Dilithium

A Post-Quantum Cryptography solution for digital signing

What is
CRYSTALS-Dilithium?

Dilithium is a lattice-based digital signing scheme that secures data against quantum computing threats. It is based on the CRYSTALS (Cryptographic Suite for Algebraic Lattices) family of Post-Quantum Cryptography (PQC) algorithms. It is particularly well suited to protect against chosen-message attacks.

Because Dilithium is based on hardness of lattice problems over module lattices, it’s a PQC scheme that’s much faster than hash-based schemes, and it’s easy to implement, because it doesn’t need Gaussian sampling.

Dilithium Is Based on Fiat-Shamir With Aborts

Dilithium Is Based on Fiat-Shamir With Aborts

At its base, Dilithium operates on Lyubashevsky’s Fiat-Shamir with Aborts for its lattice scheme. This paradigm repeats executions until verifying a loop iteration that doesn’t abort. The result of this protocol use is a significantly smaller public key, resulting in higher security and efficiency with lower energy consumption.

Dilithium Variants

Unlike other PQC signing schemes, the most recent versions of Dilithium use AES-256 instead of SHAKE. This delivers an expanded matrix and making vector. AES-256 is also used to sample secret polynomials.

Dilithium variants:

pqc_dilithium_blade_4_2

Dilithium2-AES

pqc_dilithium_blade_4_3

Dilithium3-AES

pqc_dilithium_blade_4_5

Dilithium5-AES

The inventors of Dilithium recommend Dilithium 3-AES, because it achieves at least 128 bits of security against classical and quantum attacks.

NIST Approval

NIST Approval

In 2016, the United States National Institute of Standards and Technology put out a call for proposals, requesting submissions of post-quantum cryptographic schemes. Round 1 submissions closed on November 30, 2017. Several dozen schemes were presented and considered.

CRYSTALS-Dilithium was one of four schemes recommended by NIST as an accepted standard for PQC, and one of only three recommended for digital signing.

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