miden-crypto/src/hash/rescue/rpx/mod.rs
src/hash/rescue/rpx/mod.rsRaw
1use core::ops::Range;
2
3use super::{
4 add_constants, add_constants_and_apply_inv_sbox, add_constants_and_apply_sbox, apply_inv_sbox,
5 apply_mds, apply_sbox, CubeExtension, Digest, ElementHasher, Felt, FieldElement, Hasher,
6 StarkField, ARK1, ARK2, BINARY_CHUNK_SIZE, CAPACITY_RANGE, DIGEST_BYTES, DIGEST_RANGE,
7 DIGEST_SIZE, INPUT1_RANGE, INPUT2_RANGE, MDS, NUM_ROUNDS, RATE_RANGE, RATE_WIDTH, STATE_WIDTH,
8 ZERO,
9};
10
11mod digest;
12pub use digest::RpxDigest;
13
14pub type CubicExtElement = CubeExtension<Felt>;
15
16// HASHER IMPLEMENTATION
17// ================================================================================================
18
19/// Implementation of the Rescue Prime eXtension hash function with 256-bit output.
20///
21/// The hash function is based on the XHash12 construction in [specifications](https://eprint.iacr.org/2023/1045)
22///
23/// The parameters used to instantiate the function are:
24/// * Field: 64-bit prime field with modulus 2^64 - 2^32 + 1.
25/// * State width: 12 field elements.
26/// * Capacity size: 4 field elements.
27/// * S-Box degree: 7.
28/// * Rounds: There are 3 different types of rounds:
29/// - (FB): `apply_mds` → `add_constants` → `apply_sbox` → `apply_mds` → `add_constants` → `apply_inv_sbox`.
30/// - (E): `add_constants` → `ext_sbox` (which is raising to power 7 in the degree 3 extension field).
31/// - (M): `apply_mds` → `add_constants`.
32/// * Permutation: (FB) (E) (FB) (E) (FB) (E) (M).
33///
34/// The above parameters target a 128-bit security level. The digest consists of four field elements
35/// and it can be serialized into 32 bytes (256 bits).
36///
37/// ## Hash output consistency
38/// Functions [hash_elements()](Rpx256::hash_elements), [merge()](Rpx256::merge), and
39/// [merge_with_int()](Rpx256::merge_with_int) are internally consistent. That is, computing
40/// a hash for the same set of elements using these functions will always produce the same
41/// result. For example, merging two digests using [merge()](Rpx256::merge) will produce the
42/// same result as hashing 8 elements which make up these digests using
43/// [hash_elements()](Rpx256::hash_elements) function.
44///
45/// However, [hash()](Rpx256::hash) function is not consistent with functions mentioned above.
46/// For example, if we take two field elements, serialize them to bytes and hash them using
47/// [hash()](Rpx256::hash), the result will differ from the result obtained by hashing these
48/// elements directly using [hash_elements()](Rpx256::hash_elements) function. The reason for
49/// this difference is that [hash()](Rpx256::hash) function needs to be able to handle
50/// arbitrary binary strings, which may or may not encode valid field elements - and thus,
51/// deserialization procedure used by this function is different from the procedure used to
52/// deserialize valid field elements.
53///
54/// Thus, if the underlying data consists of valid field elements, it might make more sense
55/// to deserialize them into field elements and then hash them using
56/// [hash_elements()](Rpx256::hash_elements) function rather then hashing the serialized bytes
57/// using [hash()](Rpx256::hash) function.
58#[derive(Debug, Copy, Clone, Eq, PartialEq)]
59pub struct Rpx256();
60
61impl Hasher for Rpx256 {
62 /// Rpx256 collision resistance is 128-bits.
63 const COLLISION_RESISTANCE: u32 = 128;
64
65 type Digest = RpxDigest;
66
67 fn hash(bytes: &[u8]) -> Self::Digest {
68 // initialize the state with zeroes
69 let mut state = [ZERO; STATE_WIDTH];
70
71 // determine the number of field elements needed to encode `bytes` when each field element
72 // represents at most 7 bytes.
73 let num_field_elem = bytes.len().div_ceil(BINARY_CHUNK_SIZE);
74
75 // set the first capacity element to `RATE_WIDTH + (num_field_elem % RATE_WIDTH)`. We do
76 // this to achieve:
77 // 1. Domain separating hashing of `[u8]` from hashing of `[Felt]`.
78 // 2. Avoiding collisions at the `[Felt]` representation of the encoded bytes.
79 state[CAPACITY_RANGE.start] =
80 Felt::from((RATE_WIDTH + (num_field_elem % RATE_WIDTH)) as u8);
81
82 // initialize a buffer to receive the little-endian elements.
83 let mut buf = [0_u8; 8];
84
85 // iterate the chunks of bytes, creating a field element from each chunk and copying it
86 // into the state.
87 //
88 // every time the rate range is filled, a permutation is performed. if the final value of
89 // `i` is not zero, then the chunks count wasn't enough to fill the state range, and an
90 // additional permutation must be performed.
91 let i = bytes.chunks(BINARY_CHUNK_SIZE).fold(0, |i, chunk| {
92 // copy the chunk into the buffer
93 if i != num_field_elem - 1 {
94 buf[..BINARY_CHUNK_SIZE].copy_from_slice(chunk);
95 } else {
96 // on the last iteration, we pad `buf` with a 1 followed by as many 0's as are
97 // needed to fill it
98 buf.fill(0);
99 buf[..chunk.len()].copy_from_slice(chunk);
100 buf[chunk.len()] = 1;
101 }
102
103 // set the current rate element to the input. since we take at most 7 bytes, we are
104 // guaranteed that the inputs data will fit into a single field element.
105 state[RATE_RANGE.start + i] = Felt::new(u64::from_le_bytes(buf));
106
107 // proceed filling the range. if it's full, then we apply a permutation and reset the
108 // counter to the beginning of the range.
109 if i == RATE_WIDTH - 1 {
110 Self::apply_permutation(&mut state);
111 0
112 } else {
113 i + 1
114 }
115 });
116
117 // if we absorbed some elements but didn't apply a permutation to them (would happen when
118 // the number of elements is not a multiple of RATE_WIDTH), apply the RPX permutation. we
119 // don't need to apply any extra padding because the first capacity element contains a
120 // flag indicating the number of field elements constituting the last block when the latter
121 // is not divisible by `RATE_WIDTH`.
122 if i != 0 {
123 state[RATE_RANGE.start + i..RATE_RANGE.end].fill(ZERO);
124 Self::apply_permutation(&mut state);
125 }
126
127 // return the first 4 elements of the rate as hash result.
128 RpxDigest::new(state[DIGEST_RANGE].try_into().unwrap())
129 }
130
131 fn merge(values: &[Self::Digest; 2]) -> Self::Digest {
132 // initialize the state by copying the digest elements into the rate portion of the state
133 // (8 total elements), and set the capacity elements to 0.
134 let mut state = [ZERO; STATE_WIDTH];
135 let it = Self::Digest::digests_as_elements(values.iter());
136 for (i, v) in it.enumerate() {
137 state[RATE_RANGE.start + i] = *v;
138 }
139
140 // apply the RPX permutation and return the first four elements of the state
141 Self::apply_permutation(&mut state);
142 RpxDigest::new(state[DIGEST_RANGE].try_into().unwrap())
143 }
144
145 fn merge_with_int(seed: Self::Digest, value: u64) -> Self::Digest {
146 // initialize the state as follows:
147 // - seed is copied into the first 4 elements of the rate portion of the state.
148 // - if the value fits into a single field element, copy it into the fifth rate element and
149 // set the first capacity element to 5.
150 // - if the value doesn't fit into a single field element, split it into two field
151 // elements, copy them into rate elements 5 and 6 and set the first capacity element to 6.
152 let mut state = [ZERO; STATE_WIDTH];
153 state[INPUT1_RANGE].copy_from_slice(seed.as_elements());
154 state[INPUT2_RANGE.start] = Felt::new(value);
155 if value < Felt::MODULUS {
156 state[CAPACITY_RANGE.start] = Felt::from(5_u8);
157 } else {
158 state[INPUT2_RANGE.start + 1] = Felt::new(value / Felt::MODULUS);
159 state[CAPACITY_RANGE.start] = Felt::from(6_u8);
160 }
161
162 // apply the RPX permutation and return the first four elements of the state
163 Self::apply_permutation(&mut state);
164 RpxDigest::new(state[DIGEST_RANGE].try_into().unwrap())
165 }
166}
167
168impl ElementHasher for Rpx256 {
169 type BaseField = Felt;
170
171 fn hash_elements<E: FieldElement<BaseField = Self::BaseField>>(elements: &[E]) -> Self::Digest {
172 // convert the elements into a list of base field elements
173 let elements = E::slice_as_base_elements(elements);
174
175 // initialize state to all zeros, except for the first element of the capacity part, which
176 // is set to `elements.len() % RATE_WIDTH`.
177 let mut state = [ZERO; STATE_WIDTH];
178 state[CAPACITY_RANGE.start] = Self::BaseField::from((elements.len() % RATE_WIDTH) as u8);
179
180 // absorb elements into the state one by one until the rate portion of the state is filled
181 // up; then apply the Rescue permutation and start absorbing again; repeat until all
182 // elements have been absorbed
183 let mut i = 0;
184 for &element in elements.iter() {
185 state[RATE_RANGE.start + i] = element;
186 i += 1;
187 if i % RATE_WIDTH == 0 {
188 Self::apply_permutation(&mut state);
189 i = 0;
190 }
191 }
192
193 // if we absorbed some elements but didn't apply a permutation to them (would happen when
194 // the number of elements is not a multiple of RATE_WIDTH), apply the RPX permutation after
195 // padding by as many 0 as necessary to make the input length a multiple of the RATE_WIDTH.
196 if i > 0 {
197 while i != RATE_WIDTH {
198 state[RATE_RANGE.start + i] = ZERO;
199 i += 1;
200 }
201 Self::apply_permutation(&mut state);
202 }
203
204 // return the first 4 elements of the state as hash result
205 RpxDigest::new(state[DIGEST_RANGE].try_into().unwrap())
206 }
207}
208
209// HASH FUNCTION IMPLEMENTATION
210// ================================================================================================
211
212impl Rpx256 {
213 // CONSTANTS
214 // --------------------------------------------------------------------------------------------
215
216 /// Sponge state is set to 12 field elements or 768 bytes; 8 elements are reserved for rate and
217 /// the remaining 4 elements are reserved for capacity.
218 pub const STATE_WIDTH: usize = STATE_WIDTH;
219
220 /// The rate portion of the state is located in elements 4 through 11 (inclusive).
221 pub const RATE_RANGE: Range<usize> = RATE_RANGE;
222
223 /// The capacity portion of the state is located in elements 0, 1, 2, and 3.
224 pub const CAPACITY_RANGE: Range<usize> = CAPACITY_RANGE;
225
226 /// The output of the hash function can be read from state elements 4, 5, 6, and 7.
227 pub const DIGEST_RANGE: Range<usize> = DIGEST_RANGE;
228
229 /// MDS matrix used for computing the linear layer in the (FB) and (E) rounds.
230 pub const MDS: [[Felt; STATE_WIDTH]; STATE_WIDTH] = MDS;
231
232 /// Round constants added to the hasher state in the first half of the round.
233 pub const ARK1: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = ARK1;
234
235 /// Round constants added to the hasher state in the second half of the round.
236 pub const ARK2: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = ARK2;
237
238 // TRAIT PASS-THROUGH FUNCTIONS
239 // --------------------------------------------------------------------------------------------
240
241 /// Returns a hash of the provided sequence of bytes.
242 #[inline(always)]
243 pub fn hash(bytes: &[u8]) -> RpxDigest {
244 <Self as Hasher>::hash(bytes)
245 }
246
247 /// Returns a hash of two digests. This method is intended for use in construction of
248 /// Merkle trees and verification of Merkle paths.
249 #[inline(always)]
250 pub fn merge(values: &[RpxDigest; 2]) -> RpxDigest {
251 <Self as Hasher>::merge(values)
252 }
253
254 /// Returns a hash of the provided field elements.
255 #[inline(always)]
256 pub fn hash_elements<E: FieldElement<BaseField = Felt>>(elements: &[E]) -> RpxDigest {
257 <Self as ElementHasher>::hash_elements(elements)
258 }
259
260 // DOMAIN IDENTIFIER
261 // --------------------------------------------------------------------------------------------
262
263 /// Returns a hash of two digests and a domain identifier.
264 pub fn merge_in_domain(values: &[RpxDigest; 2], domain: Felt) -> RpxDigest {
265 // initialize the state by copying the digest elements into the rate portion of the state
266 // (8 total elements), and set the capacity elements to 0.
267 let mut state = [ZERO; STATE_WIDTH];
268 let it = RpxDigest::digests_as_elements(values.iter());
269 for (i, v) in it.enumerate() {
270 state[RATE_RANGE.start + i] = *v;
271 }
272
273 // set the second capacity element to the domain value. The first capacity element is used
274 // for padding purposes.
275 state[CAPACITY_RANGE.start + 1] = domain;
276
277 // apply the RPX permutation and return the first four elements of the state
278 Self::apply_permutation(&mut state);
279 RpxDigest::new(state[DIGEST_RANGE].try_into().unwrap())
280 }
281
282 // RPX PERMUTATION
283 // --------------------------------------------------------------------------------------------
284
285 /// Applies RPX permutation to the provided state.
286 #[inline(always)]
287 pub fn apply_permutation(state: &mut [Felt; STATE_WIDTH]) {
288 Self::apply_fb_round(state, 0);
289 Self::apply_ext_round(state, 1);
290 Self::apply_fb_round(state, 2);
291 Self::apply_ext_round(state, 3);
292 Self::apply_fb_round(state, 4);
293 Self::apply_ext_round(state, 5);
294 Self::apply_final_round(state, 6);
295 }
296
297 // RPX PERMUTATION ROUND FUNCTIONS
298 // --------------------------------------------------------------------------------------------
299
300 /// (FB) round function.
301 #[inline(always)]
302 pub fn apply_fb_round(state: &mut [Felt; STATE_WIDTH], round: usize) {
303 apply_mds(state);
304 if !add_constants_and_apply_sbox(state, &ARK1[round]) {
305 add_constants(state, &ARK1[round]);
306 apply_sbox(state);
307 }
308
309 apply_mds(state);
310 if !add_constants_and_apply_inv_sbox(state, &ARK2[round]) {
311 add_constants(state, &ARK2[round]);
312 apply_inv_sbox(state);
313 }
314 }
315
316 /// (E) round function.
317 #[inline(always)]
318 pub fn apply_ext_round(state: &mut [Felt; STATE_WIDTH], round: usize) {
319 // add constants
320 add_constants(state, &ARK1[round]);
321
322 // decompose the state into 4 elements in the cubic extension field and apply the power 7
323 // map to each of the elements
324 let [s0, s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11] = *state;
325 let ext0 = Self::exp7(CubicExtElement::new(s0, s1, s2));
326 let ext1 = Self::exp7(CubicExtElement::new(s3, s4, s5));
327 let ext2 = Self::exp7(CubicExtElement::new(s6, s7, s8));
328 let ext3 = Self::exp7(CubicExtElement::new(s9, s10, s11));
329
330 // decompose the state back into 12 base field elements
331 let arr_ext = [ext0, ext1, ext2, ext3];
332 *state = CubicExtElement::slice_as_base_elements(&arr_ext)
333 .try_into()
334 .expect("shouldn't fail");
335 }
336
337 /// (M) round function.
338 #[inline(always)]
339 pub fn apply_final_round(state: &mut [Felt; STATE_WIDTH], round: usize) {
340 apply_mds(state);
341 add_constants(state, &ARK1[round]);
342 }
343
344 /// Computes an exponentiation to the power 7 in cubic extension field.
345 #[inline(always)]
346 pub fn exp7(x: CubeExtension<Felt>) -> CubeExtension<Felt> {
347 let x2 = x.square();
348 let x4 = x2.square();
349
350 let x3 = x2 * x;
351 x3 * x4
352 }
353}