twenty-first

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A collection of cryptography primitives written in Rust.

Content of this library

This library contains primarily the following cryptographic primitives:

The Tip5 hash function

• The Tip5 Hash Function for Recursive STARKs

Lattice-crypto

• arithmetic for the quotient ring $\mathbb{F}_ p[X] / \langle X^{64} + 1 \rangle$
• arithmetic for modules over this quotient ring
• a IND-CCA2-secure key encapsulation mechanism
• Lattice-Based Cryptography in Miden VM

BFieldElement, XFieldElement

• The prime-field type $\mathbb{F}_p$ where $p = 2^{64} - 2^{32} + 1$
• The extension field $\mathbb{F}_p[x]/(x^3 - x + 1)$
• A codec trait for encoding and decoding structs as Vecs of BFieldElement
• An efficient prime for number-theoretic transforms

NTT

• Number Theoretic Transform (discrete Fast Fourier Transform)
• Anatomy of a STARK, Part 6: Speeding Things Up

Univariate polynomials

Merkle Trees

Merkle Mountain Ranges

Wasm support

The twenty-first library can be built for WebAssembly. See the dedicated readme for further information.