1# Miden VM Hash Functions
 2In the Miden VM, we make use of different hash functions. Some of these are "traditional" hash functions, like `BLAKE3`, which are optimized for out-of-STARK performance, while others are algebraic hash functions, like `Rescue Prime`, and are more optimized for a better performance inside the STARK. In what follows, we benchmark several such hash functions and compare against other constructions that are used by other proving systems. More precisely, we benchmark:
 3
 4* **BLAKE3** as specified [here](https://github.com/BLAKE3-team/BLAKE3-specs/blob/master/blake3.pdf) and implemented [here](https://github.com/BLAKE3-team/BLAKE3) (with a wrapper exposed via this crate).
 5* **SHA3** as specified [here](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf) and implemented [here](https://github.com/novifinancial/winterfell/blob/46dce1adf0/crypto/src/hash/sha/mod.rs).
 6* **Poseidon** as specified [here](https://eprint.iacr.org/2019/458.pdf) and implemented [here](https://github.com/mir-protocol/plonky2/blob/806b88d7d6e69a30dc0b4775f7ba275c45e8b63b/plonky2/src/hash/poseidon_goldilocks.rs) (but in pure Rust, without vectorized instructions).
 7* **Rescue Prime (RP)** as specified [here](https://eprint.iacr.org/2020/1143) and implemented [here](https://github.com/novifinancial/winterfell/blob/46dce1adf0/crypto/src/hash/rescue/rp64_256/mod.rs).
 8* **Rescue Prime Optimized (RPO)** as specified [here](https://eprint.iacr.org/2022/1577) and implemented in this crate.
 9
10## Comparison and Instructions
11
12### Comparison
13We benchmark the above hash functions using two scenarios. The first is a 2-to-1 $(a,b)\mapsto h(a,b)$ hashing where both $a$, $b$ and $h(a,b)$ are the digests corresponding to each of the hash functions.
14The second scenario is that of sequential hashing where we take a sequence of length $100$ field elements and hash these to produce a single digest. The digests are $4$ field elements in a prime field with modulus $2^{64} - 2^{32} + 1$ (i.e., 32 bytes) for Poseidon, Rescue Prime and RPO, and an array `[u8; 32]` for SHA3 and BLAKE3.
15
16#### Scenario 1: 2-to-1 hashing `h(a,b)`
17
18| Function            | BLAKE3 | SHA3    | Poseidon  | Rp64_256  | RPO_256 |
19| ------------------- | ------ | --------| --------- | --------- | ------- |
20| Apple M1 Pro        | 80 ns  | 245 ns  |  1.5 us   |  9.1 us   | 5.4 us  |
21| Apple M2            | 76 ns  | 233 ns  |  1.3 us   |  7.9 us   | 5.0 us  |
22| Amazon Graviton 3   | 116 ns |         |           |           | 8.8 us  |
23| AMD Ryzen 9 5950X   | 64 ns  | 273 ns  |  1.2 us   |  9.1 us   | 5.5 us  |
24| Intel Core i5-8279U | 80 ns  |         |           |           | 8.7 us  |
25| Intel Xeon 8375C    | 67 ns  |         |           |           | 8.2 us  |
26
27#### Scenario 2: Sequential hashing of 100 elements `h([a_0,...,a_99])`
28
29| Function            | BLAKE3 | SHA3    | Poseidon  | Rp64_256  | RPO_256 |
30| ------------------- | -------| ------- | --------- | --------- | ------- |
31| Apple M1 Pro        | 1.0 us | 1.5 us  |  19.4 us  |   118 us  | 70 us   |
32| Apple M2            | 1.0 us | 1.5 us  |  17.4 us  |   103 us  | 65 us   |
33| Amazon Graviton 3   | 1.4 us |         |           |           | 114 us  |
34| AMD Ryzen 9 5950X   | 0.8 us | 1.7 us  |  15.7 us  |   120 us  | 72 us   |
35| Intel Core i5-8279U | 1.0 us |         |           |           | 116 us  |
36| Intel Xeon 8375C    | 0.8 ns |         |           |           | 110 us  |
37
38### Instructions
39Before you can run the benchmarks, you'll need to make sure you have Rust [installed](https://www.rust-lang.org/tools/install). After that, to run the benchmarks for RPO and BLAKE3, clone the current repository, and from the root directory of the repo run the following:
40
41 ```
42 cargo bench hash
43 ```
44
45To run the benchmarks for Rescue Prime, Poseidon and SHA3, clone the following [repository](https://github.com/Dominik1999/winterfell.git) as above, then checkout the `hash-functions-benches` branch, and from the root directory of the repo run the following:
46
47```
48cargo bench hash
49```