miden-crypto/src/hash/rescue/rpo/mod.rs
src/hash/rescue/rpo/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, Digest, ElementHasher, Felt, FieldElement, Hasher, StarkField, ARK1,
6 ARK2, BINARY_CHUNK_SIZE, CAPACITY_RANGE, DIGEST_BYTES, DIGEST_RANGE, DIGEST_SIZE, INPUT1_RANGE,
7 INPUT2_RANGE, MDS, NUM_ROUNDS, ONE, RATE_RANGE, RATE_WIDTH, STATE_WIDTH, ZERO,
8};
9
10mod digest;
11pub use digest::{RpoDigest, RpoDigestError};
12
13#[cfg(test)]
14mod tests;
15
16// HASHER IMPLEMENTATION
17// ================================================================================================
18
19/// Implementation of the Rescue Prime Optimized hash function with 256-bit output.
20///
21/// The hash function is implemented according to the Rescue Prime Optimized
22/// [specifications](https://eprint.iacr.org/2022/1577)
23///
24/// The parameters used to instantiate the function are:
25/// * Field: 64-bit prime field with modulus p = 2^64 - 2^32 + 1.
26/// * State width: 12 field elements.
27/// * Rate size: r = 8 field elements.
28/// * Capacity size: c = 4 field elements.
29/// * Number of founds: 7.
30/// * S-Box degree: 7.
31///
32/// The above parameters target a 128-bit security level. The digest consists of four field elements
33/// and it can be serialized into 32 bytes (256 bits).
34///
35/// ## Hash output consistency
36/// Functions [hash_elements()](Rpo256::hash_elements), [merge()](Rpo256::merge), and
37/// [merge_with_int()](Rpo256::merge_with_int) are internally consistent. That is, computing
38/// a hash for the same set of elements using these functions will always produce the same
39/// result. For example, merging two digests using [merge()](Rpo256::merge) will produce the
40/// same result as hashing 8 elements which make up these digests using
41/// [hash_elements()](Rpo256::hash_elements) function.
42///
43/// However, [hash()](Rpo256::hash) function is not consistent with functions mentioned above.
44/// For example, if we take two field elements, serialize them to bytes and hash them using
45/// [hash()](Rpo256::hash), the result will differ from the result obtained by hashing these
46/// elements directly using [hash_elements()](Rpo256::hash_elements) function. The reason for
47/// this difference is that [hash()](Rpo256::hash) function needs to be able to handle
48/// arbitrary binary strings, which may or may not encode valid field elements - and thus,
49/// deserialization procedure used by this function is different from the procedure used to
50/// deserialize valid field elements.
51///
52/// Thus, if the underlying data consists of valid field elements, it might make more sense
53/// to deserialize them into field elements and then hash them using
54/// [hash_elements()](Rpo256::hash_elements) function rather then hashing the serialized bytes
55/// using [hash()](Rpo256::hash) function.
56///
57/// ## Domain separation
58/// [merge_in_domain()](Rpo256::merge_in_domain) hashes two digests into one digest with some domain
59/// identifier and the current implementation sets the second capacity element to the value of
60/// this domain identifier. Using a similar argument to the one formulated for domain separation of
61/// the RPX hash function in Appendix C of its [specification](https://eprint.iacr.org/2023/1045),
62/// one sees that doing so degrades only pre-image resistance, from its initial bound of c.log_2(p),
63/// by as much as the log_2 of the size of the domain identifier space. Since pre-image resistance
64/// becomes the bottleneck for the security bound of the sponge in overwrite-mode only when it is
65/// lower than 2^128, we see that the target 128-bit security level is maintained as long as
66/// the size of the domain identifier space, including for padding, is less than 2^128.
67#[derive(Debug, Copy, Clone, Eq, PartialEq)]
68pub struct Rpo256();
69
70impl Hasher for Rpo256 {
71 /// Rpo256 collision resistance is 128-bits.
72 const COLLISION_RESISTANCE: u32 = 128;
73
74 type Digest = RpoDigest;
75
76 fn hash(bytes: &[u8]) -> Self::Digest {
77 // initialize the state with zeroes
78 let mut state = [ZERO; STATE_WIDTH];
79
80 // set the capacity (first element) to a flag on whether or not the input length is evenly
81 // divided by the rate. this will prevent collisions between padded and non-padded inputs,
82 // and will rule out the need to perform an extra permutation in case of evenly divided
83 // inputs.
84 let is_rate_multiple = bytes.len() % RATE_WIDTH == 0;
85 if !is_rate_multiple {
86 state[CAPACITY_RANGE.start] = ONE;
87 }
88
89 // initialize a buffer to receive the little-endian elements.
90 let mut buf = [0_u8; 8];
91
92 // iterate the chunks of bytes, creating a field element from each chunk and copying it
93 // into the state.
94 //
95 // every time the rate range is filled, a permutation is performed. if the final value of
96 // `i` is not zero, then the chunks count wasn't enough to fill the state range, and an
97 // additional permutation must be performed.
98 let i = bytes.chunks(BINARY_CHUNK_SIZE).fold(0, |i, chunk| {
99 // the last element of the iteration may or may not be a full chunk. if it's not, then
100 // we need to pad the remainder bytes of the chunk with zeroes, separated by a `1`.
101 // this will avoid collisions.
102 if chunk.len() == BINARY_CHUNK_SIZE {
103 buf[..BINARY_CHUNK_SIZE].copy_from_slice(chunk);
104 } else {
105 buf.fill(0);
106 buf[..chunk.len()].copy_from_slice(chunk);
107 buf[chunk.len()] = 1;
108 }
109
110 // set the current rate element to the input. since we take at most 7 bytes, we are
111 // guaranteed that the inputs data will fit into a single field element.
112 state[RATE_RANGE.start + i] = Felt::new(u64::from_le_bytes(buf));
113
114 // proceed filling the range. if it's full, then we apply a permutation and reset the
115 // counter to the beginning of the range.
116 if i == RATE_WIDTH - 1 {
117 Self::apply_permutation(&mut state);
118 0
119 } else {
120 i + 1
121 }
122 });
123
124 // if we absorbed some elements but didn't apply a permutation to them (would happen when
125 // the number of elements is not a multiple of RATE_WIDTH), apply the RPO permutation. we
126 // don't need to apply any extra padding because the first capacity element contains a
127 // flag indicating whether the input is evenly divisible by the rate.
128 if i != 0 {
129 state[RATE_RANGE.start + i..RATE_RANGE.end].fill(ZERO);
130 state[RATE_RANGE.start + i] = ONE;
131 Self::apply_permutation(&mut state);
132 }
133
134 // return the first 4 elements of the rate as hash result.
135 RpoDigest::new(state[DIGEST_RANGE].try_into().unwrap())
136 }
137
138 fn merge(values: &[Self::Digest; 2]) -> Self::Digest {
139 // initialize the state by copying the digest elements into the rate portion of the state
140 // (8 total elements), and set the capacity elements to 0.
141 let mut state = [ZERO; STATE_WIDTH];
142 let it = Self::Digest::digests_as_elements(values.iter());
143 for (i, v) in it.enumerate() {
144 state[RATE_RANGE.start + i] = *v;
145 }
146
147 // apply the RPO permutation and return the first four elements of the state
148 Self::apply_permutation(&mut state);
149 RpoDigest::new(state[DIGEST_RANGE].try_into().unwrap())
150 }
151
152 fn merge_with_int(seed: Self::Digest, value: u64) -> Self::Digest {
153 // initialize the state as follows:
154 // - seed is copied into the first 4 elements of the rate portion of the state.
155 // - if the value fits into a single field element, copy it into the fifth rate element and
156 // set the sixth rate element to 1.
157 // - if the value doesn't fit into a single field element, split it into two field elements,
158 // copy them into rate elements 5 and 6, and set the seventh rate element to 1.
159 // - set the first capacity element to 1
160 let mut state = [ZERO; STATE_WIDTH];
161 state[INPUT1_RANGE].copy_from_slice(seed.as_elements());
162 state[INPUT2_RANGE.start] = Felt::new(value);
163 if value < Felt::MODULUS {
164 state[INPUT2_RANGE.start + 1] = ONE;
165 } else {
166 state[INPUT2_RANGE.start + 1] = Felt::new(value / Felt::MODULUS);
167 state[INPUT2_RANGE.start + 2] = ONE;
168 }
169
170 // common padding for both cases
171 state[CAPACITY_RANGE.start] = ONE;
172
173 // apply the RPO permutation and return the first four elements of the state
174 Self::apply_permutation(&mut state);
175 RpoDigest::new(state[DIGEST_RANGE].try_into().unwrap())
176 }
177}
178
179impl ElementHasher for Rpo256 {
180 type BaseField = Felt;
181
182 fn hash_elements<E: FieldElement<BaseField = Self::BaseField>>(elements: &[E]) -> Self::Digest {
183 // convert the elements into a list of base field elements
184 let elements = E::slice_as_base_elements(elements);
185
186 // initialize state to all zeros, except for the first element of the capacity part, which
187 // is set to 1 if the number of elements is not a multiple of RATE_WIDTH.
188 let mut state = [ZERO; STATE_WIDTH];
189 if elements.len() % RATE_WIDTH != 0 {
190 state[CAPACITY_RANGE.start] = ONE;
191 }
192
193 // absorb elements into the state one by one until the rate portion of the state is filled
194 // up; then apply the Rescue permutation and start absorbing again; repeat until all
195 // elements have been absorbed
196 let mut i = 0;
197 for &element in elements.iter() {
198 state[RATE_RANGE.start + i] = element;
199 i += 1;
200 if i % RATE_WIDTH == 0 {
201 Self::apply_permutation(&mut state);
202 i = 0;
203 }
204 }
205
206 // if we absorbed some elements but didn't apply a permutation to them (would happen when
207 // the number of elements is not a multiple of RATE_WIDTH), apply the RPO permutation after
208 // padding by appending a 1 followed by as many 0 as necessary to make the input length a
209 // multiple of the RATE_WIDTH.
210 if i > 0 {
211 state[RATE_RANGE.start + i] = ONE;
212 i += 1;
213 while i != RATE_WIDTH {
214 state[RATE_RANGE.start + i] = ZERO;
215 i += 1;
216 }
217 Self::apply_permutation(&mut state);
218 }
219
220 // return the first 4 elements of the state as hash result
221 RpoDigest::new(state[DIGEST_RANGE].try_into().unwrap())
222 }
223}
224
225// HASH FUNCTION IMPLEMENTATION
226// ================================================================================================
227
228impl Rpo256 {
229 // CONSTANTS
230 // --------------------------------------------------------------------------------------------
231
232 /// The number of rounds is set to 7 to target 128-bit security level.
233 pub const NUM_ROUNDS: usize = NUM_ROUNDS;
234
235 /// Sponge state is set to 12 field elements or 768 bytes; 8 elements are reserved for rate and
236 /// the remaining 4 elements are reserved for capacity.
237 pub const STATE_WIDTH: usize = STATE_WIDTH;
238
239 /// The rate portion of the state is located in elements 4 through 11 (inclusive).
240 pub const RATE_RANGE: Range<usize> = RATE_RANGE;
241
242 /// The capacity portion of the state is located in elements 0, 1, 2, and 3.
243 pub const CAPACITY_RANGE: Range<usize> = CAPACITY_RANGE;
244
245 /// The output of the hash function can be read from state elements 4, 5, 6, and 7.
246 pub const DIGEST_RANGE: Range<usize> = DIGEST_RANGE;
247
248 /// MDS matrix used for computing the linear layer in a RPO round.
249 pub const MDS: [[Felt; STATE_WIDTH]; STATE_WIDTH] = MDS;
250
251 /// Round constants added to the hasher state in the first half of the RPO round.
252 pub const ARK1: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = ARK1;
253
254 /// Round constants added to the hasher state in the second half of the RPO round.
255 pub const ARK2: [[Felt; STATE_WIDTH]; NUM_ROUNDS] = ARK2;
256
257 // TRAIT PASS-THROUGH FUNCTIONS
258 // --------------------------------------------------------------------------------------------
259
260 /// Returns a hash of the provided sequence of bytes.
261 #[inline(always)]
262 pub fn hash(bytes: &[u8]) -> RpoDigest {
263 <Self as Hasher>::hash(bytes)
264 }
265
266 /// Returns a hash of two digests. This method is intended for use in construction of
267 /// Merkle trees and verification of Merkle paths.
268 #[inline(always)]
269 pub fn merge(values: &[RpoDigest; 2]) -> RpoDigest {
270 <Self as Hasher>::merge(values)
271 }
272
273 /// Returns a hash of the provided field elements.
274 #[inline(always)]
275 pub fn hash_elements<E: FieldElement<BaseField = Felt>>(elements: &[E]) -> RpoDigest {
276 <Self as ElementHasher>::hash_elements(elements)
277 }
278
279 // DOMAIN IDENTIFIER
280 // --------------------------------------------------------------------------------------------
281
282 /// Returns a hash of two digests and a domain identifier.
283 pub fn merge_in_domain(values: &[RpoDigest; 2], domain: Felt) -> RpoDigest {
284 // initialize the state by copying the digest elements into the rate portion of the state
285 // (8 total elements), and set the capacity elements to 0.
286 let mut state = [ZERO; STATE_WIDTH];
287 let it = RpoDigest::digests_as_elements(values.iter());
288 for (i, v) in it.enumerate() {
289 state[RATE_RANGE.start + i] = *v;
290 }
291
292 // set the second capacity element to the domain value. The first capacity element is used
293 // for padding purposes.
294 state[CAPACITY_RANGE.start + 1] = domain;
295
296 // apply the RPO permutation and return the first four elements of the state
297 Self::apply_permutation(&mut state);
298 RpoDigest::new(state[DIGEST_RANGE].try_into().unwrap())
299 }
300
301 // RESCUE PERMUTATION
302 // --------------------------------------------------------------------------------------------
303
304 /// Applies RPO permutation to the provided state.
305 #[inline(always)]
306 pub fn apply_permutation(state: &mut [Felt; STATE_WIDTH]) {
307 for i in 0..NUM_ROUNDS {
308 Self::apply_round(state, i);
309 }
310 }
311
312 /// RPO round function.
313 #[inline(always)]
314 pub fn apply_round(state: &mut [Felt; STATE_WIDTH], round: usize) {
315 // apply first half of RPO round
316 apply_mds(state);
317 if !add_constants_and_apply_sbox(state, &ARK1[round]) {
318 add_constants(state, &ARK1[round]);
319 apply_sbox(state);
320 }
321
322 // apply second half of RPO round
323 apply_mds(state);
324 if !add_constants_and_apply_inv_sbox(state, &ARK2[round]) {
325 add_constants(state, &ARK2[round]);
326 apply_inv_sbox(state);
327 }
328 }
329}