruction.dst,
next.instruction.dst,
);
// needed for memory reads
block_transition.assert_eq(local.instruction.e, next.instruction.e);
// these are not used and hence not necessary, but putting for safety until performance becomes an issue:
block_transition.assert_eq(local.instruction.dst_ptr, next.instruction.dst_ptr);
block_transition.assert_eq(local.instruction.src_ptr, next.instruction.src_ptr);
block_transition.assert_eq(local.instruction.len_ptr, next.instruction.len_ptr);
// no constraint on `instruction.len` because we use `remaining_len` instead
// Move the src pointer over based on the number of bytes read.
// This should always be RATE_BYTES since it's a non-final block.
block_transition.assert_eq(
next.instruction.src,
local.instruction.src + AB::F::from_canonical_usize(KECCAK_RATE_BYTES),
);
// Advance timestamp by the number of memory accesses from reading
// `dst, src, len` and block input bytes.
block_transition.assert_eq(next.instruction.start_timestamp, start_write_timestamp);
block_transition.assert_eq(
next.instruction.remaining_len,
local.instruction.remaining_len - AB::F::from_canonical_usize(KECCAK_RATE_BYTES),
);
// Padding transition is constrained in `constrain_padding`.
}
/// Keccak follows the 10*1 padding rule.
/// See Section 5.1 of https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf
/// Note this is the ONLY difference between Keccak and SHA-3
///
/// Constrains padding constraints and length between rounds and
/// between blocks. Padding logic is tied to constraints on `is_new_start`.
pub fn constrain_padding<AB: AirBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
next: &KeccakVmCols<AB::Var>,
) {
let is_padding_byte = local.sponge.is_padding_byte;
let block_bytes = &local.sponge.block_bytes;
let remaining_len = local.remaining_len();
// is_padding_byte should all be boolean
for &is_padding_byte in is_padding_byte.iter() {
builder.assert_bool(is_padding_byte);
}
// is_padding_byte should transition from 0 to 1 only once and then stay 1
for i in 1..KECCAK_RATE_BYTES {
builder
.when(is_padding_byte[i - 1])
.assert_one(is_padding_byte[i]);
}
// is_padding_byte must stay the same on all rounds in a block
// we use next instead of local.step_flags.last() because the last row of the trace overall may not
// end on a last round
let is_last_round = next.inner.step_flags[0];
let is_not_last_round = not(is_last_round);
for i in 0..KECCAK_RATE_BYTES {
builder.when(is_not_last_round.clone()).assert_eq(
local.sponge.is_padding_byte[i],
next.sponge.is_padding_byte[i],
);
}
let num_padding_bytes = local
.sponge
.is_padding_byte
.iter()
.fold(AB::Expr::ZERO, |a, &b| a + b);
// If final rate block of input, then last byte must be padding
let is_final_block = is_padding_byte[KECCAK_RATE_BYTES - 1];
// is_padding_byte must be consistent with remaining_len
builder.when(is_final_block).assert_eq(
remaining_len,
AB::Expr::from_canonical_usize(KECCAK_RATE_BYTES) - num_padding_bytes,
);
// If this block is not final, when transitioning to next block, remaining len
// must decrease by `KECCAK_RATE_BYTES`.
builder
.when(is_last_round)
.when(not(is_final_block))
.assert_eq(
remaining_len - AB::F::from_canonical_usize(KECCAK_RATE_BYTES),
next.remaining_len(),
);
// To enforce that is_padding_byte must be set appropriately for an input, we require
// the block before a new start to have padding
builder
.when(is_last_round)
.when(next.is_new_start())
.assert_one(is_final_block);
// Make sure there are not repeated padding blocks
builder
.when(is_last_round)
.when(is_final_block)
.assert_one(next.is_new_start());
// The chain above enforces that for an input, the remaining length must decrease by RATE
// block-by-block until it reaches a final block with padding.
// ====== Constrain the block_bytes are padded according to is_padding_byte =====
// If the first padding byte is at the end of the block, then the block has a
// single padding byte
let has_single_padding_byte: AB::Expr =
is_padding_byte[KECCAK_RATE_BYTES - 1] - is_padding_byte[KECCAK_RATE_BYTES - 2];
// If the row has a single padding byte, then it must be the last byte with
// value 0b10000001
builder.when(has_single_padding_byte.clone()).assert_eq(
block_bytes[KECCAK_RATE_BYTES - 1],
AB::F::from_canonical_u8(0b10000001),
);
let has_multiple_padding_bytes: AB::Expr = not(has_single_padding_byte.clone());
for i in 0..KECCAK_RATE_BYTES - 1 {
let is_first_padding_byte: AB::Expr = {
if i > 0 {
is_padding_byte[i] - is_padding_byte[i - 1]
} else {
is_padding_byte[i].into()
}
};
// If the row has multiple padding bytes, the first padding byte must be 0x01
// because the padding 1*0 is *little-endian*
builder
.when(has_multiple_padding_bytes.clone())
.when(is_first_padding_byte.clone())
.assert_eq(block_bytes[i], AB::F::from_canonical_u8(0x01));
// If the row has multiple padding bytes, the other padding bytes
// except the last one must be 0
builder
.when(is_padding_byte[i])
.when(not::<AB::Expr>(is_first_padding_byte)) // hence never when single padding byte
.assert_zero(block_bytes[i]);
}
// If the row has multiple padding bytes, then the last byte must be 0x80
// because the padding *01 is *little-endian*
builder
.when(is_final_block)
.when(has_multiple_padding_bytes)
.assert_eq(
block_bytes[KECCAK_RATE_BYTES - 1],
AB::F::from_canonical_u8(0x80),
);
}
/// Constrain state transition between keccak-f permutations is valid absorb of input bytes.
/// The end-state in last round is given by `a_prime_prime_prime()` in `u16` limbs.
/// The pre-state is given by `preimage` also in `u16` limbs.
/// The input `block_bytes` will be given as **bytes**.
///
/// We will XOR `block_bytes` with `a_prime_prime_prime()` and constrain to be `next.preimage`.
/// This will be done using 8-bit XOR lookup in a separate AIR via interactions.
/// This will require decomposing `u16` into bytes.
/// Note that the XOR lookup automatically range checks its inputs to be bytes.
///
/// We use the following trick to keep `u16` limbs and avoid changing
/// the `keccak-f` AIR itself:
/// if we already have a 16-bit limb `x` and we also provide a 8-bit limb
/// `hi = x >> 8`, assuming `x` and `hi` have been range checked,
/// we can use the expression `lo = x - hi * 256` for the low byte.
/// If `lo` is range checked to `8`-bits, this constrains a valid byte
/// decomposition of `x` into `hi, lo`.
/// This means in terms of trace cells, it is equivalent to provide
/// `x, hi` versus `hi, lo`.
pub fn constrain_absorb<AB: InteractionBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
next: &KeccakVmCols<AB::Var>,
) {
let updated_state_bytes = (0..NUM_ABSORB_ROUNDS).flat_map(|i| {
let y = i / 5;
let x = i % 5;
(0..U64_LIMBS).flat_map(move |limb| {
let state_limb = local.postimage(y, x, limb);
let hi = local.sponge.state_hi[i * U64_LIMBS + limb];
let lo = state_limb - hi * AB::F::from_canonical_u64(1 << 8);
// Conversion from bytes to u64 is little-endian
[lo, hi.into()]
})
});
let post_absorb_state_bytes = (0..NUM_ABSORB_ROUNDS).flat_map(|i| {
let y = i / 5;
let x = i % 5;
(0..U64_LIMBS).flat_map(move |limb| {
let state_limb = next.inner.preimage[y][x][limb];
let hi = next.sponge.state_hi[i * U64_LIMBS + limb];
let lo = state_limb - hi * AB::F::from_canonical_u64(1 << 8);
[lo, hi.into()]
})
});
// We xor on last round of each block, even if it is a final block,
// because we use xor to range check the output bytes (= updated_state_bytes)
let is_final_block = *local.sponge.is_padding_byte.last().unwrap();
for (input, prev, post) in izip!(
next.sponge.block_bytes,
updated_state_bytes,
post_absorb_state_bytes
) {
// Add new send interaction to lookup (x, y, x ^ y) where x, y, z
// will all be range checked to be 8-bits (assuming the bus is
// received by an 8-bit xor chip).
// When absorb, input ^ prev = post
// Otherwise, 0 ^ prev = prev
// The interaction fields are degree 2, leading to degree 3 constraint
self.bitwise_lookup_bus
.send_xor(
input * not(is_final_block),
prev.clone(),
select(is_final_block, prev, post),
)
.eval(
builder,
local.is_last_round() * local.instruction.is_enabled,
);
}
// We separately constrain that when(local.is_new_start), the preimage (u16s) equals the block bytes
let local_preimage_bytes = (0..NUM_ABSORB_ROUNDS).flat_map(|i| {
let y = i / 5;
let x = i % 5;
(0..U64_LIMBS).flat_map(move |limb| {
let state_limb = local.inner.preimage[y][x][limb];
let hi = local.sponge.state_hi[i * U64_LIMBS + limb];
let lo = state_limb - hi * AB::F::from_canonical_u64(1 << 8);
[lo, hi.into()]
})
});
let mut when_is_new_start =
builder.when(local.is_new_start() * local.instruction.is_enabled);
for (preimage_byte, block_byte) in zip(local_preimage_bytes, local.sponge.block_bytes) {
when_is_new_start.assert_eq(preimage_byte, block_byte);
}
// constrain transition on the state outside rate
let mut reset_builder = builder.when(local.is_new_start());
for i in KECCAK_RATE_U16S..KECCAK_WIDTH_U16S {
let y = i / U64_LIMBS / 5;
let x = (i / U64_LIMBS) % 5;
let limb = i % U64_LIMBS;
reset_builder.assert_zero(local.inner.preimage[y][x][limb]);
}
let mut absorb_builder = builder.when(local.is_last_round() * not(next.is_new_start()));
for i in KECCAK_RATE_U16S..KECCAK_WIDTH_U16S {
let y = i / U64_LIMBS / 5;
let x = (i / U64_LIMBS) % 5;
let limb = i % U64_LIMBS;
absorb_builder.assert_eq(local.postimage(y, x, limb), next.inner.preimage[y][x][limb]);
}
}
/// Receive the instruction itself on program bus. Send+receive on execution bus.
/// Then does memory read in addr space 1 to get `dst, src, len` from memory.
///
/// Adds range check interactions for the most significant limbs of the register values
/// using BitwiseOperationLookupBus.
///
/// Returns `start_read_timestamp` which is only relevant when `local.instruction.is_enabled`.
/// Note that `start_read_timestamp` is a linear expression.
pub fn eval_instruction<AB: InteractionBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
register_aux: &[MemoryReadAuxCols<AB::Var, RV32_REGISTER_NUM_LIMBS>; KECCAK_REGISTER_READS],
) -> AB::Expr {
let instruction = local.instruction;
// Only receive opcode if:
// - enabled row (not dummy row)
// - first round of block
// - is_new_start
// Note this is degree 3, which results in quotient degree 2 if used
// as `count` in interaction
let should_receive = local.instruction.is_enabled * local.sponge.is_new_start;
let [dst_ptr, src_ptr, len_ptr] = [
instruction.dst_ptr,
instruction.src_ptr,
instruction.len_ptr,
];
let reg_addr_sp = AB::F::ONE;
let timestamp_change: AB::Expr = Self::timestamp_change(instruction.remaining_len);
self.execution_bridge
.execute_and_increment_pc(
AB::Expr::from_canonical_usize(Rv32KeccakOpcode::KECCAK256 as usize + self.offset),
[
dst_ptr.into(),
src_ptr.into(),
len_ptr.into(),
reg_addr_sp.into(),
instruction.e.into(),
],
ExecutionState::new(instruction.pc, instruction.start_timestamp),
timestamp_change,
)
.eval(builder, should_receive.clone());
let mut timestamp: AB::Expr = instruction.start_timestamp.into();
let recover_limbs = |limbs: [AB::Var; RV32_REGISTER_NUM_LIMBS - 1],
val: AB::Var|
-> [AB::Expr; RV32_REGISTER_NUM_LIMBS] {
from_fn(|i| {
if i == 0 {
limbs
.into_iter()
.enumerate()
.fold(val.into(), |acc, (j, limb)| {
acc - limb
* AB::Expr::from_canonical_usize(1 << ((j + 1) * RV32_CELL_BITS))
})
} else {
limbs[i - 1].into()
}
})
};
// Only when it is an input do we want to do memory read for
// dst <- word[a]_d, src <- word[b]_d
let dst_data = instruction.dst.map(Into::into);
let src_data = recover_limbs(instruction.src_limbs, instruction.src);
let len_data = recover_limbs(instruction.len_limbs, instruction.remaining_len);
for (ptr, value, aux) in izip!(
[dst_ptr, src_ptr, len_ptr],
[dst_data, src_data, len_data],
register_aux,
) {
self.memory_bridge
.read(
MemoryAddress::new(reg_addr_sp, ptr),
value,
timestamp.clone(),
aux,
)
.eval(builder, should_receive.clone());
timestamp += AB::Expr::ONE;
}
// See Rv32VecHeapAdapterAir
// TODO[jpw]: reduce code duplication
// repeat len for even number
// We range check `len` to `max_ptr_bits` to ensure `remaining_len` doesn't overflow.
// We could range check it to some other size, but `max_ptr_bits` is convenient.
let need_range_check = [
*instruction.dst.last().unwrap(),
*instruction.src_limbs.last().unwrap(),
*instruction.len_limbs.last().unwrap(),
*instruction.len_limbs.last().unwrap(),
];
let limb_shift = AB::F::from_canonical_usize(
1 << (RV32_CELL_BITS * RV32_REGISTER_NUM_LIMBS - self.ptr_max_bits),
);
for pair in need_range_check.chunks_exact(2) {
self.bitwise_lookup_bus
.send_range(pair[0] * limb_shift, pair[1] * limb_shift)
.eval(builder, should_receive.clone());
}
timestamp
}
/// Constrain reading the input as `block_bytes` from memory.
/// Reads input based on `is_padding_byte`.
/// Constrains timestamp transitions between blocks if input crosses blocks.
///
/// Expects `start_read_timestamp` to be a linear expression.
/// Returns the `start_write_timestamp` which is the timestamp to start from
/// for writing digest to memory.
pub fn constrain_input_read<AB: InteractionBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
start_read_timestamp: AB::Expr,
mem_aux: &[MemoryReadAuxCols<AB::Var, KECCAK_WORD_SIZE>; KECCAK_ABSORB_READS],
) -> AB::Expr {
let partial_block = &local.mem_oc.partial_block;
// Only read input from memory when it is an opcode-related row
// and only on the first round of block
let is_input = local.instruction.is_enabled_first_round;
let mut timestamp = start_read_timestamp;
// read `state` into `word[src + ...]_e`
// iterator of state as u16:
for (i, (input, is_padding, mem_aux)) in izip!(
local.sponge.block_bytes.chunks_exact(KECCAK_WORD_SIZE),
local.sponge.is_padding_byte.chunks_exact(KECCAK_WORD_SIZE),
mem_aux
)
.enumerate()
{
let ptr = local.instruction.src + AB::F::from_canonical_usize(i * KECCAK_WORD_SIZE);
// Only read block i if it is not entirely padding bytes
// count is degree 2
let count = is_input * not(is_padding[0]);
// The memory block read is partial if first byte is not padding but the last byte is padding. Since `count` is only 1 when first byte isn't padding, use check just if last byte is padding.
let is_partial_read = *is_padding.last().unwrap();
// word is degree 2
let word: [_; KECCAK_WORD_SIZE] = from_fn(|i| {
if i == 0 {
// first byte is always ok
input[0].into()
} else {
// use `partial_block` if this is a partial read, otherwise use the normal input block
select(is_partial_read, partial_block[i - 1], input[i])
}
});
for i in 1..KECCAK_WORD_SIZE {
let not_padding: AB::Expr = not(is_padding[i]);
// When not a padding byte, the word byte and input byte must be equal
// This is constraint degree 3
builder.assert_eq(
not_padding.clone() * word[i].clone(),
not_padding.clone() * input[i],
);
}
self.memory_bridge
.read(
MemoryAddress::new(local.instruction.e, ptr),
word, // degree 2
timestamp.clone(),
mem_aux,
)
.eval(builder, count);
timestamp += AB::Expr::ONE;
}
timestamp
}
pub fn constrain_output_write<AB: InteractionBuilder>(
&self,
builder: &mut AB,
local: &KeccakVmCols<AB::Var>,
start_write_timestamp: AB::Expr,
mem_aux: &[MemoryWriteAuxCols<AB::Var, KECCAK_WORD_SIZE>; KECCAK_DIGEST_WRITES],
) {
let instruction = local.instruction;
let is_final_block = *local.sponge.is_padding_byte.last().unwrap();
// since keccak-f AIR has this column, we might as well use it
builder.assert_eq(
local.inner.export,
instruction.is_enabled * is_final_block * local.is_last_round(),
);
// See `constrain_absorb` on how we derive the postimage bytes from u16 limbs
// **SAFETY:** we always XOR the final state with 0 in `constrain_absorb`,
// so the output bytes **are** range checked.
let updated_state_bytes = (0..NUM_ABSORB_ROUNDS).flat_map(|i| {
let y = i / 5;
let x = i % 5;
(0..U64_LIMBS).flat_map(move |limb| {
let state_limb = local.postimage(y, x, limb);
let hi = local.sponge.state_hi[i * U64_LIMBS + limb];
let lo = state_limb - hi * AB::F::from_canonical_u64(1 << 8);
// Conversion from bytes to u64 is little-endian
[lo, hi.into()]
})
});
let dst = abstract_compose::<AB::Expr, _>(instruction.dst);
for (i, digest_bytes) in updated_state_bytes
.take(KECCAK_DIGEST_BYTES)
.chunks(KECCAK_WORD_SIZE)
.into_iter()
.enumerate()
{
let digest_bytes = digest_bytes.collect_vec();
let timestamp = start_write_timestamp.clone() + AB::Expr::from_canonical_usize(i);
self.memory_bridge
.write(
MemoryAddress::new(
instruction.e,
dst.clone() + AB::F::from_canonical_usize(i * KECCAK_WORD_SIZE),
),
digest_bytes.try_into().unwrap(),
timestamp,
&mem_aux[i],
)
.eval(builder, local.inner.export)
}
}
/// Amount to advance timestamp by after execution of one opcode instruction.
/// This is an upper bound dependant on the length `len` operand, which is unbounded.
pub fn timestamp_change<T: AbstractField>(len: impl Into<T>) -> T {
// actual number is ceil(len / 136) * (3 + 17) + KECCAK_DIGEST_WRITES
// digest writes only done on last row of multi-block
// add another KECCAK_ABSORB_READS to round up so we don't deal with padding
len.into()
+ T::from_canonical_usize(
KECCAK_REGISTER_READS + KECCAK_ABSORB_READS + KECCAK_DIGEST_WRITES,
)
}
}