binius_field/
aes_field.rs

1// Copyright 2024-2025 Irreducible Inc.
2
3use std::{
4	fmt::{Debug, Display, Formatter},
5	iter::{Product, Sum},
6	marker::PhantomData,
7	ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
8};
9
10use binius_utils::{
11	DeserializeBytes, SerializationError, SerializeBytes,
12	bytes::{Buf, BufMut},
13};
14use bytemuck::{Pod, Zeroable};
15
16use super::{
17	PackedExtension, PackedSubfield,
18	arithmetic_traits::InvertOrZero,
19	binary_field::{BinaryField, BinaryField1b, binary_field, impl_field_extension},
20	binary_field_arithmetic::TowerFieldArithmetic,
21	mul_by_binary_field_1b,
22};
23use crate::{
24	ExtensionField, Field, TowerField, binary_field_arithmetic::impl_arithmetic_using_packed,
25	linear_transformation::Transformation, underlier::U1,
26};
27
28// These fields represent a tower based on AES GF(2^8) field (GF(256)/x^8+x^4+x^3+x+1)
29// that is isomorphically included into binary tower, i.e.:
30//  - AESTowerField16b is GF(2^16) / (x^2 + x * x_2 + 1) where `x_2` is 0x10 from
31// BinaryField8b isomorphically projected to AESTowerField8b.
32//  - AESTowerField32b is GF(2^32) / (x^2 + x * x_3 + 1), where `x_3` is 0x1000 from
33//    AESTowerField16b.
34//  ...
35binary_field!(pub AESTowerField8b(u8), 0xD0);
36
37unsafe impl Pod for AESTowerField8b {}
38
39impl_field_extension!(BinaryField1b(U1) < @3 => AESTowerField8b(u8));
40
41mul_by_binary_field_1b!(AESTowerField8b);
42
43impl_arithmetic_using_packed!(AESTowerField8b);
44
45impl TowerField for AESTowerField8b {
46	fn min_tower_level(self) -> usize {
47		match self {
48			Self::ZERO | Self::ONE => 0,
49			_ => 3,
50		}
51	}
52}
53
54/// A 3- step transformation :
55/// 1. Cast to base b-bit packed field
56/// 2. Apply linear transformation between aes and binary b8 tower fields
57/// 3. Cast back to the target field
58pub struct SubfieldTransformer<IF, OF, T> {
59	inner_transform: T,
60	_ip_pd: PhantomData<IF>,
61	_op_pd: PhantomData<OF>,
62}
63
64impl<IF, OF, IEP, OEP, T> Transformation<IEP, OEP> for SubfieldTransformer<IF, OF, T>
65where
66	IF: Field,
67	OF: Field,
68	IEP: PackedExtension<IF>,
69	OEP: PackedExtension<OF>,
70	T: Transformation<PackedSubfield<IEP, IF>, PackedSubfield<OEP, OF>>,
71{
72	fn transform(&self, input: &IEP) -> OEP {
73		OEP::cast_ext(self.inner_transform.transform(IEP::cast_base_ref(input)))
74	}
75}
76
77impl SerializeBytes for AESTowerField8b {
78	fn serialize(&self, write_buf: impl BufMut) -> Result<(), SerializationError> {
79		self.0.serialize(write_buf)
80	}
81}
82
83impl DeserializeBytes for AESTowerField8b {
84	fn deserialize(read_buf: impl Buf) -> Result<Self, SerializationError>
85	where
86		Self: Sized,
87	{
88		Ok(Self(DeserializeBytes::deserialize(read_buf)?))
89	}
90}
91
92#[cfg(test)]
93mod tests {
94	use binius_utils::{SerializeBytes, bytes::BytesMut};
95	use proptest::{arbitrary::any, proptest};
96	use rand::prelude::*;
97
98	use super::*;
99	use crate::{Random, binary_field::tests::is_binary_field_valid_generator};
100
101	fn check_square(f: impl Field) {
102		assert_eq!(f.square(), f * f);
103	}
104
105	proptest! {
106		#[test]
107		fn test_square_8(a in any::<u8>()) {
108			check_square(AESTowerField8b::from(a))
109		}
110	}
111
112	fn check_invert(f: impl Field) {
113		let inversed = f.invert();
114		if f.is_zero() {
115			assert!(inversed.is_none());
116		} else {
117			assert_eq!(inversed.unwrap() * f, Field::ONE);
118		}
119	}
120
121	proptest! {
122		#[test]
123		fn test_invert_8(a in any::<u8>()) {
124			check_invert(AESTowerField8b::from(a))
125		}
126	}
127
128	fn check_mul_by_one<F: Field>(f: F) {
129		assert_eq!(F::ONE * f, f);
130		assert_eq!(f * F::ONE, f);
131	}
132
133	fn check_commutative<F: Field>(f_1: F, f_2: F) {
134		assert_eq!(f_1 * f_2, f_2 * f_1);
135	}
136
137	fn check_associativity_and_lineraity<F: Field>(f_1: F, f_2: F, f_3: F) {
138		assert_eq!(f_1 * (f_2 * f_3), (f_1 * f_2) * f_3);
139		assert_eq!(f_1 * (f_2 + f_3), f_1 * f_2 + f_1 * f_3);
140	}
141
142	fn check_mul<F: Field>(f_1: F, f_2: F, f_3: F) {
143		check_mul_by_one(f_1);
144		check_mul_by_one(f_2);
145		check_mul_by_one(f_3);
146
147		check_commutative(f_1, f_2);
148		check_commutative(f_1, f_3);
149		check_commutative(f_2, f_3);
150
151		check_associativity_and_lineraity(f_1, f_2, f_3);
152		check_associativity_and_lineraity(f_1, f_3, f_2);
153		check_associativity_and_lineraity(f_2, f_1, f_3);
154		check_associativity_and_lineraity(f_2, f_3, f_1);
155		check_associativity_and_lineraity(f_3, f_1, f_2);
156		check_associativity_and_lineraity(f_3, f_2, f_1);
157	}
158
159	proptest! {
160		#[test]
161		fn test_mul_8(a in any::<u8>(), b in any::<u8>(), c in any::<u8>()) {
162			check_mul(AESTowerField8b::from(a), AESTowerField8b::from(b), AESTowerField8b::from(c))
163		}
164	}
165
166	#[test]
167	fn test_multiplicative_generators() {
168		assert!(is_binary_field_valid_generator::<AESTowerField8b>());
169	}
170
171	#[test]
172	fn test_serialization() {
173		let mut buffer = BytesMut::new();
174		let mut rng = StdRng::seed_from_u64(0);
175		let aes8 = AESTowerField8b::random(&mut rng);
176
177		SerializeBytes::serialize(&aes8, &mut buffer).unwrap();
178
179		let mut read_buffer = buffer.freeze();
180
181		assert_eq!(AESTowerField8b::deserialize(&mut read_buffer).unwrap(), aes8);
182	}
183}
binius_field/aes_field.rs

binius_field/
aes_field.rs
