Struct winter_crypto::hashers::Rp64_256

pub struct Rp64_256();

Implementation of Hasher trait for Rescue Prime hash function with 256-bit output.

The hash function is implemented according to the Rescue Prime specifications with the following exception:

• We set the number of rounds to 7, which implies a 40% security margin instead of the 50% margin used in the specifications (a 50% margin rounds up to 8 rounds). The primary motivation for this is that having the number of rounds be one less than a power of two simplifies AIR design for computations involving the hash function.
• When hashing a sequence of elements, we do not append Fp(1) followed by Fp(0) elements to the end of the sequence as padding. Instead, we initialize the first capacity element to the number of elements to be hashed, and pad the sequence with Fp(0) elements only. This ensures consistency of hash outputs between different hashing methods (see section below). However, it also means that our instantiation of Rescue Prime cannot be used in a stream mode as the number of elements to be hashed must be known upfront.
• We use the first 4 elements of the state (rather than the last 4 elements of the state) for capacity and the remaining 8 elements for rate. The output of the hash function comes from the first four elements of the rate portion of the state (elements 4, 5, 6, and 7). This effectively applies a fixed bit permutation before and after XLIX permutation. We assert without proof that this does not affect security of the construction.
• Instead of using Vandermonde matrices as a standard way of generating an MDS matrix as described in Rescue Prime paper, we use a methodology developed by Polygon Zero to find an MDS matrix with coefficients which are small powers of two in frequency domain. This allows us to dramatically reduce MDS matrix multiplication time. Using a different MDS matrix does not affect security of the hash function as any MDS matrix satisfies Rescue Prime construction (as described in section 4.2 of the paper).

The parameters used to instantiate the function are:

• Field: 64-bit prime field with modulus 2^64 - 2^32 + 1.
• State width: 12 field elements.
• Capacity size: 4 field elements.
• Number of founds: 7.
• S-Box degree: 7.

The above parameters target 128-bit security level. The digest consists of four field elements and it can be serialized into 32 bytes (256 bits).

Hash output consistency

Functions hash_elements(), merge(), and merge_with_int() are internally consistent. That is, computing a hash for the same set of elements using these functions will always produce the same result. For example, merging two digests using merge() will produce the same result as hashing 8 elements which make up these digests using hash_elements() function.

However, hash() function is not consistent with functions mentioned above. For example, if we take two field elements, serialize them to bytes and hash them using hash(), the result will differ from the result obtained by hashing these elements directly using hash_elements() function. The reason for this difference is that hash() function needs to be able to handle arbitrary binary strings, which may or may not encode valid field elements - and thus, deserialization procedure used by this function is different from the procedure used to deserialize valid field elements.

Thus, if the underlying data consists of valid field elements, it might make more sense to deserialize them into field elements and then hash them using hash_elements() function rather then hashing the serialized bytes using hash() function.

Implementations

impl Rp64_256

pub const NUM_ROUNDS: usize = 7usize

The number of rounds is set to 7 to target 128-bit security level with 40% security margin.

pub const STATE_WIDTH: usize = 12usize

Sponge state is set to 12 field elements or 96 bytes; 8 elements are reserved for rate and the remaining 4 elements are reserved for capacity.

pub const RATE_RANGE: Range<usize> = RATE_RANGE

The rate portion of the state is located in elements 4 through 11 (inclusive).

pub const CAPACITY_RANGE: Range<usize> = CAPACITY_RANGE

The capacity portion of the state is located in elements 0, 1, 2, and 3.

pub const DIGEST_RANGE: Range<usize> = DIGEST_RANGE

The output of the hash function can be read from state elements 4, 5, 6, and 7.

pub const MDS: [[BaseElement; 12]; 12] = MDS

MDS matrix used for computing the linear layer in a Rescue Prime round.

pub const INV_MDS: [[BaseElement; 12]; 12] = INV_MDS

Inverse of the MDS matrix.

pub const ARK1: [[BaseElement; 12]; 7] = ARK1

Round constants added to the hasher state in the first half of the Rescue Prime round.

pub const ARK2: [[BaseElement; 12]; 7] = ARK2

Round constants added to the hasher state in the second half of the Rescue Prime round.

pub fn apply_permutation(state: &mut [BaseElement; 12])

Applies Rescue-XLIX permutation to the provided state.

pub fn apply_round(state: &mut [BaseElement; 12], round: usize)

Rescue-XLIX round function.

Trait Implementations

impl ElementHasher for Rp64_256

type BaseField = BaseElement

Specifies a base field for elements which can be hashed with this hasher.

fn hash_elements<E: FieldElement<BaseField = Self::BaseField>>( elements: &[E] ) -> Self::Digest

Returns a hash of the provided field elements.

impl Hasher for Rp64_256

type Digest = ElementDigest

Specifies a digest type returned by this hasher.

const COLLISION_RESISTANCE: u32 = 128u32

Collision resistance of the hash function measured in bits.

fn hash(bytes: &[u8]) -> Self::Digest

Returns a hash of the provided sequence of bytes.

fn merge(values: &[Self::Digest; 2]) -> Self::Digest

Returns a hash of two digests. This method is intended for use in construction of Merkle trees.

fn merge_with_int(seed: Self::Digest, value: u64) -> Self::Digest

Returns hash(seed || value). This method is intended for use in PRNG and PoW contexts.