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docs: minor updates to main and benchmark README files

al-gkr-basic-workflow
Bobbin Threadbare 2 years ago
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README.md

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* [BLAKE3](https://github.com/BLAKE3-team/BLAKE3) hash function with 256-bit, 192-bit, or 160-bit output. The 192-bit and 160-bit outputs are obtained by truncating the 256-bit output of the standard BLAKE3.
* [RPO](https://eprint.iacr.org/2022/1577) hash function with 256-bit output. This hash function is an algebraic hash function suitable for recursive STARKs.
For performance benchmarks of these hash functions and their comparison to other popular hash functions please see [here](./benches/).
## Merkle
[Merkle module](./src/merkle/) provides a set of data structures related to Merkle trees. All these data structures are implemented using the RPO hash function described above. The data structures are:

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# Miden VM Hash Functions
In 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:
* **Rescue Prime:**
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).
* **Rescue Prime Optimized:**
As specified [here](https://eprint.iacr.org/2022/1577) and implemented in this crate.
* **BLAKE3:**
As specified [here](https://github.com/BLAKE3-team/BLAKE3-specs/blob/master/blake3.pdf) and implemented in this crate.
* **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).
* **Poseidon:**
As specified [here](https://eprint.iacr.org/2019/458.pdf) and implemented (in pure Rust, without vectorized instructions) [here](https://github.com/mir-protocol/plonky2/blob/main/plonky2/src/hash/poseidon_goldilocks.rs).
* **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).
* **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).
* **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).
* **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).
* **Rescue Prime Optimized (RPO)** as specified [here](https://eprint.iacr.org/2022/1577) and implemented in this crate.
## Comparison and Instructions
### Comparison
We 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.
The 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 (i.e. 256-bit) for Poseidon, Rescue Prime and RPO, and an array `[u8;32]` for SHA3 and BLAKE3.
The 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.
#### Scenario 1: 2-to-1 hashing `h(a,b)`
| Function | BLAKE3 | SHA3 | Poseidon | Rp64_256 | RPO_256 |
| ----------------- | ------ | --------| --------- | --------- | ------- |
| Apple M1 Pro | 80 ns | 245 ns | 1.3 us | 9.1 us | 5.4 us |
| Apple M2 | 76 ns | 233 ns | 1.2 us | 7.9 us | 5.0 us |
| AMD Ryzen 9 5950X | 64 ns | 273 ns | 1.2 us | 9.1 us | 5.5 us |
| Function | BLAKE3 | SHA3 | Poseidon | Rp64_256 | RPO_256 |
| ------------------- | ------ | --------| --------- | --------- | ------- |
| Apple M1 Pro | 80 ns | 245 ns | 1.5 us | 9.1 us | 5.4 us |
| Apple M2 | 76 ns | 233 ns | 1.3 us | 7.9 us | 5.0 us |
| Amazon Graviton 3 | 116 ns | | | | 8.8 us |
| AMD Ryzen 9 5950X | 64 ns | 273 ns | 1.2 us | 9.1 us | 5.5 us |
| Intel Core i5-8279U | 80 ns | | | | 8.7 us |
| Intel Xeon 8375C | 67 ns | | | | 8.2 us |
#### Scenario 2: Sequential hashing of 100 elements `h([a_0,...,a_99])`
| Function | BLAKE3 | SHA3 | Poseidon | Rp64_256 | RPO_256 |
| ----------------- | -------| ------- | --------- | --------- | ------- |
| Apple M1 Pro | 1.1 us | 1.5 us | 17.3 us | 118 us | 70 us |
| Apple M2 | 1.0 us | 1.5 us | 15.5 us | 103 us | 65 us |
| AMD Ryzen 9 5950X | 0.8 us | 1.7 us | 15.7 us | 120 us | 72 us |
| Function | BLAKE3 | SHA3 | Poseidon | Rp64_256 | RPO_256 |
| ------------------- | -------| ------- | --------- | --------- | ------- |
| Apple M1 Pro | 1.1 us | 1.5 us | 19.4 us | 118 us | 70 us |
| Apple M2 | 1.0 us | 1.5 us | 17.4 us | 103 us | 65 us |
| Amazon Graviton 3 | 1.4 us | | | | 114 us |
| AMD Ryzen 9 5950X | 0.8 us | 1.7 us | 15.7 us | 120 us | 72 us |
| Intel Core i5-8279U | 1.0 us | | | | 116 us |
| Intel Xeon 8375C | 0.8 ns | | | | 110 us |
### Instructions
Before 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:
```
cargo bench --bench hash
cargo bench hash
```
To 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:
```
cargo bench --bench hash
cargo bench hash
```

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