miden-crypto/crypto/src/hash/rpo/mod.rs
crypto/src/hash/rpo/mod.rsRaw
1use super::{ElementHasher, HashFn};
2use crate::{Felt, FieldElement, StarkField, ONE, ZERO};
3use core::{convert::TryInto, ops::Range};
4
5mod digest;
6pub use digest::RpoDigest256;
7
8#[cfg(test)]
9mod tests;
10
11mod mds_freq;
12use mds_freq::mds_multiply_freq;
13
14// CONSTANTS
15// ================================================================================================
16
17/// Sponge state is set to 12 field elements or 96 bytes; 8 elements are reserved for rate and
18/// the remaining 4 elements are reserved for capacity.
19const STATE_WIDTH: usize = 12;
20
21/// The rate portion of the state is located in elements 4 through 11.
22const RATE_RANGE: Range<usize> = 4..12;
23const RATE_WIDTH: usize = RATE_RANGE.end - RATE_RANGE.start;
24
25const INPUT1_RANGE: Range<usize> = 4..8;
26const INPUT2_RANGE: Range<usize> = 8..12;
27
28/// The capacity portion of the state is located in elements 0, 1, 2, and 3.
29const CAPACITY_RANGE: Range<usize> = 0..4;
30
31/// The output of the hash function is a digest which consists of 4 field elements or 32 bytes.
32///
33/// The digest is returned from state elements 4, 5, 6, and 7 (the first four elements of the
34/// rate portion).
35const DIGEST_RANGE: Range<usize> = 4..8;
36const DIGEST_SIZE: usize = DIGEST_RANGE.end - DIGEST_RANGE.start;
37
38/// The number of rounds is set to 7 to target 128-bit security level
39const NUM_ROUNDS: usize = 7;
40
41/// S-Box and Inverse S-Box powers;
42///
43/// The constants are defined for tests only because the exponentiations in the code are unrolled
44/// for efficiency reasons.
45#[cfg(test)]
46const ALPHA: u64 = 7;
47#[cfg(test)]
48const INV_ALPHA: u64 = 10540996611094048183;
49
50// HASHER IMPLEMENTATION
51// ================================================================================================
52
53/// Implementation of [Hasher] trait for Rescue Prime Optimized (Rpo256) hash function with 256-bit output.
54///
55/// The hash function is implemented according to the Rescue Prime Optimized
56/// [specifications](https://github.com/ASDiscreteMathematics/rpo)
57///
58/// The parameters used to instantiate the function are:
59/// * Field: 64-bit prime field with modulus 2^64 - 2^32 + 1.
60/// * State width: 12 field elements.
61/// * Capacity size: 4 field elements.
62/// * Number of founds: 7.
63/// * S-Box degree: 7.
64///
65/// The above parameters target 128-bit security level. The digest consists of four field elements
66/// and it can be serialized into 32 bytes (256 bits).
67///
68/// ## Hash output consistency
69/// Functions [hash_elements()](Rpo256::hash_elements), [merge()](Rpo256::merge), and
70/// [merge_with_int()](Rpo256::merge_with_int) are internally consistent. That is, computing
71/// a hash for the same set of elements using these functions will always produce the same
72/// result. For example, merging two digests using [merge()](Rpo256::merge) will produce the
73/// same result as hashing 8 elements which make up these digests using
74/// [hash_elements()](Rpo256::hash_elements) function.
75///
76/// However, [hash()](Rpo256::hash) function is not consistent with functions mentioned above.
77/// For example, if we take two field elements, serialize them to bytes and hash them using
78/// [hash()](Rpo256::hash), the result will differ from the result obtained by hashing these
79/// elements directly using [hash_elements()](Rpo256::hash_elements) function. The reason for
80/// this difference is that [hash()](Rpo256::hash) function needs to be able to handle
81/// arbitrary binary strings, which may or may not encode valid field elements - and thus,
82/// deserialization procedure used by this function is different from the procedure used to
83/// deserialize valid field elements.
84///
85/// Thus, if the underlying data consists of valid field elements, it might make more sense
86/// to deserialize them into field elements and then hash them using
87/// [hash_elements()](Rpo256::hash_elements) function rather then hashing the serialized bytes
88/// using [hash()](Rpo256::hash) function.
89pub struct Rpo256();
90
91impl HashFn for Rpo256 {
92 type Digest = RpoDigest256;
93
94 fn hash(bytes: &[u8]) -> Self::Digest {
95 // compute the number of elements required to represent the string; we will be processing
96 // the string in 7-byte chunks, thus the number of elements will be equal to the number
97 // of such chunks (including a potential partial chunk at the end).
98 let num_elements = if bytes.len() % 7 == 0 {
99 bytes.len() / 7
100 } else {
101 bytes.len() / 7 + 1
102 };
103
104 // initialize state to all zeros, except for the first element of the capacity part, which
105 // is set to the number of elements to be hashed. this is done so that adding zero elements
106 // at the end of the list always results in a different hash.
107 let mut state = [ZERO; STATE_WIDTH];
108 state[CAPACITY_RANGE.start] = Felt::new(num_elements as u64);
109
110 // break the string into 7-byte chunks, convert each chunk into a field element, and
111 // absorb the element into the rate portion of the state. we use 7-byte chunks because
112 // every 7-byte chunk is guaranteed to map to some field element.
113 let mut i = 0;
114 let mut buf = [0_u8; 8];
115 for chunk in bytes.chunks(7) {
116 if i < num_elements - 1 {
117 buf[..7].copy_from_slice(chunk);
118 } else {
119 // if we are dealing with the last chunk, it may be smaller than 7 bytes long, so
120 // we need to handle it slightly differently. we also append a byte with value 1
121 // to the end of the string; this pads the string in such a way that adding
122 // trailing zeros results in different hash
123 let chunk_len = chunk.len();
124 buf = [0_u8; 8];
125 buf[..chunk_len].copy_from_slice(chunk);
126 buf[chunk_len] = 1;
127 }
128
129 // convert the bytes into a field element and absorb it into the rate portion of the
130 // state; if the rate is filled up, apply the Rescue permutation and start absorbing
131 // again from zero index.
132 state[RATE_RANGE.start + i] += Felt::new(u64::from_le_bytes(buf));
133 i += 1;
134 if i % RATE_WIDTH == 0 {
135 Self::apply_permutation(&mut state);
136 i = 0;
137 }
138 }
139
140 // if we absorbed some elements but didn't apply a permutation to them (would happen when
141 // the number of elements is not a multiple of RATE_WIDTH), apply the Rescue permutation.
142 // we don't need to apply any extra padding because we injected total number of elements
143 // in the input list into the capacity portion of the state during initialization.
144 if i > 0 {
145 Self::apply_permutation(&mut state);
146 }
147
148 // return the first 4 elements of the state as hash result
149 RpoDigest256::new(state[DIGEST_RANGE].try_into().unwrap())
150 }
151
152 fn merge(values: &[Self::Digest; 2]) -> Self::Digest {
153 // initialize the state by copying the digest elements into the rate portion of the state
154 // (8 total elements), and set the capacity elements to 0.
155 let mut state = [ZERO; STATE_WIDTH];
156 let it = Self::Digest::digests_as_elements(values.iter());
157 for (i, v) in it.enumerate() {
158 state[RATE_RANGE.start + i] = *v;
159 }
160
161 // apply the RPO permutation and return the first four elements of the state
162 Self::apply_permutation(&mut state);
163 RpoDigest256::new(state[DIGEST_RANGE].try_into().unwrap())
164 }
165
166 fn merge_with_int(seed: Self::Digest, value: u64) -> Self::Digest {
167 // initialize the state as follows:
168 // - seed is copied into the first 4 elements of the rate portion of the state.
169 // - if the value fits into a single field element, copy it into the fifth rate element
170 // and set the sixth rate element to 1.
171 // - if the value doesn't fit into a single field element, split it into two field
172 // elements, copy them into rate elements 5 and 6, and set the seventh rate element
173 // to 1.
174 // - set the first capacity element to 1
175 let mut state = [ZERO; STATE_WIDTH];
176 state[INPUT1_RANGE].copy_from_slice(seed.as_elements());
177 state[INPUT2_RANGE.start] = Felt::new(value);
178 if value < Felt::MODULUS {
179 state[INPUT2_RANGE.start + 1] = ONE;
180 } else {
181 state[INPUT2_RANGE.start + 1] = Felt::new(value / Felt::MODULUS);
182 state[INPUT2_RANGE.start + 2] = ONE;
183 }
184
185 // common padding for both cases
186 state[CAPACITY_RANGE.start] = ONE;
187
188 // apply the RPO permutation and return the first four elements of the state
189 Self::apply_permutation(&mut state);
190 RpoDigest256::new(state[DIGEST_RANGE].try_into().unwrap())
191 }
192}
193
194impl ElementHasher for Rpo256 {
195 type BaseField = Felt;
196
197 fn hash_elements<E: FieldElement<BaseField = Self::BaseField>>(elements: &[E]) -> Self::Digest {
198 // convert the elements into a list of base field elements
199 let elements = E::as_base_elements(elements);
200
201 // initialize state to all zeros, except for the first element of the capacity part, which
202 // is set to 1 if the number of elements is not a multiple of RATE_WIDTH.
203 let mut state = [ZERO; STATE_WIDTH];
204 if elements.len() % RATE_WIDTH != 0 {
205 state[CAPACITY_RANGE.start] = ONE;
206 }
207
208 // absorb elements into the state one by one until the rate portion of the state is filled
209 // up; then apply the Rescue permutation and start absorbing again; repeat until all
210 // elements have been absorbed
211 let mut i = 0;
212 for &element in elements.iter() {
213 state[RATE_RANGE.start + i] = element;
214 i += 1;
215 if i % RATE_WIDTH == 0 {
216 Self::apply_permutation(&mut state);
217 i = 0;
218 }
219 }
220
221 // if we absorbed some elements but didn't apply a permutation to them (would happen when
222 // the number of elements is not a multiple of RATE_WIDTH), apply the RPO permutation after
223 // padding by appending a 1 followed by as many 0 as necessary to make the input length a
224 // multiple of the RATE_WIDTH.
225 if i > 0 {
226 state[RATE_RANGE.start + i] = ONE;
227 i += 1;
228 while i != RATE_WIDTH {
229 state[RATE_RANGE.start + i] = ZERO;
230 i += 1;
231 }
232 Self::apply_permutation(&mut state);
233 }
234
235 // return the first 4 elements of the state as hash result
236 RpoDigest256::new(state[DIGEST_RANGE].try_into().unwrap())
237 }
238}
239
240// HASH FUNCTION IMPLEMENTATION
241// ================================================================================================
242
243impl Rpo256 {
244 // RESCUE PERMUTATION
245 // --------------------------------------------------------------------------------------------
246
247 /// Applies RPO permutation to the provided state.
248 pub fn apply_permutation(state: &mut [Felt; STATE_WIDTH]) {
249 for i in 0..NUM_ROUNDS {
250 Self::apply_round(state, i);
251 }
252 }
253
254 /// RPO round function.
255 #[inline(always)]
256 pub fn apply_round(state: &mut [Felt; STATE_WIDTH], round: usize) {
257 // apply first half of RPO round
258 Self::apply_mds(state);
259 Self::add_constants(state, &ARK1[round]);
260 Self::apply_sbox(state);
261
262 // apply second half of RPO round
263 Self::apply_mds(state);
264 Self::add_constants(state, &ARK2[round]);
265 Self::apply_inv_sbox(state);
266 }
267
268 // HELPER FUNCTIONS
269 // --------------------------------------------------------------------------------------------
270
271 #[inline(always)]
272 fn apply_mds(state: &mut [Felt; STATE_WIDTH]) {
273 let mut result = [ZERO; STATE_WIDTH];
274
275 // Using the linearity of the operations we can split the state into a low||high decomposition
276 // and operate on each with no overflow and then combine/reduce the result to a field element.
277 // The no overflow is guaranteed by the fact that the MDS matrix is a small powers of two in
278 // frequency domain.
279 let mut state_l = [0u64; STATE_WIDTH];
280 let mut state_h = [0u64; STATE_WIDTH];
281
282 for r in 0..STATE_WIDTH {
283 let s = state[r].inner();
284 state_h[r] = s >> 32;
285 state_l[r] = (s as u32) as u64;
286 }
287
288 let state_h = mds_multiply_freq(state_h);
289 let state_l = mds_multiply_freq(state_l);
290
291 for r in 0..STATE_WIDTH {
292 let s = state_l[r] as u128 + ((state_h[r] as u128) << 32);
293 let s_hi = (s >> 64) as u64;
294 let s_lo = s as u64;
295 let z = (s_hi << 32) - s_hi;
296 let (res, over) = s_lo.overflowing_add(z);
297
298 result[r] = Felt::from_mont(res.wrapping_add(0u32.wrapping_sub(over as u32) as u64));
299 }
300 *state = result;
301 }
302
303 #[inline(always)]
304 fn add_constants(state: &mut [Felt; STATE_WIDTH], ark: &[Felt; STATE_WIDTH]) {
305 state.iter_mut().zip(ark).for_each(|(s, &k)| *s += k);
306 }
307
308 #[inline(always)]
309 fn apply_sbox(state: &mut [Felt; STATE_WIDTH]) {
310 state[0] = state[0].exp7();
311 state[1] = state[1].exp7();
312 state[2] = state[2].exp7();
313 state[3] = state[3].exp7();
314 state[4] = state[4].exp7();
315 state[5] = state[5].exp7();
316 state[6] = state[6].exp7();
317 state[7] = state[7].exp7();
318 state[8] = state[8].exp7();
319 state[9] = state[9].exp7();
320 state[10] = state[10].exp7();
321 state[11] = state[11].exp7();
322 }
323
324 #[inline(always)]
325 fn apply_inv_sbox(state: &mut [Felt; STATE_WIDTH]) {
326 // compute base^10540996611094048183 using 72 multiplications per array element
327 // 10540996611094048183 = b1001001001001001001001001001000110110110110110110110110110110111
328
329 // compute base^10
330 let mut t1 = *state;
331 t1.iter_mut().for_each(|t| *t = t.square());
332
333 // compute base^100
334 let mut t2 = t1;
335 t2.iter_mut().for_each(|t| *t = t.square());
336
337 // compute base^100100
338 let t3 = Self::exp_acc::<Felt, STATE_WIDTH, 3>(t2, t2);
339
340 // compute base^100100100100
341 let t4 = Self::exp_acc::<Felt, STATE_WIDTH, 6>(t3, t3);
342
343 // compute base^100100100100100100100100
344 let t5 = Self::exp_acc::<Felt, STATE_WIDTH, 12>(t4, t4);
345
346 // compute base^100100100100100100100100100100
347 let t6 = Self::exp_acc::<Felt, STATE_WIDTH, 6>(t5, t3);
348
349 // compute base^1001001001001001001001001001000100100100100100100100100100100
350 let t7 = Self::exp_acc::<Felt, STATE_WIDTH, 31>(t6, t6);
351
352 // compute base^1001001001001001001001001001000110110110110110110110110110110111
353 for (i, s) in state.iter_mut().enumerate() {
354 let a = (t7[i].square() * t6[i]).square().square();
355 let b = t1[i] * t2[i] * *s;
356 *s = a * b;
357 }
358 }
359
360 #[inline(always)]
361 fn exp_acc<B: StarkField, const N: usize, const M: usize>(
362 base: [B; N],
363 tail: [B; N],
364 ) -> [B; N] {
365 let mut result = base;
366 for _ in 0..M {
367 result.iter_mut().for_each(|r| *r = r.square());
368 }
369 result.iter_mut().zip(tail).for_each(|(r, t)| *r *= t);
370 result
371 }
372}
373
374// MDS
375// ================================================================================================
376/// RPO MDS matrix
377const MDS: [[Felt; STATE_WIDTH]; STATE_WIDTH] = [
378 [
379 Felt::new(7),
380 Felt::new(23),
381 Felt::new(8),
382 Felt::new(26),
383 Felt::new(13),
384 Felt::new(10),
385 Felt::new(9),
386 Felt::new(7),
387 Felt::new(6),
388 Felt::new(22),
389 Felt::new(21),
390 Felt::new(8),
391 ],
392 [
393 Felt::new(8),
394 Felt::new(7),
395 Felt::new(23),
396 Felt::new(8),
397 Felt::new(26),
398 Felt::new(13),
399 Felt::new(10),
400 Felt::new(9),
401 Felt::new(7),
402 Felt::new(6),
403 Felt::new(22),
404 Felt::new(21),
405 ],
406 [
407 Felt::new(21),
408 Felt::new(8),
409 Felt::new(7),
410 Felt::new(23),
411 Felt::new(8),
412 Felt::new(26),
413 Felt::new(13),
414 Felt::new(10),
415 Felt::new(9),
416 Felt::new(7),
417 Felt::new(6),
418 Felt::new(22),
419 ],
420 [
421 Felt::new(22),
422 Felt::new(21),
423 Felt::new(8),
424 Felt::new(7),
425 Felt::new(23),
426 Felt::new(8),
427 Felt::new(26),
428 Felt::new(13),
429 Felt::new(10),
430 Felt::new(9),
431 Felt::new(7),
432 Felt::new(6),
433 ],
434 [
435 Felt::new(6),
436 Felt::new(22),
437 Felt::new(21),
438 Felt::new(8),
439 Felt::new(7),
440 Felt::new(23),
441 Felt::new(8),
442 Felt::new(26),
443 Felt::new(13),
444 Felt::new(10),
445 Felt::new(9),
446 Felt::new(7),
447 ],
448 [
449 Felt::new(7),
450 Felt::new(6),
451 Felt::new(22),
452 Felt::new(21),
453 Felt::new(8),
454 Felt::new(7),
455 Felt::new(23),
456 Felt::new(8),
457 Felt::new(26),
458 Felt::new(13),
459 Felt::new(10),
460 Felt::new(9),
461 ],
462 [
463 Felt::new(9),
464 Felt::new(7),
465 Felt::new(6),
466 Felt::new(22),
467 Felt::new(21),
468 Felt::new(8),
469 Felt::new(7),
470 Felt::new(23),
471 Felt::new(8),
472 Felt::new(26),
473 Felt::new(13),
474 Felt::new(10),
475 ],
476 [
477 Felt::new(10),
478 Felt::new(9),
479 Felt::new(7),
480 Felt::new(6),
481 Felt::new(22),
482 Felt::new(21),
483 Felt::new(8),
484 Felt::new(7),
485 Felt::new(23),
486 Felt::new(8),
487 Felt::new(26),
488 Felt::new(13),
489 ],
490 [
491 Felt::new(13),
492 Felt::new(10),
493 Felt::new(9),
494 Felt::new(7),
495 Felt::new(6),
496 Felt::new(22),
497 Felt::new(21),
498 Felt::new(8),
499 Felt::new(7),
500 Felt::new(23),
501 Felt::new(8),
502 Felt::new(26),
503 ],
504 [
505 Felt::new(26),
506 Felt::new(13),
507 Felt::new(10),
508 Felt::new(9),
509 Felt::new(7),
510 Felt::new(6),
511 Felt::new(22),
512 Felt::new(21),
513 Felt::new(8),
514 Felt::new(7),
515 Felt::new(23),
516 Felt::new(8),
517 ],
518 [
519 Felt::new(8),
520 Felt::new(26),
521 Felt::new(13),
522 Felt::new(10),
523 Felt::new(9),
524 Felt::new(7),
525 Felt::new(6),
526 Felt::new(22),
527 Felt::new(21),
528 Felt::new(8),
529 Felt::new(7),
530 Felt::new(23),
531 ],
532 [
533 Felt::new(23),
534 Felt::new(8),
535 Felt::new(26),
536 Felt::new(13),
537 Felt::new(10),
538 Felt::new(9),
539 Felt::new(7),
540 Felt::new(6),
541 Felt::new(22),
542 Felt::new(21),
543 Felt::new(8),
544 Felt::new(7),
545 ],
546];
547
548/// RPO Inverse MDS matrix
549const INV_MDS: [[Felt; STATE_WIDTH]; STATE_WIDTH] = [
550 [
551 Felt::new(14868391535953158196),
552 Felt::new(13278298489594233127),
553 Felt::new(389999932707070822),
554 Felt::new(9782021734907796003),
555 Felt::new(4829905704463175582),
556 Felt::new(7567822018949214430),
557 Felt::new(14205019324568680367),
558 Felt::new(15489674211196160593),
559 Felt::new(17636013826542227504),
560 Felt::new(16254215311946436093),
561 Felt::new(3641486184877122796),
562 Felt::new(11069068059762973582),
563 ],
564 [
565 Felt::new(11069068059762973582),
566 Felt::new(14868391535953158196),
567 Felt::new(13278298489594233127),
568 Felt::new(389999932707070822),
569 Felt::new(9782021734907796003),
570 Felt::new(4829905704463175582),
571 Felt::new(7567822018949214430),
572 Felt::new(14205019324568680367),
573 Felt::new(15489674211196160593),
574 Felt::new(17636013826542227504),
575 Felt::new(16254215311946436093),
576 Felt::new(3641486184877122796),
577 ],
578 [
579 Felt::new(3641486184877122796),
580 Felt::new(11069068059762973582),
581 Felt::new(14868391535953158196),
582 Felt::new(13278298489594233127),
583 Felt::new(389999932707070822),
584 Felt::new(9782021734907796003),
585 Felt::new(4829905704463175582),
586 Felt::new(7567822018949214430),
587 Felt::new(14205019324568680367),
588 Felt::new(15489674211196160593),
589 Felt::new(17636013826542227504),
590 Felt::new(16254215311946436093),
591 ],
592 [
593 Felt::new(16254215311946436093),
594 Felt::new(3641486184877122796),
595 Felt::new(11069068059762973582),
596 Felt::new(14868391535953158196),
597 Felt::new(13278298489594233127),
598 Felt::new(389999932707070822),
599 Felt::new(9782021734907796003),
600 Felt::new(4829905704463175582),
601 Felt::new(7567822018949214430),
602 Felt::new(14205019324568680367),
603 Felt::new(15489674211196160593),
604 Felt::new(17636013826542227504),
605 ],
606 [
607 Felt::new(17636013826542227504),
608 Felt::new(16254215311946436093),
609 Felt::new(3641486184877122796),
610 Felt::new(11069068059762973582),
611 Felt::new(14868391535953158196),
612 Felt::new(13278298489594233127),
613 Felt::new(389999932707070822),
614 Felt::new(9782021734907796003),
615 Felt::new(4829905704463175582),
616 Felt::new(7567822018949214430),
617 Felt::new(14205019324568680367),
618 Felt::new(15489674211196160593),
619 ],
620 [
621 Felt::new(15489674211196160593),
622 Felt::new(17636013826542227504),
623 Felt::new(16254215311946436093),
624 Felt::new(3641486184877122796),
625 Felt::new(11069068059762973582),
626 Felt::new(14868391535953158196),
627 Felt::new(13278298489594233127),
628 Felt::new(389999932707070822),
629 Felt::new(9782021734907796003),
630 Felt::new(4829905704463175582),
631 Felt::new(7567822018949214430),
632 Felt::new(14205019324568680367),
633 ],
634 [
635 Felt::new(14205019324568680367),
636 Felt::new(15489674211196160593),
637 Felt::new(17636013826542227504),
638 Felt::new(16254215311946436093),
639 Felt::new(3641486184877122796),
640 Felt::new(11069068059762973582),
641 Felt::new(14868391535953158196),
642 Felt::new(13278298489594233127),
643 Felt::new(389999932707070822),
644 Felt::new(9782021734907796003),
645 Felt::new(4829905704463175582),
646 Felt::new(7567822018949214430),
647 ],
648 [
649 Felt::new(7567822018949214430),
650 Felt::new(14205019324568680367),
651 Felt::new(15489674211196160593),
652 Felt::new(17636013826542227504),
653 Felt::new(16254215311946436093),
654 Felt::new(3641486184877122796),
655 Felt::new(11069068059762973582),
656 Felt::new(14868391535953158196),
657 Felt::new(13278298489594233127),
658 Felt::new(389999932707070822),
659 Felt::new(9782021734907796003),
660 Felt::new(4829905704463175582),
661 ],
662 [
663 Felt::new(4829905704463175582),
664 Felt::new(7567822018949214430),
665 Felt::new(14205019324568680367),
666 Felt::new(15489674211196160593),
667 Felt::new(17636013826542227504),
668 Felt::new(16254215311946436093),
669 Felt::new(3641486184877122796),
670 Felt::new(11069068059762973582),
671 Felt::new(14868391535953158196),
672 Felt::new(13278298489594233127),
673 Felt::new(389999932707070822),
674 Felt::new(9782021734907796003),
675 ],
676 [
677 Felt::new(9782021734907796003),
678 Felt::new(4829905704463175582),
679 Felt::new(7567822018949214430),
680 Felt::new(14205019324568680367),
681 Felt::new(15489674211196160593),
682 Felt::new(17636013826542227504),
683 Felt::new(16254215311946436093),
684 Felt::new(3641486184877122796),
685 Felt::new(11069068059762973582),
686 Felt::new(14868391535953158196),
687 Felt::new(13278298489594233127),
688 Felt::new(389999932707070822),
689 ],
690 [
691 Felt::new(389999932707070822),
692 Felt::new(9782021734907796003),
693 Felt::new(4829905704463175582),
694 Felt::new(7567822018949214430),
695 Felt::new(14205019324568680367),
696 Felt::new(15489674211196160593),
697 Felt::new(17636013826542227504),
698 Felt::new(16254215311946436093),
699 Felt::new(3641486184877122796),
700 Felt::new(11069068059762973582),
701 Felt::new(14868391535953158196),
702 Felt::new(13278298489594233127),
703 ],
704 [
705 Felt::new(13278298489594233127),
706 Felt::new(389999932707070822),
707 Felt::new(9782021734907796003),
708 Felt::new(4829905704463175582),
709 Felt::new(7567822018949214430),
710 Felt::new(14205019324568680367),
711 Felt::new(15489674211196160593),
712 Felt::new(17636013826542227504),
713 Felt::new(16254215311946436093),
714 Felt::new(3641486184877122796),
715 Felt::new(11069068059762973582),
716 Felt::new(14868391535953158196),
717 ],
718];
719
720// ROUND CONSTANTS
721// ================================================================================================
722
723/// Rescue round constants;
724/// computed as in [specifications](https://github.com/ASDiscreteMathematics/rpo)
725///
726/// The constants are broken up into two arrays ARK1 and ARK2; ARK1 contains the constants for the
727/// first half of RPO round, and ARK2 contains constants for the second half of RPO round.
728const ARK1: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = [
729 [
730 Felt::new(5789762306288267392),
731 Felt::new(6522564764413701783),
732 Felt::new(17809893479458208203),
733 Felt::new(107145243989736508),
734 Felt::new(6388978042437517382),
735 Felt::new(15844067734406016715),
736 Felt::new(9975000513555218239),
737 Felt::new(3344984123768313364),
738 Felt::new(9959189626657347191),
739 Felt::new(12960773468763563665),
740 Felt::new(9602914297752488475),
741 Felt::new(16657542370200465908),
742 ],
743 [
744 Felt::new(12987190162843096997),
745 Felt::new(653957632802705281),
746 Felt::new(4441654670647621225),
747 Felt::new(4038207883745915761),
748 Felt::new(5613464648874830118),
749 Felt::new(13222989726778338773),
750 Felt::new(3037761201230264149),
751 Felt::new(16683759727265180203),
752 Felt::new(8337364536491240715),
753 Felt::new(3227397518293416448),
754 Felt::new(8110510111539674682),
755 Felt::new(2872078294163232137),
756 ],
757 [
758 Felt::new(18072785500942327487),
759 Felt::new(6200974112677013481),
760 Felt::new(17682092219085884187),
761 Felt::new(10599526828986756440),
762 Felt::new(975003873302957338),
763 Felt::new(8264241093196931281),
764 Felt::new(10065763900435475170),
765 Felt::new(2181131744534710197),
766 Felt::new(6317303992309418647),
767 Felt::new(1401440938888741532),
768 Felt::new(8884468225181997494),
769 Felt::new(13066900325715521532),
770 ],
771 [
772 Felt::new(5674685213610121970),
773 Felt::new(5759084860419474071),
774 Felt::new(13943282657648897737),
775 Felt::new(1352748651966375394),
776 Felt::new(17110913224029905221),
777 Felt::new(1003883795902368422),
778 Felt::new(4141870621881018291),
779 Felt::new(8121410972417424656),
780 Felt::new(14300518605864919529),
781 Felt::new(13712227150607670181),
782 Felt::new(17021852944633065291),
783 Felt::new(6252096473787587650),
784 ],
785 [
786 Felt::new(4887609836208846458),
787 Felt::new(3027115137917284492),
788 Felt::new(9595098600469470675),
789 Felt::new(10528569829048484079),
790 Felt::new(7864689113198939815),
791 Felt::new(17533723827845969040),
792 Felt::new(5781638039037710951),
793 Felt::new(17024078752430719006),
794 Felt::new(109659393484013511),
795 Felt::new(7158933660534805869),
796 Felt::new(2955076958026921730),
797 Felt::new(7433723648458773977),
798 ],
799 [
800 Felt::new(16308865189192447297),
801 Felt::new(11977192855656444890),
802 Felt::new(12532242556065780287),
803 Felt::new(14594890931430968898),
804 Felt::new(7291784239689209784),
805 Felt::new(5514718540551361949),
806 Felt::new(10025733853830934803),
807 Felt::new(7293794580341021693),
808 Felt::new(6728552937464861756),
809 Felt::new(6332385040983343262),
810 Felt::new(13277683694236792804),
811 Felt::new(2600778905124452676),
812 ],
813 [
814 Felt::new(7123075680859040534),
815 Felt::new(1034205548717903090),
816 Felt::new(7717824418247931797),
817 Felt::new(3019070937878604058),
818 Felt::new(11403792746066867460),
819 Felt::new(10280580802233112374),
820 Felt::new(337153209462421218),
821 Felt::new(13333398568519923717),
822 Felt::new(3596153696935337464),
823 Felt::new(8104208463525993784),
824 Felt::new(14345062289456085693),
825 Felt::new(17036731477169661256),
826 ],
827];
828
829const ARK2: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = [
830 [
831 Felt::new(6077062762357204287),
832 Felt::new(15277620170502011191),
833 Felt::new(5358738125714196705),
834 Felt::new(14233283787297595718),
835 Felt::new(13792579614346651365),
836 Felt::new(11614812331536767105),
837 Felt::new(14871063686742261166),
838 Felt::new(10148237148793043499),
839 Felt::new(4457428952329675767),
840 Felt::new(15590786458219172475),
841 Felt::new(10063319113072092615),
842 Felt::new(14200078843431360086),
843 ],
844 [
845 Felt::new(6202948458916099932),
846 Felt::new(17690140365333231091),
847 Felt::new(3595001575307484651),
848 Felt::new(373995945117666487),
849 Felt::new(1235734395091296013),
850 Felt::new(14172757457833931602),
851 Felt::new(707573103686350224),
852 Felt::new(15453217512188187135),
853 Felt::new(219777875004506018),
854 Felt::new(17876696346199469008),
855 Felt::new(17731621626449383378),
856 Felt::new(2897136237748376248),
857 ],
858 [
859 Felt::new(8023374565629191455),
860 Felt::new(15013690343205953430),
861 Felt::new(4485500052507912973),
862 Felt::new(12489737547229155153),
863 Felt::new(9500452585969030576),
864 Felt::new(2054001340201038870),
865 Felt::new(12420704059284934186),
866 Felt::new(355990932618543755),
867 Felt::new(9071225051243523860),
868 Felt::new(12766199826003448536),
869 Felt::new(9045979173463556963),
870 Felt::new(12934431667190679898),
871 ],
872 [
873 Felt::new(18389244934624494276),
874 Felt::new(16731736864863925227),
875 Felt::new(4440209734760478192),
876 Felt::new(17208448209698888938),
877 Felt::new(8739495587021565984),
878 Felt::new(17000774922218161967),
879 Felt::new(13533282547195532087),
880 Felt::new(525402848358706231),
881 Felt::new(16987541523062161972),
882 Felt::new(5466806524462797102),
883 Felt::new(14512769585918244983),
884 Felt::new(10973956031244051118),
885 ],
886 [
887 Felt::new(6982293561042362913),
888 Felt::new(14065426295947720331),
889 Felt::new(16451845770444974180),
890 Felt::new(7139138592091306727),
891 Felt::new(9012006439959783127),
892 Felt::new(14619614108529063361),
893 Felt::new(1394813199588124371),
894 Felt::new(4635111139507788575),
895 Felt::new(16217473952264203365),
896 Felt::new(10782018226466330683),
897 Felt::new(6844229992533662050),
898 Felt::new(7446486531695178711),
899 ],
900 [
901 Felt::new(3736792340494631448),
902 Felt::new(577852220195055341),
903 Felt::new(6689998335515779805),
904 Felt::new(13886063479078013492),
905 Felt::new(14358505101923202168),
906 Felt::new(7744142531772274164),
907 Felt::new(16135070735728404443),
908 Felt::new(12290902521256031137),
909 Felt::new(12059913662657709804),
910 Felt::new(16456018495793751911),
911 Felt::new(4571485474751953524),
912 Felt::new(17200392109565783176),
913 ],
914 [
915 Felt::new(17130398059294018733),
916 Felt::new(519782857322261988),
917 Felt::new(9625384390925085478),
918 Felt::new(1664893052631119222),
919 Felt::new(7629576092524553570),
920 Felt::new(3485239601103661425),
921 Felt::new(9755891797164033838),
922 Felt::new(15218148195153269027),
923 Felt::new(16460604813734957368),
924 Felt::new(9643968136937729763),
925 Felt::new(3611348709641382851),
926 Felt::new(18256379591337759196),
927 ],
928];