binius_field/
polyval.rs

1// Copyright 2023-2025 Irreducible Inc.
2
3//! Binary field implementation of GF(2^128) with a modulus of X^128 + X^127 + X^126 + 1.
4
5use std::{
6	any::TypeId,
7	fmt::{self, Debug, Display, Formatter},
8	iter::{Product, Sum},
9	ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
10};
11
12use binius_utils::{
13	bytes::{Buf, BufMut},
14	iter::IterExtensions,
15	DeserializeBytes, SerializationError, SerializationMode, SerializeBytes,
16};
17use bytemuck::{Pod, TransparentWrapper, Zeroable};
18use rand::{Rng, RngCore};
19use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
20
21use super::{
22	aes_field::AESTowerField128b,
23	arithmetic_traits::InvertOrZero,
24	binary_field::{BinaryField, BinaryField128b, BinaryField1b, TowerField},
25	error::Error,
26	extension::ExtensionField,
27	underlier::WithUnderlier,
28};
29use crate::{
30	arch::packed_polyval_128::PackedBinaryPolyval1x128b,
31	arithmetic_traits::Square,
32	binary_field_arithmetic::{
33		invert_or_zero_using_packed, multiple_using_packed, square_using_packed,
34	},
35	linear_transformation::{FieldLinearTransformation, Transformation},
36	underlier::{IterationMethods, IterationStrategy, NumCast, UnderlierWithBitOps, U1},
37	Field,
38};
39
40#[derive(
41	Default,
42	Clone,
43	Copy,
44	PartialEq,
45	Eq,
46	PartialOrd,
47	Ord,
48	Hash,
49	Zeroable,
50	bytemuck::TransparentWrapper,
51)]
52#[repr(transparent)]
53pub struct BinaryField128bPolyval(pub(crate) u128);
54
55impl BinaryField128bPolyval {
56	#[inline]
57	pub fn new(value: u128) -> Self {
58		Self(value).to_montgomery()
59	}
60}
61
62unsafe impl WithUnderlier for BinaryField128bPolyval {
63	type Underlier = u128;
64
65	fn to_underlier(self) -> Self::Underlier {
66		TransparentWrapper::peel(self)
67	}
68
69	fn to_underlier_ref(&self) -> &Self::Underlier {
70		TransparentWrapper::peel_ref(self)
71	}
72
73	fn to_underlier_ref_mut(&mut self) -> &mut Self::Underlier {
74		TransparentWrapper::peel_mut(self)
75	}
76
77	fn to_underliers_ref(val: &[Self]) -> &[Self::Underlier] {
78		TransparentWrapper::peel_slice(val)
79	}
80
81	fn to_underliers_ref_mut(val: &mut [Self]) -> &mut [Self::Underlier] {
82		TransparentWrapper::peel_slice_mut(val)
83	}
84
85	fn from_underlier(val: Self::Underlier) -> Self {
86		TransparentWrapper::wrap(val)
87	}
88
89	fn from_underlier_ref(val: &Self::Underlier) -> &Self {
90		TransparentWrapper::wrap_ref(val)
91	}
92
93	fn from_underlier_ref_mut(val: &mut Self::Underlier) -> &mut Self {
94		TransparentWrapper::wrap_mut(val)
95	}
96
97	fn from_underliers_ref(val: &[Self::Underlier]) -> &[Self] {
98		TransparentWrapper::wrap_slice(val)
99	}
100
101	fn from_underliers_ref_mut(val: &mut [Self::Underlier]) -> &mut [Self] {
102		TransparentWrapper::wrap_slice_mut(val)
103	}
104}
105
106impl Neg for BinaryField128bPolyval {
107	type Output = Self;
108
109	#[inline]
110	fn neg(self) -> Self::Output {
111		self
112	}
113}
114
115impl Add<Self> for BinaryField128bPolyval {
116	type Output = Self;
117
118	#[allow(clippy::suspicious_arithmetic_impl)]
119	fn add(self, rhs: Self) -> Self::Output {
120		Self(self.0 ^ rhs.0)
121	}
122}
123
124impl Add<&Self> for BinaryField128bPolyval {
125	type Output = Self;
126
127	#[allow(clippy::suspicious_arithmetic_impl)]
128	fn add(self, rhs: &Self) -> Self::Output {
129		Self(self.0 ^ rhs.0)
130	}
131}
132
133impl Sub<Self> for BinaryField128bPolyval {
134	type Output = Self;
135
136	#[allow(clippy::suspicious_arithmetic_impl)]
137	fn sub(self, rhs: Self) -> Self::Output {
138		Self(self.0 ^ rhs.0)
139	}
140}
141
142impl Sub<&Self> for BinaryField128bPolyval {
143	type Output = Self;
144
145	#[allow(clippy::suspicious_arithmetic_impl)]
146	fn sub(self, rhs: &Self) -> Self::Output {
147		Self(self.0 ^ rhs.0)
148	}
149}
150
151impl Mul<Self> for BinaryField128bPolyval {
152	type Output = Self;
153
154	#[inline]
155	fn mul(self, rhs: Self) -> Self::Output {
156		multiple_using_packed::<PackedBinaryPolyval1x128b>(self, rhs)
157	}
158}
159
160impl Mul<&Self> for BinaryField128bPolyval {
161	type Output = Self;
162
163	#[inline]
164	fn mul(self, rhs: &Self) -> Self::Output {
165		self * *rhs
166	}
167}
168
169impl AddAssign<Self> for BinaryField128bPolyval {
170	#[inline]
171	fn add_assign(&mut self, rhs: Self) {
172		*self = *self + rhs;
173	}
174}
175
176impl AddAssign<&Self> for BinaryField128bPolyval {
177	#[inline]
178	fn add_assign(&mut self, rhs: &Self) {
179		*self = *self + rhs;
180	}
181}
182
183impl SubAssign<Self> for BinaryField128bPolyval {
184	#[inline]
185	fn sub_assign(&mut self, rhs: Self) {
186		*self = *self - rhs;
187	}
188}
189
190impl SubAssign<&Self> for BinaryField128bPolyval {
191	#[inline]
192	fn sub_assign(&mut self, rhs: &Self) {
193		*self = *self - rhs;
194	}
195}
196
197impl MulAssign<Self> for BinaryField128bPolyval {
198	#[inline]
199	fn mul_assign(&mut self, rhs: Self) {
200		*self = *self * rhs;
201	}
202}
203
204impl MulAssign<&Self> for BinaryField128bPolyval {
205	#[inline]
206	fn mul_assign(&mut self, rhs: &Self) {
207		*self = *self * rhs;
208	}
209}
210
211impl Sum<Self> for BinaryField128bPolyval {
212	#[inline]
213	fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
214		iter.fold(Self::ZERO, |acc, x| acc + x)
215	}
216}
217
218impl<'a> Sum<&'a Self> for BinaryField128bPolyval {
219	#[inline]
220	fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
221		iter.fold(Self::ZERO, |acc, x| acc + x)
222	}
223}
224
225impl Product<Self> for BinaryField128bPolyval {
226	#[inline]
227	fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
228		iter.fold(Self::ONE, |acc, x| acc * x)
229	}
230}
231
232impl<'a> Product<&'a Self> for BinaryField128bPolyval {
233	#[inline]
234	fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
235		iter.fold(Self::ONE, |acc, x| acc * x)
236	}
237}
238
239impl ConstantTimeEq for BinaryField128bPolyval {
240	#[inline]
241	fn ct_eq(&self, other: &Self) -> Choice {
242		self.0.ct_eq(&other.0)
243	}
244}
245
246impl ConditionallySelectable for BinaryField128bPolyval {
247	#[inline]
248	fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
249		Self(ConditionallySelectable::conditional_select(&a.0, &b.0, choice))
250	}
251}
252
253impl Square for BinaryField128bPolyval {
254	#[inline]
255	fn square(self) -> Self {
256		square_using_packed::<PackedBinaryPolyval1x128b>(self)
257	}
258}
259
260impl Field for BinaryField128bPolyval {
261	const ZERO: Self = Self(0);
262	const ONE: Self = Self(0xc2000000000000000000000000000001);
263	const CHARACTERISTIC: usize = 2;
264
265	fn random(mut rng: impl RngCore) -> Self {
266		Self(rng.gen())
267	}
268
269	fn double(&self) -> Self {
270		Self(0)
271	}
272}
273
274impl InvertOrZero for BinaryField128bPolyval {
275	#[inline]
276	fn invert_or_zero(self) -> Self {
277		invert_or_zero_using_packed::<PackedBinaryPolyval1x128b>(self)
278	}
279}
280
281impl From<u128> for BinaryField128bPolyval {
282	#[inline]
283	fn from(value: u128) -> Self {
284		Self(value)
285	}
286}
287
288impl From<BinaryField128bPolyval> for u128 {
289	#[inline]
290	fn from(value: BinaryField128bPolyval) -> Self {
291		value.0
292	}
293}
294
295impl Display for BinaryField128bPolyval {
296	fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
297		write!(f, "0x{repr:0>32x}", repr = self.from_montgomery().0)
298	}
299}
300
301impl Debug for BinaryField128bPolyval {
302	fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
303		write!(f, "BinaryField128bPolyval({})", self)
304	}
305}
306
307impl BinaryField128bPolyval {
308	#[inline]
309	pub(super) fn to_montgomery(self) -> Self {
310		self * Self(0x1e563df92ea7081b4563df92ea7081b5)
311	}
312
313	// Clippy wants us to use a reference here as API design
314	// but we can ignore it as we'd need to copy otherwise.
315	#[allow(clippy::wrong_self_convention)]
316	pub(super) fn from_montgomery(self) -> Self {
317		self * Self(1)
318	}
319}
320
321unsafe impl Pod for BinaryField128bPolyval {}
322
323impl TryInto<BinaryField1b> for BinaryField128bPolyval {
324	type Error = ();
325
326	#[inline]
327	fn try_into(self) -> Result<BinaryField1b, Self::Error> {
328		let result = CtOption::new(BinaryField1b::ZERO, self.ct_eq(&Self::ZERO))
329			.or_else(|| CtOption::new(BinaryField1b::ONE, self.ct_eq(&Self::ONE)));
330		Option::from(result).ok_or(())
331	}
332}
333
334impl From<BinaryField1b> for BinaryField128bPolyval {
335	#[inline]
336	fn from(value: BinaryField1b) -> Self {
337		debug_assert_eq!(Self::ZERO, Self(0));
338
339		Self(Self::ONE.0 & u128::fill_with_bit(value.val().val()))
340	}
341}
342
343impl Add<BinaryField1b> for BinaryField128bPolyval {
344	type Output = Self;
345
346	#[inline]
347	fn add(self, rhs: BinaryField1b) -> Self::Output {
348		self + Self::from(rhs)
349	}
350}
351
352impl Sub<BinaryField1b> for BinaryField128bPolyval {
353	type Output = Self;
354
355	#[inline]
356	fn sub(self, rhs: BinaryField1b) -> Self::Output {
357		self - Self::from(rhs)
358	}
359}
360
361impl Mul<BinaryField1b> for BinaryField128bPolyval {
362	type Output = Self;
363
364	#[inline]
365	#[allow(clippy::suspicious_arithmetic_impl)]
366	fn mul(self, rhs: BinaryField1b) -> Self::Output {
367		crate::tracing::trace_multiplication!(BinaryField128bPolyval, BinaryField1b);
368
369		Self(self.0 & u128::fill_with_bit(u8::from(rhs.0)))
370	}
371}
372
373impl AddAssign<BinaryField1b> for BinaryField128bPolyval {
374	#[inline]
375	fn add_assign(&mut self, rhs: BinaryField1b) {
376		*self = *self + rhs;
377	}
378}
379
380impl SubAssign<BinaryField1b> for BinaryField128bPolyval {
381	#[inline]
382	fn sub_assign(&mut self, rhs: BinaryField1b) {
383		*self = *self - rhs;
384	}
385}
386
387impl MulAssign<BinaryField1b> for BinaryField128bPolyval {
388	#[inline]
389	fn mul_assign(&mut self, rhs: BinaryField1b) {
390		*self = *self * rhs;
391	}
392}
393
394impl Add<BinaryField128bPolyval> for BinaryField1b {
395	type Output = BinaryField128bPolyval;
396
397	#[inline]
398	fn add(self, rhs: BinaryField128bPolyval) -> Self::Output {
399		rhs + self
400	}
401}
402
403impl Sub<BinaryField128bPolyval> for BinaryField1b {
404	type Output = BinaryField128bPolyval;
405
406	#[inline]
407	fn sub(self, rhs: BinaryField128bPolyval) -> Self::Output {
408		rhs - self
409	}
410}
411
412impl Mul<BinaryField128bPolyval> for BinaryField1b {
413	type Output = BinaryField128bPolyval;
414
415	#[inline]
416	fn mul(self, rhs: BinaryField128bPolyval) -> Self::Output {
417		rhs * self
418	}
419}
420
421impl ExtensionField<BinaryField1b> for BinaryField128bPolyval {
422	const LOG_DEGREE: usize = 7;
423
424	#[inline]
425	fn basis(i: usize) -> Result<Self, Error> {
426		if i >= 128 {
427			return Err(Error::ExtensionDegreeMismatch);
428		}
429		Ok(Self::new(1 << i))
430	}
431
432	#[inline]
433	fn from_bases_sparse(
434		base_elems: impl IntoIterator<Item = BinaryField1b>,
435		log_stride: usize,
436	) -> Result<Self, Error> {
437		if log_stride != 7 {
438			return Err(Error::ExtensionDegreeMismatch);
439		}
440		// REVIEW: is this actually correct for a monomial field?
441		let value = base_elems
442			.into_iter()
443			.enumerate()
444			.fold(0, |value, (i, elem)| value | (u128::from(elem.0) << i));
445		Ok(Self::new(value))
446	}
447
448	#[inline]
449	fn iter_bases(&self) -> impl Iterator<Item = BinaryField1b> {
450		IterationMethods::<U1, Self::Underlier>::value_iter(self.0)
451			.map_skippable(BinaryField1b::from)
452	}
453
454	#[inline]
455	fn into_iter_bases(self) -> impl Iterator<Item = BinaryField1b> {
456		IterationMethods::<U1, Self::Underlier>::value_iter(self.0)
457			.map_skippable(BinaryField1b::from)
458	}
459
460	#[inline]
461	unsafe fn get_base_unchecked(&self, i: usize) -> BinaryField1b {
462		BinaryField1b(U1::num_cast_from(self.0 >> i))
463	}
464}
465
466impl SerializeBytes for BinaryField128bPolyval {
467	fn serialize(
468		&self,
469		write_buf: impl BufMut,
470		mode: SerializationMode,
471	) -> Result<(), SerializationError> {
472		match mode {
473			SerializationMode::Native => self.0.serialize(write_buf, mode),
474			SerializationMode::CanonicalTower => {
475				BinaryField128b::from(*self).serialize(write_buf, mode)
476			}
477		}
478	}
479}
480
481impl DeserializeBytes for BinaryField128bPolyval {
482	fn deserialize(read_buf: impl Buf, mode: SerializationMode) -> Result<Self, SerializationError>
483	where
484		Self: Sized,
485	{
486		match mode {
487			SerializationMode::Native => Ok(Self(DeserializeBytes::deserialize(read_buf, mode)?)),
488			SerializationMode::CanonicalTower => {
489				Ok(Self::from(BinaryField128b::deserialize(read_buf, mode)?))
490			}
491		}
492	}
493}
494
495impl BinaryField for BinaryField128bPolyval {
496	const MULTIPLICATIVE_GENERATOR: Self = Self(0x72bdf2504ce49c03105433c1c25a4a7);
497}
498
499impl TowerField for BinaryField128bPolyval {
500	type Canonical = BinaryField128b;
501
502	fn min_tower_level(self) -> usize {
503		match self {
504			Self::ZERO | Self::ONE => 0,
505			_ => 7,
506		}
507	}
508
509	fn mul_primitive(self, _iota: usize) -> Result<Self, Error> {
510		// This method could be implemented by multiplying by isomorphic alpha value
511		// But it's not being used as for now
512		unimplemented!()
513	}
514}
515
516pub const BINARY_TO_POLYVAL_TRANSFORMATION: FieldLinearTransformation<BinaryField128bPolyval> =
517	FieldLinearTransformation::new_const(&[
518		BinaryField128bPolyval(0xc2000000000000000000000000000001),
519		BinaryField128bPolyval(0x21a09a4bf26aadcd3eb19c5f1a06b528),
520		BinaryField128bPolyval(0xe62f1a804db43b94852cef0e61d7353d),
521		BinaryField128bPolyval(0xadcde131ca862a6ba378ea68e992a5b6),
522		BinaryField128bPolyval(0x5474611d07bdcd1f72e9bdc82ec4fe6c),
523		BinaryField128bPolyval(0xf9a472d4a4965f4caa3532aa6258c986),
524		BinaryField128bPolyval(0x10bd76c920260f81877681ed1a50b210),
525		BinaryField128bPolyval(0xe7f3264523858ca36ef84934fdd225f2),
526		BinaryField128bPolyval(0x586704bda927015fedb8ddceb7f825d6),
527		BinaryField128bPolyval(0x552dab8acfd831aeb65f8aaec9cef096),
528		BinaryField128bPolyval(0xeccdac666a363defde6792e475892fb3),
529		BinaryField128bPolyval(0x4a621d01701247f6e4a8327e33d95aa2),
530		BinaryField128bPolyval(0x8ed5002fed1f4b9a9a11840f87149e2d),
531		BinaryField128bPolyval(0x3c65abbd41c759f0302467db5a791e09),
532		BinaryField128bPolyval(0xc2df68a5949a96b3aa643692e93caaab),
533		BinaryField128bPolyval(0x4455027df88c165117daf9822eb57383),
534		BinaryField128bPolyval(0xc50e3a207f91d7cd6dd1e116d55455fb),
535		BinaryField128bPolyval(0xc89c3920b9b24b755fd08543d8caf5a2),
536		BinaryField128bPolyval(0xfa583eb935de76a2ec180360b6548830),
537		BinaryField128bPolyval(0xc4d3d3b9938f3af77800a5cd03690171),
538		BinaryField128bPolyval(0xe1faff3b895be1e2bec91c0836143b44),
539		BinaryField128bPolyval(0x256bd50f868b82cf1c83552eeb1cd844),
540		BinaryField128bPolyval(0x82fd35d590073ae9595cab38e9b59d79),
541		BinaryField128bPolyval(0x08dadd230bc90e192304a2533cdce9e6),
542		BinaryField128bPolyval(0xf4400f37acedc7d9502abeff6cead84c),
543		BinaryField128bPolyval(0x5438d34e2b5b90328cc88b7384deedfb),
544		BinaryField128bPolyval(0x7d798db71ef80a3e447cd7d1d4a0385d),
545		BinaryField128bPolyval(0xa50d5ef4e33979db8012303dc09cbf35),
546		BinaryField128bPolyval(0x91c4b5e29de5759e0bb337efbc5b8115),
547		BinaryField128bPolyval(0xbbb0d4aaba0fab72848f461ed0a4b110),
548		BinaryField128bPolyval(0x3c9de86b9a306d6d11cc078904076865),
549		BinaryField128bPolyval(0xb5f43a166aa1f15f99db6d689ca1b370),
550		BinaryField128bPolyval(0xa26153cb8c150af8243ecbd46378e59e),
551		BinaryField128bPolyval(0xccaa154bab1dd7aca876f81fe0c950ab),
552		BinaryField128bPolyval(0x4185b7e3ee1dddbc761a6139cdb07755),
553		BinaryField128bPolyval(0x2c9f95285b7aa574653ed207337325f2),
554		BinaryField128bPolyval(0xc8ba616ab131bfd242195c4c82d54dbb),
555		BinaryField128bPolyval(0x2a9b07221a34865faa36a28da1ab1c24),
556		BinaryField128bPolyval(0x7e6e572804b548a88b92900e0196dd39),
557		BinaryField128bPolyval(0x4e9060deff44c9ef9882a0015debd575),
558		BinaryField128bPolyval(0x00a3a4d8c163c95ac7ac9a5b424e1c65),
559		BinaryField128bPolyval(0xf67c7eb5dde73d96f8f5eecba6033679),
560		BinaryField128bPolyval(0x54d78d187bbb57d19b536094ba539fde),
561		BinaryField128bPolyval(0x76c553699edc5d4a033139975ab7f264),
562		BinaryField128bPolyval(0x74ae8da43b2f587df3e41bbf5c6be650),
563		BinaryField128bPolyval(0x8a2941b59774c41acd850aa6098e5fd2),
564		BinaryField128bPolyval(0x9ddf65660a6f8f3c0058165a063de84c),
565		BinaryField128bPolyval(0xbb52da733635cc3d1ff02ef96ee64cf3),
566		BinaryField128bPolyval(0x564032a0d5d3773b7b7ed18bebf1c668),
567		BinaryField128bPolyval(0xef5c765e64b24b1b00222054ff0040ef),
568		BinaryField128bPolyval(0xade661c18acba6233d484726e6249bee),
569		BinaryField128bPolyval(0x9939ba35c969cdeea29f2ef849c2d170),
570		BinaryField128bPolyval(0x2b100b39761d4f23eb42d05b80174ce2),
571		BinaryField128bPolyval(0xfbc25b179830f9eec765bd6229125d6c),
572		BinaryField128bPolyval(0xb58e089ebe7ad0b2698e30184ab93141),
573		BinaryField128bPolyval(0x53874933a148be94d12025afa876234c),
574		BinaryField128bPolyval(0x41bbc7902188f4e9880f1d81fa580ffb),
575		BinaryField128bPolyval(0xea4199916a5d127d25da1fe777b2dcbb),
576		BinaryField128bPolyval(0xe7bc816547efbe987d9359ee0de0c287),
577		BinaryField128bPolyval(0x02e0f1f67e7139835892155a7addd9da),
578		BinaryField128bPolyval(0xdc6beb6eade9f875e74955ca950af235),
579		BinaryField128bPolyval(0x786d616edeadfa356453a78d8f103230),
580		BinaryField128bPolyval(0xe84e70191accaddac8034da936737487),
581		BinaryField128bPolyval(0x012b8669ff3f451e5363edfddd37fb3c),
582		BinaryField128bPolyval(0x756209f0893e96877833c194b9c943a0),
583		BinaryField128bPolyval(0xb2ac9efc9a1891369f63bd1e0d1439ac),
584		BinaryField128bPolyval(0x4de88e9a5bbb4c3df650cc3994c3d2d8),
585		BinaryField128bPolyval(0x8de7b5c85c07f3359849e7c85e426b54),
586		BinaryField128bPolyval(0xcadd54ae6a7e72a4f184e6761cf226d4),
587		BinaryField128bPolyval(0xcdb182fb8d95496f55b5f3952f81bc30),
588		BinaryField128bPolyval(0x40013bc3c81722753a05bb2aca01a02e),
589		BinaryField128bPolyval(0x704e7ce55e9033883e97351591adf18a),
590		BinaryField128bPolyval(0xf330cd9a74a5e884988c3f36567d26f4),
591		BinaryField128bPolyval(0x18f4535304c0d74ac3bdf09d78cbde50),
592		BinaryField128bPolyval(0xfe739c97fc26bed28885b838405c7e7e),
593		BinaryField128bPolyval(0x492479260f2dcd8af980c3d74b3ec345),
594		BinaryField128bPolyval(0x96b6440a34de0aad4ea2f744396691af),
595		BinaryField128bPolyval(0x98355d1b4f7cfb03960a59aa564a7a26),
596		BinaryField128bPolyval(0x2703fda0532095ca8b1886b12ca37d64),
597		BinaryField128bPolyval(0x59c9dabe49bebf6b468c3c120f142822),
598		BinaryField128bPolyval(0xf8f3c35c671bac841b14381a592e6cdd),
599		BinaryField128bPolyval(0xd7b888791bd83b13d80d2e9324894861),
600		BinaryField128bPolyval(0x113ab0405354dd1c5aab9658137fa73f),
601		BinaryField128bPolyval(0xae56192d5e9c309e461f797121b28ce6),
602		BinaryField128bPolyval(0xb7927ec7a84c2e04811a6dac6b997783),
603		BinaryField128bPolyval(0x9e2f8d67fc600703ba9b4189ce751cb4),
604		BinaryField128bPolyval(0x574e95df2d8bb9e2c8fc29729eb723ca),
605		BinaryField128bPolyval(0x38bc6fc47739c06cd9fa20f9a5088f26),
606		BinaryField128bPolyval(0x69d3b9b1d9483174b3c38d8f95ce7a5f),
607		BinaryField128bPolyval(0xd6e4bb147cc82b6e90e27e882f18640d),
608		BinaryField128bPolyval(0x027338db641804d985cd9fece12f7adc),
609		BinaryField128bPolyval(0x523cb73968169ccce76f523928c4364e),
610		BinaryField128bPolyval(0xcdcf898117f927208a11b0dcc941f2f6),
611		BinaryField128bPolyval(0xc908287814c8cba67f7892fec7a5b217),
612		BinaryField128bPolyval(0x92b99988bb26215d104968d4cbbb285a),
613		BinaryField128bPolyval(0x4dbca8fd835d00ea4b95692534ef5068),
614		BinaryField128bPolyval(0xcd8b92c8a6e0e65e167a2b851f32fd9c),
615		BinaryField128bPolyval(0xc3473dfda9f97d6ac1e2d544628e7845),
616		BinaryField128bPolyval(0x0260e7badc64dbfde0dc39a240365722),
617		BinaryField128bPolyval(0x3966125b40fe2bca9719c80e41953868),
618		BinaryField128bPolyval(0xac0211506eda3cba57b709a360d4a2c7),
619		BinaryField128bPolyval(0x0e4f0e47d02fedd15b337fefa219c52b),
620		BinaryField128bPolyval(0x1d5907ccdc659f7aace675511f754ee3),
621		BinaryField128bPolyval(0x4ad5b368eaddc4bb097284863b2a5b6e),
622		BinaryField128bPolyval(0x2eae07273b8c4fc5cef553a4a46cde5b),
623		BinaryField128bPolyval(0x096a310e7b1e3a3179d4a3b5d8dd9396),
624		BinaryField128bPolyval(0x8c81362eeb1656a91dde08d05018a353),
625		BinaryField128bPolyval(0x387e59e44cc0d53fecf7f057b6fdba0b),
626		BinaryField128bPolyval(0x9d29670bbd0e8051ac82d91ca97561d6),
627		BinaryField128bPolyval(0xaf1310d0f5cac4e89714e48065be74a4),
628		BinaryField128bPolyval(0x9b684a3865c2b59c411d14182a36fb6b),
629		BinaryField128bPolyval(0x3e7de163516ffdcaca22b4e848340fbe),
630		BinaryField128bPolyval(0x3c37dbe331de4b0dc2f5db315d5e7fda),
631		BinaryField128bPolyval(0x19e7f4b53ff86990e3d5a1c40c3769a0),
632		BinaryField128bPolyval(0x56469ab32b2b82e8cc93fdb1b14a4775),
633		BinaryField128bPolyval(0x9c01cefde47816300d8ad49d260bb71b),
634		BinaryField128bPolyval(0x6100101b8cebde7381366fec1e4e52c0),
635		BinaryField128bPolyval(0xa28d30c3cbd8b69632143fa65158ee4f),
636		BinaryField128bPolyval(0x3db7a902ec509e58151c45f71eee6368),
637		BinaryField128bPolyval(0x42d5a505e8ab70097107d37d79ebbaba),
638		BinaryField128bPolyval(0xe47b83247cb2b162c7d6d15c84cca8ce),
639		BinaryField128bPolyval(0x076caf0e23541c753e4c87ff505737a5),
640		BinaryField128bPolyval(0x590a8d1cdbd17ae83980f5d1d3b84a89),
641		BinaryField128bPolyval(0x77d649ff61a7cd0da53497edd34c4204),
642		BinaryField128bPolyval(0xefbe0c34eeab379ea4a8feed84fd3993),
643		BinaryField128bPolyval(0x90540cf7957a8a3051629cdde777f968),
644		BinaryField128bPolyval(0x8749050496dd288244c49c70aa92831f),
645		BinaryField128bPolyval(0x0fc80b1d600406b2370368d94947961a),
646	]);
647
648impl From<BinaryField128b> for BinaryField128bPolyval {
649	fn from(value: BinaryField128b) -> Self {
650		BINARY_TO_POLYVAL_TRANSFORMATION.transform(&value)
651	}
652}
653
654pub const POLYVAL_TO_BINARY_TRANSFORMATION: FieldLinearTransformation<BinaryField128b> =
655	FieldLinearTransformation::new_const(&[
656		BinaryField128b(0x66e1d645d7eb87dca8fc4d30a32dadcc),
657		BinaryField128b(0x53ca87ba77172fd8c5675d78c59c1901),
658		BinaryField128b(0x1a9cf63d31827dcda15acb755a948567),
659		BinaryField128b(0xa8f28bdf6d29cee2474b0401a99f6c0a),
660		BinaryField128b(0x4eefa9efe87ed19c06b39ca9799c8d73),
661		BinaryField128b(0x06ec578f505abf1e9885a6b2bc494f3e),
662		BinaryField128b(0x70ecdfe1f601f8509a96d3fb9cd3348a),
663		BinaryField128b(0xcb0d16fc7f13733deb25f618fc3faf28),
664		BinaryField128b(0x4e9a97aa2c84139ffcb578115fcbef3c),
665		BinaryField128b(0xc6de6210afe8c6bd9a441bffe19219ad),
666		BinaryField128b(0x73e3e8a7c59748601be5bf1e30c488d3),
667		BinaryField128b(0x1f6d67e2e64bd6c4b39e7f4bb37dce9c),
668		BinaryField128b(0xc34135d567eada885f5095b4c155f3b5),
669		BinaryField128b(0x23f165958d59a55e4790b8e2e37330e4),
670		BinaryField128b(0x4f2be978f16908e405b88802add08d17),
671		BinaryField128b(0x6442b00f5bbf4009907936513c3a7d45),
672		BinaryField128b(0xac63f0397d911a7a5d61b9f18137026f),
673		BinaryField128b(0x8e70543ae0e43313edf07cbc6698e144),
674		BinaryField128b(0xcb417a646d59f652aa5a07984066d026),
675		BinaryField128b(0xf028de8dd616318735bd8f76de7bb84e),
676		BinaryField128b(0x2e03a12472d21599f15b4bcaa9bf186c),
677		BinaryField128b(0x54a376cc03e5b2cfa27d8e48d1b9ca76),
678		BinaryField128b(0xd22894c253031b1b201b87da07cb58ae),
679		BinaryField128b(0x6bc1416afea6308ff77d902dd5d2a563),
680		BinaryField128b(0x9958ecd28adbebf850055f8ac3095121),
681		BinaryField128b(0x595a1b37062233d7e6bb6f54c227fb91),
682		BinaryField128b(0x41ffcfcdda4583c4f671558ee315d809),
683		BinaryField128b(0x780c2490f3e5cb4763e982ec4b3e6ea2),
684		BinaryField128b(0xf7a450b35931fa76722a6b9037b6db34),
685		BinaryField128b(0xe21991100e84821328592772430ad07e),
686		BinaryField128b(0x360d4079f62863cc60c65ec87d6f9277),
687		BinaryField128b(0xd898bfa0b076cc4eaca590e7a60dbe92),
688		BinaryField128b(0xcaacddd5e114fe5c2e1647fc34b549bf),
689		BinaryField128b(0x3042e34911c28e90617776ddb2d3f888),
690		BinaryField128b(0x3728a3b0da53cdfecfd8455b13cb9b14),
691		BinaryField128b(0x2f2eb3d5bc7b2c48a7c643bffbddc6b2),
692		BinaryField128b(0x3b71a5c04010c0aa501b04302706b908),
693		BinaryField128b(0x0701845b090e79bb9be54df766e48c51),
694		BinaryField128b(0x1e9eac7bf45b14c8db06fcfff7408f78),
695		BinaryField128b(0x6b1b8e39a339423d0eb3bef69eee8b0b),
696		BinaryField128b(0x8b06616385967df95d3a99cff1edcf0a),
697		BinaryField128b(0x5d921137890a3ded58e1dd1a51fe6a30),
698		BinaryField128b(0x828ed6fba42805b2628b705d38121acc),
699		BinaryField128b(0x9b7a95220e9d5b0ff70ecb6116cabd81),
700		BinaryField128b(0x0eb9055cb11711ed047f136cab751c88),
701		BinaryField128b(0xd6f590777c17a6d0ca451290f7d5c78a),
702		BinaryField128b(0x401a922a6461fbe691f910cb0893e71f),
703		BinaryField128b(0x15a549308bc53902c927ebad9ed253f7),
704		BinaryField128b(0x45dccafc72a584480f340a43f11a1b84),
705		BinaryField128b(0x19d2a2c057d60656e6d3e20451335d5b),
706		BinaryField128b(0x035af143a5827a0f99197c8b9a811454),
707		BinaryField128b(0x7ee35d174ad7cc692191fd0e013f163a),
708		BinaryField128b(0xc4c0401d841f965c9599fac8831effa9),
709		BinaryField128b(0x63e809a843fc04f84acfca3fc5630691),
710		BinaryField128b(0xdb2f3301594e3de49fb7d78e2d6643c4),
711		BinaryField128b(0x1b31772535984ef93d709319cc130a7c),
712		BinaryField128b(0x036dc9c884cd6d6c918071b62a0593f3),
713		BinaryField128b(0x4700cd0e81c88045132360b078027103),
714		BinaryField128b(0xdfa3f35eb236ea63b0350e17ed2d625d),
715		BinaryField128b(0xf0fd7c7760099f1ac28be91822978e15),
716		BinaryField128b(0x852a1eba3ad160e95034e9eed1f21205),
717		BinaryField128b(0x4a07dd461892df45ca9efee1701763c3),
718		BinaryField128b(0xadbbaa0add4c82fe85fd61b42f707384),
719		BinaryField128b(0x5c63d0673f33c0f2c231db13f0e15600),
720		BinaryField128b(0x24ddc1516501135626e0e794dd4b3076),
721		BinaryField128b(0xb60c601bbf72924e38afd02d201fb05b),
722		BinaryField128b(0x2ef68918f416caca84334bcf70649aeb),
723		BinaryField128b(0x0b72a3124c504bcad815534c707343f2),
724		BinaryField128b(0xcfd8b2076040c43d5d396f8523d80fe0),
725		BinaryField128b(0x098d9daf64154a63504192bb27cc65e1),
726		BinaryField128b(0x3ae44070642e6720283621f8fb6a6704),
727		BinaryField128b(0x19cd9b2843d0ff936bfe2b373f47fd05),
728		BinaryField128b(0x451e2e4159c78e65db10450431d26122),
729		BinaryField128b(0x797b753e29b9d0e9423b36807c70f3ae),
730		BinaryField128b(0xa8d0e8ba9bb634f6ea30600915664e22),
731		BinaryField128b(0xdf8c74bbd66f86809c504cb944475b0a),
732		BinaryField128b(0x32831a457ced3a417a5a94d498128018),
733		BinaryField128b(0x1aca728985936a6147119b9b5f00350e),
734		BinaryField128b(0x6f436d64b4ee1a556b66764ed05bb1db),
735		BinaryField128b(0x25930eaed3fd982915e483cb21e5a1a2),
736		BinaryField128b(0x21735f5eb346e56006bf1d7e151780ab),
737		BinaryField128b(0x55fc6f607f10e17f805eb16d7bd5345c),
738		BinaryField128b(0x4b4d289591f878114965292af4aeb57e),
739		BinaryField128b(0x30608bc7444bcbaff67998c1883c1cf3),
740		BinaryField128b(0xa12a72abe4152e4a657c6e6395404343),
741		BinaryField128b(0x7579186d4e0959dec73f9cd68fb0e2fb),
742		BinaryField128b(0xb5560ce63f7894cc965c822892b7bfda),
743		BinaryField128b(0x6b06d7165072861eba63d9fd645995d7),
744		BinaryField128b(0x359f439f5ec9107dde3c8ef8f9bf4e29),
745		BinaryField128b(0xcbfe7985c6006a46105821cd8b55b06b),
746		BinaryField128b(0x2110b3b51f5397ef1129fb9076474061),
747		BinaryField128b(0x1928478b6f3275c944c33b275c388c47),
748		BinaryField128b(0x23f978e6a0a54802437111aa4652421a),
749		BinaryField128b(0xe8c526bf924dc5cd1dd32dbedd310f5b),
750		BinaryField128b(0xa0ac29f901f79ed5f43c73d22a05c8e4),
751		BinaryField128b(0x55e0871c6e97408f47f4635b747145ea),
752		BinaryField128b(0x6c2114c3381f53667d3c2dfefd1ebcb3),
753		BinaryField128b(0x42d23c18722fbd58863c3aceaaa3eef7),
754		BinaryField128b(0xbb0821ab38d5de133838f8408a72fdf1),
755		BinaryField128b(0x035d7239054762b131fa387773bb9153),
756		BinaryField128b(0x8fa898aafe8b154f9ab652e8979139e7),
757		BinaryField128b(0x6a383e5cd4a16923c658193f16cb726c),
758		BinaryField128b(0x9948caa8c6cefb0182022f32ae3f68b9),
759		BinaryField128b(0x8d2a8decf9855bd4df7bac577ed73b44),
760		BinaryField128b(0x09c7b8300f0f984259d548c5aa959879),
761		BinaryField128b(0x92e16d2d24e070efdca8b8e134047afc),
762		BinaryField128b(0x47d8621457f4118aaf24877fb5031512),
763		BinaryField128b(0x25576941a55f0a0c19583a966a85667f),
764		BinaryField128b(0xb113cad79cd35f2e83fda3bc6285a8dc),
765		BinaryField128b(0xc76968eecb2748d0c3e6318431ffe580),
766		BinaryField128b(0x7211122aa7e7f6fe39e6618395b68416),
767		BinaryField128b(0x88463599bf7d3e92f450d00a45146d11),
768		BinaryField128b(0x6e12b7d5adf95da33bbb7f79a18ee123),
769		BinaryField128b(0xe0a98ac4025bc568eaca7e7b7280ff16),
770		BinaryField128b(0xc13fc79f6c35048df274057ac892ff77),
771		BinaryField128b(0x93c1a3145d4e47dee39cae4de47eb505),
772		BinaryField128b(0x780064be3036df98f1e5d7c53bdbd52b),
773		BinaryField128b(0x48c467b5cec265628b709172ecaff561),
774		BinaryField128b(0x5bbbab77ce5552ff7682094560524a7e),
775		BinaryField128b(0x551537ef6048831fb128fec4e4a23a63),
776		BinaryField128b(0xe7ef397fcc095ead439317a13568b284),
777		BinaryField128b(0xbc5d2927eac0a720f9d75d62d92c6332),
778		BinaryField128b(0x3bfeb420021f93e9b2bc992b5b59e61e),
779		BinaryField128b(0xc651dc438e2f1bc64af1b7307b574ed9),
780		BinaryField128b(0xbfe0a17ee2b777542a1ddb55413a4e43),
781		BinaryField128b(0xa062da2427df3d1a7dfc01c05d732a32),
782		BinaryField128b(0x1e4889fd72b70ecf93417ba0b085e1e8),
783		BinaryField128b(0xc4f4769f4f9c2e33c26a6bf2ca842f17),
784	]);
785
786impl From<BinaryField128bPolyval> for BinaryField128b {
787	fn from(value: BinaryField128bPolyval) -> Self {
788		POLYVAL_TO_BINARY_TRANSFORMATION.transform(&value)
789	}
790}
791
792pub const AES_TO_POLYVAL_TRANSFORMATION: FieldLinearTransformation<BinaryField128bPolyval> =
793	FieldLinearTransformation::new_const(&[
794		BinaryField128bPolyval(0xc2000000000000000000000000000001),
795		BinaryField128bPolyval(0xe632e878241983acfe888a04c4d9a761),
796		BinaryField128bPolyval(0xac11ddf4a4b79d5c48ac4c527597b579),
797		BinaryField128bPolyval(0x6b9e5d3f1b690b05f3313f030e46356c),
798		BinaryField128bPolyval(0x2b04f6e5ed1de8f556e7d64ddd06e9cb),
799		BinaryField128bPolyval(0x31001e7abbe11a74c26378b8a5589564),
800		BinaryField128bPolyval(0xa7698d9fd5f16f53cb2ea07a2e92f955),
801		BinaryField128bPolyval(0xfc2bf21f1b48c91511a841fb19894992),
802		BinaryField128bPolyval(0x586704bda927015fedb8ddceb7f825d6),
803		BinaryField128bPolyval(0x141f1af5b6fc687390fa434e9b3df535),
804		BinaryField128bPolyval(0xe2fab31ae2a86c482d15591868e50692),
805		BinaryField128bPolyval(0x5b1ab4f647466009452d4152d4a2d9b7),
806		BinaryField128bPolyval(0x5e0f7136a0b09b8039655d2dea094bf2),
807		BinaryField128bPolyval(0x6f2075bc8788f28152a66d96ce4680bb),
808		BinaryField128bPolyval(0x4140c7bd1f7aedd86b92e5fd101ee1c6),
809		BinaryField128bPolyval(0xdde2a8ec4d0e54eeb5a4a25f51c6e4fa),
810		BinaryField128bPolyval(0xc50e3a207f91d7cd6dd1e116d55455fb),
811		BinaryField128bPolyval(0xfa1ac734a9812f783652ef8b68356a41),
812		BinaryField128bPolyval(0x36513023ad98424cb71c04fe89e160a7),
813		BinaryField128bPolyval(0x049537ba21f47f9b04d482dde77f1d35),
814		BinaryField128bPolyval(0x62da2377f5423631f244f3eb099cf2b7),
815		BinaryField128bPolyval(0x4a23f578b5ea2846dcc6c290ef1e8aaa),
816		BinaryField128bPolyval(0x6e95c9eedf7f47b3d594d365d23f0664),
817		BinaryField128bPolyval(0xd2a1e8b6757668d5c29a321b50d6f02d),
818		BinaryField128bPolyval(0xf4400f37acedc7d9502abeff6cead84c),
819		BinaryField128bPolyval(0xf200b20bda2bad094b52961d78c3b76d),
820		BinaryField128bPolyval(0x6d80e955976082ba5db58a84889d3418),
821		BinaryField128bPolyval(0x44c1b7aca2c318b69501d626d8e3e1be),
822		BinaryField128bPolyval(0xfc140c4a4801a6f1ca47bea4142a8e09),
823		BinaryField128bPolyval(0xe7dc049975b85a68922acd362cba0aae),
824		BinaryField128bPolyval(0x0d2181f080634f18c69d05ea5068dcc7),
825		BinaryField128bPolyval(0x66b185642341f6a71c11a443ec30bcfa),
826		BinaryField128bPolyval(0xa26153cb8c150af8243ecbd46378e59e),
827		BinaryField128bPolyval(0x8f3b44831e624145fb0b4dffddbd0338),
828		BinaryField128bPolyval(0x238a42154a23b1278ba6133fa32887d2),
829		BinaryField128bPolyval(0xaea5e0bd0f23bb3755ca8a198e51a02c),
830		BinaryField128bPolyval(0x382af0a162eb58f6888bd591d34850ee),
831		BinaryField128bPolyval(0x7c7ab1035fd703fdaef544d7f152f9ff),
832		BinaryField128bPolyval(0xd81f70c2928c2a2e45c3ff8900f225b7),
833		BinaryField128bPolyval(0x05d5f641d32186b75064f07fefaade44),
834		BinaryField128bPolyval(0x00a3a4d8c163c95ac7ac9a5b424e1c65),
835		BinaryField128bPolyval(0xdc951260493c96fca603481ab501d438),
836		BinaryField128bPolyval(0x99400402d352c6a6879277fa8e022149),
837		BinaryField128bPolyval(0x3bebf7af750eace1e434f9a5925288ee),
838		BinaryField128bPolyval(0x9f171f736eff43513721ae2942afe01d),
839		BinaryField128bPolyval(0xe3e184abe50f7387c5fdd01faf6c95d3),
840		BinaryField128bPolyval(0x1fae32af2dc4238dcce57975be1b2400),
841		BinaryField128bPolyval(0x282116c0f04b6707698f1ea25790ea10),
842		BinaryField128bPolyval(0x564032a0d5d3773b7b7ed18bebf1c668),
843		BinaryField128bPolyval(0xe40d8bdaad8fdd00b3f004e706e35b10),
844		BinaryField128bPolyval(0x675892c7e2ead5594ef74c71079069d2),
845		BinaryField128bPolyval(0x25e285580c933861739d2b031eb4b2d3),
846		BinaryField128bPolyval(0x51e78b32d4dd25445b2d1f30689d6abb),
847		BinaryField128bPolyval(0x133994dbfd8ce08ae714538d557eb150),
848		BinaryField128bPolyval(0x278247597906a3b1f990119cde5ffb24),
849		BinaryField128bPolyval(0xef387e28a39a63ed81710b9bdbc74005),
850		BinaryField128bPolyval(0x41bbc7902188f4e9880f1d81fa580ffb),
851		BinaryField128bPolyval(0x415afa934ada855ba61bbef36d27db58),
852		BinaryField128bPolyval(0xe477f6fac6a1c2057662a149aa0ae061),
853		BinaryField128bPolyval(0xe98aee0eeb136ee02e2be740d058fe5d),
854		BinaryField128bPolyval(0x777ead11e8dc98c5ffd710b823fc5093),
855		BinaryField128bPolyval(0xa4e9927e7da484643651b5532106b1e3),
856		BinaryField128bPolyval(0x9fdfc576fcf0b33b829f1a052e9355f2),
857		BinaryField128bPolyval(0x342bbe0ad297a239b415fc050f1a23f7),
858		BinaryField128bPolyval(0x756209f0893e96877833c194b9c943a0),
859		BinaryField128bPolyval(0xc763ed07e05784c3ca283e12f9f22368),
860		BinaryField128bPolyval(0xb04147b7592c8c80508e1ee45b2c4806),
861		BinaryField128bPolyval(0x4f0557d1988f518b39bd6fc3c2fba372),
862		BinaryField128bPolyval(0x7259d355775035632bfb7b003178ae0e),
863		BinaryField128bPolyval(0x7826c6a2e9e37bbd991ef41faa246832),
864		BinaryField128bPolyval(0x4d12f861b14f57602cd121d6622efcf6),
865		BinaryField128bPolyval(0x47979b6dc50802e344b543260f9f14e4),
866		BinaryField128bPolyval(0xf330cd9a74a5e884988c3f36567d26f4),
867		BinaryField128bPolyval(0xb9d4fca088a982f6a9add501644e56b2),
868		BinaryField128bPolyval(0xee9e3f0fbab5cc33378947fd04769519),
869		BinaryField128bPolyval(0x0819f0cb4253a5ab7cb10f583ce13537),
870		BinaryField128bPolyval(0x0ba10d161c76ba69a4b68d140886097a),
871		BinaryField128bPolyval(0x7850cec4236f7ea4698d1b15707a8bf8),
872		BinaryField128bPolyval(0x5a712763179ba0a99e8bbe5e3b73146f),
873		BinaryField128bPolyval(0x8d825f45c33f7a1f45be2e3938a0fcfc),
874		BinaryField128bPolyval(0xf8f3c35c671bac841b14381a592e6cdd),
875		BinaryField128bPolyval(0x96d15acd59e4c4852735c30c972140ee),
876		BinaryField128bPolyval(0x87d0c6a97af12deec54ecfd097c5a4ff),
877		BinaryField128bPolyval(0x4152fe90327dcbe147e8771ba0334ba1),
878		BinaryField128bPolyval(0xb6793169bc400bfc14ed05b58db2b472),
879		BinaryField128bPolyval(0x071df72b3ce39b686d6f52b53e608c7a),
880		BinaryField128bPolyval(0xcf97a03df90400718aff5257888970f5),
881		BinaryField128bPolyval(0xa05e7602d3f74d882329c158a0ad9f37),
882		BinaryField128bPolyval(0x69d3b9b1d9483174b3c38d8f95ce7a5f),
883		BinaryField128bPolyval(0x54882e1b0f3f749397cbeff7c70f0c73),
884		BinaryField128bPolyval(0x1df3271f8f5398ff2937a4f0fd041cfa),
885		BinaryField128bPolyval(0xc964a4d09783b7483c1845943333022b),
886		BinaryField128bPolyval(0x64991e811d81abc5cef407bebff096bd),
887		BinaryField128bPolyval(0x12a6345cacc97a7992ad6647c2833af8),
888		BinaryField128bPolyval(0xe04112ac095f1c67b9792b0fb82cc4fe),
889		BinaryField128bPolyval(0x744c1206d550d565d994fe159c5cd699),
890		BinaryField128bPolyval(0xcd8b92c8a6e0e65e167a2b851f32fd9c),
891		BinaryField128bPolyval(0x994beaf6226f215c7b4187e0c36e08a6),
892		BinaryField128bPolyval(0x71d346897647348c7eb7752a3a893424),
893		BinaryField128bPolyval(0xb0f49cce03da921b5f8999cc18311b43),
894		BinaryField128bPolyval(0x45b6960f54a16e547a329f79210629d0),
895		BinaryField128bPolyval(0x4535377d8b9718b1f6991e57fea36922),
896		BinaryField128bPolyval(0xbf97b9a9bda638f42cc98233021d69fd),
897		BinaryField128bPolyval(0x02e346c80352ad186c77b88c9f9317d0),
898		BinaryField128bPolyval(0x2eae07273b8c4fc5cef553a4a46cde5b),
899		BinaryField128bPolyval(0x86c51811ef12c72fcabfc51b2a2e0c2a),
900		BinaryField128bPolyval(0x8a828ea9f6b97e5c3b0b4c6faed116e6),
901		BinaryField128bPolyval(0x0f69898966b112c45f01e70a26142623),
902		BinaryField128bPolyval(0x109173f0af80af37cf9d6ef791d2feed),
903		BinaryField128bPolyval(0x984655091ad81e2befa87a6688ddc784),
904		BinaryField128bPolyval(0x21851b1a985e40395abe3d15fff2d770),
905		BinaryField128bPolyval(0x045610d75e4ee7b53deb1c4149179a3a),
906		BinaryField128bPolyval(0x3c37dbe331de4b0dc2f5db315d5e7fda),
907		BinaryField128bPolyval(0x09ca74968860fc3d723b7966d8574ce1),
908		BinaryField128bPolyval(0x8892f14b27f8e4d1b01efa51eeaa4ad4),
909		BinaryField128bPolyval(0xc7339f4d332b0fa99f58a62453d76401),
910		BinaryField128bPolyval(0xfc81ac07b51d1d165b5525b77bf5f969),
911		BinaryField128bPolyval(0x7bdcb39270e3891d486160e47bc4015c),
912		BinaryField128bPolyval(0x7967964f6e9d62b6b50a50ee51c927d2),
913		BinaryField128bPolyval(0xd11b8526eed516e3dfa7b8e2b17bbf40),
914		BinaryField128bPolyval(0xe47b83247cb2b162c7d6d15c84cca8ce),
915		BinaryField128bPolyval(0x5136c420c1a70a4b697e000c637ec876),
916		BinaryField128bPolyval(0x2114cffeda72b157abb70ae549b39e97),
917		BinaryField128bPolyval(0x7f72edec22f7d7caac7b78cbca5ce3bb),
918		BinaryField128bPolyval(0xfb5ac3eb65636373828e242c79ef5046),
919		BinaryField128bPolyval(0x8819e336afff44542a76ee524a033645),
920		BinaryField128bPolyval(0x8be0251a2790b20b19f6343efaf425e7),
921		BinaryField128bPolyval(0x2a49adc1114d5dcf91783fafe0542c8a),
922	]);
923
924impl From<AESTowerField128b> for BinaryField128bPolyval {
925	fn from(value: AESTowerField128b) -> Self {
926		AES_TO_POLYVAL_TRANSFORMATION.transform(&value)
927	}
928}
929
930pub const POLYVAL_TO_AES_TRANSFORMARION: FieldLinearTransformation<AESTowerField128b> =
931	FieldLinearTransformation::new_const(&[
932		AESTowerField128b(0xaffaa99fa8aa55f93974735e68d0882a),
933		AESTowerField128b(0x402655567dde6c49c7aea09cc7d73e01),
934		AESTowerField128b(0x83d724035fe42d2bd4ad27c1ad3be9ae),
935		AESTowerField128b(0x39940944fe609647237fb001386aff50),
936		AESTowerField128b(0xce1a381a1790a4d70cbbd7389dd705cd),
937		AESTowerField128b(0x0ca7f0b9fdade73367e9d9ba5ac3cfbe),
938		AESTowerField128b(0x70a744fa2401c4fddb871879d718ee08),
939		AESTowerField128b(0x275ddf74916ecd03aa3c243f74bf3461),
940		AESTowerField128b(0xcedb8685d1e86e6a74b79cd21c271a02),
941		AESTowerField128b(0x7a451fd334177a5bdb9e82c9fa373e88),
942		AESTowerField128b(0xcd4617d8c786c2a3824ae7335ec6b418),
943		AESTowerField128b(0x32feae47f77fa9c6bb6b917fbb2d96d7),
944		AESTowerField128b(0xcb2fef14aeabf5b41cfd3ab6774c95b7),
945		AESTowerField128b(0x3029123a0510641d238bea4746cd5e4b),
946		AESTowerField128b(0xcfdc169c294eec4bb1eab4bc88a505de),
947		AESTowerField128b(0x139206e1ace72eed8b9d52fc020e2d9f),
948		AESTowerField128b(0x891e28b32d8a8320a0a2eb295953bc42),
949		AESTowerField128b(0xb8704d0efb4be36ea6282c5aaf67fa9e),
950		AESTowerField128b(0x272f2013fe10244185ad0d672eafa581),
951		AESTowerField128b(0x28614505a9df5f55ef5bb97c4521eace),
952		AESTowerField128b(0x6dbdd43dcc19626629ac7f2638e73fff),
953		AESTowerField128b(0x4d687c2abd4aba97692db8c2a4eb267c),
954		AESTowerField128b(0x19613bca40bd82828d8255f50d271135),
955		AESTowerField128b(0xf2772ff3c8d95eb9252d8bd01419641e),
956		AESTowerField128b(0x6611a71908f4aac4fdb11c08cbedfc8c),
957		AESTowerField128b(0x10ad82530c31e3a8f757424dca80798a),
958		AESTowerField128b(0x2fc9972bf59fe5c624714cb8466249ed),
959		AESTowerField128b(0x9c5c3d8b954a27231e16e4a77fbe4369),
960		AESTowerField128b(0x2565fdbb105f787cccddf28b530af4ee),
961		AESTowerField128b(0x473e8ad3e0e8e46e611080cc9350a590),
962		AESTowerField128b(0x525d2e9d24611e2aa37a1d9a2d42377d),
963		AESTowerField128b(0x4967e7d5067c2ace89648bf6d95de637),
964		AESTowerField128b(0x2689f814fa63c8a16ddf2374eeb7c3e7),
965		AESTowerField128b(0x5e9246c3d2cab88ba27d7cf8ba18c4b4),
966		AESTowerField128b(0x53616806f5402bc897499fac6e27da63),
967		AESTowerField128b(0x6c6dbb145a21d1c2d87a93e779f87aba),
968		AESTowerField128b(0x0f7164762ed37685fd82b05e800cebec),
969		AESTowerField128b(0x0d01e8acede09d57da4a7325af4b04fc),
970		AESTowerField128b(0x336b892198ac639af40c74c9252eb99c),
971		AESTowerField128b(0xf282b8b368b39203e0bbe6246b1b0951),
972		AESTowerField128b(0x090ca21ee9872dc5a00e669729a69750),
973		AESTowerField128b(0xa037d253b55003a611faf883fcc8f35e),
974		AESTowerField128b(0xe4b8a9796561b1ba1f0970a0b26f832a),
975		AESTowerField128b(0xda203a31e0d6ace125e027a2df265b59),
976		AESTowerField128b(0xe0ebb1a107ded2a6b0916eff84c18fb4),
977		AESTowerField128b(0xa9998b7d2cded9a5269f6f8b25147b08),
978		AESTowerField128b(0x2e8337dd13a279f78ac5d327ec36f632),
979		AESTowerField128b(0x6264c35e09c7b3bc9b80aa886b194025),
980		AESTowerField128b(0x9ff92674cc64e8c2e1ee5093298382e8),
981		AESTowerField128b(0x3e196976f0a90cf1f71847b0fce3a0ac),
982		AESTowerField128b(0xbdad299364e420e1663e2c09db59634d),
983		AESTowerField128b(0x9046a0de7ea82a4e8c8a75e001bfdf0e),
984		AESTowerField128b(0xc6762e8ee83287a13a66789ae533c938),
985		AESTowerField128b(0x1e17ed399374b0c47e9726bfc71e0c8a),
986		AESTowerField128b(0xf46ce30110ce034b6a0ba8b8d0af93c6),
987		AESTowerField128b(0x825f7d3cef67cec50370363e2a6e502c),
988		AESTowerField128b(0xbdfe9b9ae82bfeff8a58710addb13695),
989		AESTowerField128b(0x23002be0599a589f6e30a3069cbc71bd),
990		AESTowerField128b(0x4468951dba52ab1e06efe0dea6d01fa0),
991		AESTowerField128b(0x28752c7da3ed6a83ca09163f3186b862),
992		AESTowerField128b(0xe9dd33560ea4a316fdee161ba4946fb1),
993		AESTowerField128b(0x7e0df8223f37449f266bc8fa70de1ecb),
994		AESTowerField128b(0x88578550f872e4c8e975a2b66c70cde8),
995		AESTowerField128b(0xa11ea5aebfe37694ca5ff46e28faf100),
996		AESTowerField128b(0x3df877fc12016ef181fbf63bf87f5e7c),
997		AESTowerField128b(0x0a5ca382e7cc37ceb234a5d08d3206ac),
998		AESTowerField128b(0x6d24b53f98df2626e8e37f977013dbaa),
999		AESTowerField128b(0x51cc686f72fd7f264962407270cd9394),
1000		AESTowerField128b(0x9749ba0da32ec603a0b342e93049e1fb),
1001		AESTowerField128b(0xed05d63413627e1efd2f3757802a12fa),
1002		AESTowerField128b(0x0e4b2e70136dae8d61528cc479f3aeb0),
1003		AESTowerField128b(0x3e2bda6193a5c936f2c8dc53bf2375b1),
1004		AESTowerField128b(0x9f336d2f107bb812f4d39fb05f19a231),
1005		AESTowerField128b(0x9d21c1be60eba516920f52582c709535),
1006		AESTowerField128b(0x39a51756da0aee24ab5ea3ed62afce31),
1007		AESTowerField128b(0x4404c057a9425458d7fd72eb9e23ac50),
1008		AESTowerField128b(0xe2e5839f2ca60e2f20ad3b15676f583f),
1009		AESTowerField128b(0x8326ccb5e936f3a223d2dada1c00efe0),
1010		AESTowerField128b(0x4293fe13b61b834cf2af7ccea5ac07f4),
1011		AESTowerField128b(0x3c36e03518756760624be5278c4ad469),
1012		AESTowerField128b(0x8ccd1c1dbb224aa30ce78e9062de5884),
1013		AESTowerField128b(0x4c7442a391d3fa91581d07fe2114eea1),
1014		AESTowerField128b(0x7f73613a8ac49cd2c31260dd9835b790),
1015		AESTowerField128b(0x5ea3097b9e7f2734249d6777b4028f95),
1016		AESTowerField128b(0xd4ddcc844b626d7e122c431e3a2e9393),
1017		AESTowerField128b(0xc19d3ffeceed10457bbfd7a9b9064779),
1018		AESTowerField128b(0xb7f15cf7bf9c3b2a87a1e461370be7f5),
1019		AESTowerField128b(0xf20ca8dffdcc5433561e487513103aa8),
1020		AESTowerField128b(0xef6a936a1d9bd32d4502b8c4c5e7ce60),
1021		AESTowerField128b(0x27c89de97a00f322d3118c2b094c06f2),
1022		AESTowerField128b(0x8cd3bbb73240861ad260798b7c232ea2),
1023		AESTowerField128b(0x3e61230942e2c19b9ecb0f80a1b20423),
1024		AESTowerField128b(0x30c59cf7d564c2bc9371d28522419283),
1025		AESTowerField128b(0x17c781e73773c72b8e18d0e6f85fe1ac),
1026		AESTowerField128b(0xd58960c501256b149802cd19ddb19a4b),
1027		AESTowerField128b(0x4cfb558f43862eb923981eacc0719fab),
1028		AESTowerField128b(0xff8c63cbb23240af2d02d0c875335abb),
1029		AESTowerField128b(0x9219023fcc6c5b1154020e9685681b25),
1030		AESTowerField128b(0x57ec8c84b214456eb2b2c42e08cc7529),
1031		AESTowerField128b(0xbda0ccb3b1231f075f78b27dcd578a40),
1032		AESTowerField128b(0xb9396785c80962cfdb0a4117868ab3f6),
1033		AESTowerField128b(0xf3b2bea115d44e307a113ebfdf27ccff),
1034		AESTowerField128b(0x66c226397a967901e4bc6ce235bf4feb),
1035		AESTowerField128b(0x05dd05a7c5e9ac15442189f090a80f9e),
1036		AESTowerField128b(0xed7bea5ee1e167921014c2c7853a679d),
1037		AESTowerField128b(0x37fafed03dfb701af939eafaeeb02074),
1038		AESTowerField128b(0x23491f63f098d208343d5591b7bd626f),
1039		AESTowerField128b(0x3cf04e2f641c505c3e110e87f3e9af91),
1040		AESTowerField128b(0x076e26a8d7181c6de575685a1fe939f9),
1041		AESTowerField128b(0x7b4e4f1b2780c2a5cbf75fe85fc94a58),
1042		AESTowerField128b(0xccd26fddd8f624c8b3f7a2e53a0ae8df),
1043		AESTowerField128b(0xb422ef66e72dbe3798fda5509f63fed2),
1044		AESTowerField128b(0x436f0b1488c5a0680f57919dd4b8fa30),
1045		AESTowerField128b(0xfb3808c6bcacc74fab269021cc58c9df),
1046		AESTowerField128b(0x77bf7b6affefb00594c0b1209a37c97d),
1047		AESTowerField128b(0x36776863a0ce234546d735734b90b7b1),
1048		AESTowerField128b(0x9c0013e65e524467294aa8c70ff414dc),
1049		AESTowerField128b(0xc2c6aeb796ca121f09708acca73499a2),
1050		AESTowerField128b(0xac57847d964c41c97ce4ed9fa3417e90),
1051		AESTowerField128b(0x4c62531aa3c2e5320761c8c64b690e1e),
1052		AESTowerField128b(0xf61ab3912aed1d889336ded4ef4fbae8),
1053		AESTowerField128b(0x5aa06080ab76d88dc5a8a01f48d11ee2),
1054		AESTowerField128b(0x0fc8b68dbc323616ba5a66dcac10f733),
1055		AESTowerField128b(0x7afcf993b86c827a7e290b5e21f0ce48),
1056		AESTowerField128b(0xe7fbd490470b7d4ddd8ef44c2f0ece93),
1057		AESTowerField128b(0xd51ff53d804403832d740176a0cddde2),
1058		AESTowerField128b(0x33c2b575cc0be097362f21d506e9fa17),
1059		AESTowerField128b(0xc6987c6acfd76de3caf3f29426e86cde),
1060	]);
1061
1062impl From<BinaryField128bPolyval> for AESTowerField128b {
1063	fn from(value: BinaryField128bPolyval) -> Self {
1064		POLYVAL_TO_AES_TRANSFORMARION.transform(&value)
1065	}
1066}
1067
1068#[inline(always)]
1069pub fn is_polyval_tower<F: TowerField>() -> bool {
1070	TypeId::of::<F>() == TypeId::of::<BinaryField128bPolyval>()
1071		|| TypeId::of::<F>() == TypeId::of::<BinaryField1b>()
1072}
1073
1074#[cfg(test)]
1075mod tests {
1076	use binius_utils::{bytes::BytesMut, SerializationMode, SerializeBytes};
1077	use proptest::prelude::*;
1078	use rand::thread_rng;
1079
1080	use super::*;
1081	use crate::{
1082		arch::{
1083			packed_polyval_256::PackedBinaryPolyval2x128b,
1084			packed_polyval_512::PackedBinaryPolyval4x128b,
1085		},
1086		binary_field::tests::is_binary_field_valid_generator,
1087		linear_transformation::PackedTransformationFactory,
1088		AESTowerField128b, PackedAESBinaryField1x128b, PackedAESBinaryField2x128b,
1089		PackedAESBinaryField4x128b, PackedBinaryField1x128b, PackedBinaryField2x128b,
1090		PackedBinaryField4x128b, PackedField,
1091	};
1092
1093	#[test]
1094	fn test_display() {
1095		assert_eq!(
1096			"0x00000000000000000000000000000001",
1097			format!("{}", BinaryField128bPolyval::ONE)
1098		);
1099		assert_eq!(
1100			"0x2a9055e4e69a61f0b5cfd6f4161087ba",
1101			format!("{}", BinaryField128bPolyval::new(0x2a9055e4e69a61f0b5cfd6f4161087ba))
1102		);
1103	}
1104
1105	proptest! {
1106		#[test]
1107		fn test_multiplicative_identity(v in any::<u128>()) {
1108			let v = BinaryField128bPolyval::new(v);
1109			assert_eq!(v, v * BinaryField128bPolyval::ONE);
1110		}
1111	}
1112
1113	#[test]
1114	fn test_mul() {
1115		assert_eq!(
1116			BinaryField128bPolyval::new(0x2a9055e4e69a61f0b5cfd6f4161087ba)
1117				* BinaryField128bPolyval::new(0x3843cf87fb7c84e18276983bed670337),
1118			BinaryField128bPolyval::new(0x5b2619c8a035206a12100d7a171aa988)
1119		);
1120	}
1121
1122	#[test]
1123	fn test_sqr() {
1124		assert_eq!(
1125			Square::square(BinaryField128bPolyval::new(0x2a9055e4e69a61f0b5cfd6f4161087ba)),
1126			BinaryField128bPolyval::new(0x59aba0d4ffa9dca427b5b489f293e529)
1127		);
1128	}
1129
1130	#[test]
1131	fn test_multiplicative_generator() {
1132		assert!(is_binary_field_valid_generator::<BinaryField128bPolyval>());
1133	}
1134
1135	fn test_packed_conversion<
1136		PT1: PackedField<Scalar: BinaryField> + PackedTransformationFactory<PT2>,
1137		PT2: PackedField<Scalar: BinaryField>,
1138	>(
1139		val: PT1,
1140		transformation: FieldLinearTransformation<PT2::Scalar>,
1141	) {
1142		let expected = PT2::from_fn(|i| transformation.transform(&val.get(i)));
1143		let transformed =
1144			<PT1 as PackedTransformationFactory<PT2>>::make_packed_transformation(transformation)
1145				.transform(&val);
1146		assert_eq!(transformed, expected);
1147	}
1148
1149	proptest! {
1150		#[test]
1151		fn test_to_from_tower_basis(a_val in any::<u128>(), b_val in any::<u128>()) {
1152			let a_tower = BinaryField128b::new(a_val);
1153			let b_tower = BinaryField128b::new(b_val);
1154			let a_polyval = BinaryField128bPolyval::from(a_tower);
1155			let b_polyval = BinaryField128bPolyval::from(b_tower);
1156			assert_eq!(BinaryField128b::from(a_polyval * b_polyval), a_tower * b_tower);
1157		}
1158
1159		#[test]
1160		fn test_conversion_roundtrip(a in any::<u128>()) {
1161			let a_val = BinaryField128bPolyval(a);
1162			let converted = BinaryField128b::from(a_val);
1163			assert_eq!(a_val, BinaryField128bPolyval::from(converted));
1164
1165			let a_val = AESTowerField128b(a);
1166			let converted = BinaryField128bPolyval::from(a_val);
1167			assert_eq!(a_val, AESTowerField128b::from(converted));
1168		}
1169
1170		#[test]
1171		fn test_conversion_128b(a in any::<u128>()) {
1172			test_packed_conversion::<PackedBinaryPolyval1x128b, PackedBinaryField1x128b>(a.into(), POLYVAL_TO_BINARY_TRANSFORMATION);
1173			test_packed_conversion::<PackedBinaryField1x128b, PackedBinaryPolyval1x128b>(a.into(), BINARY_TO_POLYVAL_TRANSFORMATION);
1174
1175			test_packed_conversion::<PackedBinaryPolyval1x128b, PackedAESBinaryField1x128b>(a.into(), POLYVAL_TO_AES_TRANSFORMARION);
1176			test_packed_conversion::<PackedAESBinaryField1x128b, PackedBinaryPolyval1x128b>(a.into(), AES_TO_POLYVAL_TRANSFORMATION);
1177		}
1178
1179		#[test]
1180		fn test_conversion_256b(a in any::<[u128; 2]>()) {
1181			test_packed_conversion::<PackedBinaryPolyval2x128b, PackedBinaryField2x128b>(a.into(), POLYVAL_TO_BINARY_TRANSFORMATION);
1182			test_packed_conversion::<PackedBinaryField2x128b, PackedBinaryPolyval2x128b>(a.into(), BINARY_TO_POLYVAL_TRANSFORMATION);
1183
1184			test_packed_conversion::<PackedBinaryPolyval2x128b, PackedAESBinaryField2x128b>(a.into(), POLYVAL_TO_AES_TRANSFORMARION);
1185			test_packed_conversion::<PackedAESBinaryField2x128b, PackedBinaryPolyval2x128b>(a.into(), AES_TO_POLYVAL_TRANSFORMATION);
1186		}
1187
1188		#[test]
1189		fn test_conversion_512b(a in any::<[u128; 4]>()) {
1190			test_packed_conversion::<PackedBinaryPolyval4x128b, PackedBinaryField4x128b>(PackedBinaryPolyval4x128b::from_underlier(a.into()), POLYVAL_TO_BINARY_TRANSFORMATION);
1191			test_packed_conversion::<PackedBinaryField4x128b, PackedBinaryPolyval4x128b>(PackedBinaryField4x128b::from_underlier(a.into()), BINARY_TO_POLYVAL_TRANSFORMATION);
1192
1193			test_packed_conversion::<PackedBinaryPolyval4x128b, PackedAESBinaryField4x128b>(PackedBinaryPolyval4x128b::from_underlier(a.into()), POLYVAL_TO_AES_TRANSFORMARION);
1194			test_packed_conversion::<PackedAESBinaryField4x128b, PackedBinaryPolyval4x128b>(PackedAESBinaryField4x128b::from_underlier(a.into()), AES_TO_POLYVAL_TRANSFORMATION);
1195		}
1196
1197
1198		#[test]
1199		fn test_invert_or_zero(a_val in any::<u128>()) {
1200			let a = BinaryField128bPolyval::new(a_val);
1201			let a_invert = InvertOrZero::invert_or_zero(a);
1202			if a == BinaryField128bPolyval::ZERO {
1203				assert_eq!(a_invert, BinaryField128bPolyval::ZERO);
1204			} else {
1205				assert_eq!(a * a_invert, BinaryField128bPolyval::ONE);
1206			}
1207		}
1208	}
1209
1210	/// Test that `invert` method properly wraps `invert_or_zero`
1211	#[test]
1212	fn test_invert() {
1213		let x = BinaryField128bPolyval::new(2);
1214		let y = x.invert().unwrap();
1215
1216		assert_eq!(x * y, BinaryField128bPolyval::ONE);
1217	}
1218
1219	#[test]
1220	fn test_conversion_from_1b() {
1221		assert_eq!(
1222			BinaryField128bPolyval::from(BinaryField1b::from(0)),
1223			BinaryField128bPolyval::ZERO
1224		);
1225		assert_eq!(
1226			BinaryField128bPolyval::from(BinaryField1b::from(1)),
1227			BinaryField128bPolyval::ONE
1228		);
1229	}
1230
1231	#[test]
1232	fn test_canonical_serialization() {
1233		let mode = SerializationMode::CanonicalTower;
1234		let mut buffer = BytesMut::new();
1235		let mut rng = thread_rng();
1236
1237		let b128_poly1 = <BinaryField128bPolyval as Field>::random(&mut rng);
1238		let b128_poly2 = <BinaryField128bPolyval as Field>::random(&mut rng);
1239
1240		SerializeBytes::serialize(&b128_poly1, &mut buffer, mode).unwrap();
1241		SerializeBytes::serialize(&b128_poly2, &mut buffer, mode).unwrap();
1242
1243		let mode = SerializationMode::CanonicalTower;
1244		let mut read_buffer = buffer.freeze();
1245
1246		assert_eq!(
1247			BinaryField128bPolyval::deserialize(&mut read_buffer, mode).unwrap(),
1248			b128_poly1
1249		);
1250		assert_eq!(
1251			BinaryField128bPolyval::deserialize(&mut read_buffer, mode).unwrap(),
1252			b128_poly2
1253		);
1254	}
1255}
binius_field/polyval.rs

binius_field/
polyval.rs
