## Lean 4 Poseidon implementation

This repository contains an implementation of the Poseidon hash function in Lean 4.

### Usage

The main function of this implementation is `Poseidon.hash`

found in `Poseidon.HashImpl`

. The function has signature:

```
def hash (prof : HashProfile)
(context : Hash.Context prof)
(preimage : Array (Zmod prof.p))
(domain : Domain) : Zmod prof.p
```

The parameters to the function can be briefly described as follows:

`HashProfile`

: Contains the parameters prime`p`

, width`t`

, security parameters`M`

, and S-box exponent`a`

`Hash.Context`

: Contains the necessary parameters to compute the Poseidon hash, in particular the MDS matrix and the array of round constants.`Array (Zmod profile.p)`

: The message to hash. If the length of the array does not match the specified arity a dummy value of`0`

is returned`Domain`

: The domain in which to hash the function. Right now it is either a fixed-arity Merkle tree hash or fixed length input.

The output is the result of the hash (the second component of the final vector, consistent with the Filecoin specification.)

Pre-computed profiles and contexts are available in the `Poseidon.Parameters`

folder.

For Lurk specific hashing purposes, the `Poseidon.ForLurk`

module contains

```
namespace Poseidon.Lurk
abbrev F := Zmod Lurk.Profile.p
def Context : Hash.Context Profile :=
⟨Lurk.MDS, Lurk.roundConstants⟩
def hash (f₁ f₂ f₃ f₄ : F) : F :=
Poseidon.hash Profile Context #[f₁, f₂, f₃, f₄] .merkleTree
```

which computes the arity 4 hashes found in the lurk-rs.

#### Generating new profiles

Also included in the repository are round number, and round constant generators to generate profiles and contexts from an input set of parameters. The generated constants and MDS matrices are consistent with the Filecoin specification.

### Comparison with other implementations

The aim of this Lean 4 implementation is to maintain consistency with the other major implementations of the Poseidon hashing protocol. In particular

This is achieved through the test suite described below, and writing the core algorithm agnostic to implementation details.

### Tests

This repository contains a robust suite of tests that checks that the hashing, round constant generation, and round number generation match those found in the other implementations.

The test suite contains and expands on the tests in the reference, Python, and Filecoin/rust
implementations. See the corresponding test in the `Tests`

folder to find more about what is being
tested and how the tests were generated.

Included in the test suite are tests that check the parameters contained in the pre-computed profiles match those that would be computed according to the relevant specification in which they are defined.