Faster Dual Lattice Attacks by Using Coding Theory

Kévin Carrier (1) , Yixin Shen (2) , Jean-Pierre Tillich (3)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 RHUL - Royal Holloway [University of London]
3 COSMIQ - Cryptologie symétrique, cryptologie fondée sur les codes et information quantique

We present a faster dual lattice attack on the Learning with Errors (LWE) problem, based on ideas from coding theory. Basically, it consists of revisiting the most recent dual attack of [MATZOV22] and replacing modulus switching by a decoding algorithm. This replacement achieves a reduction from small LWE to plain LWE with a very significant reduction of the secret dimension. We also replace the enumeration part of this attack by betting that the secret is zero on the part where we want to enumerate it and iterate this bet over other choices of the enumeration part. We estimate the complexity of this attack by making the optimistic, but realistic guess that we can use polar codes for this decoding task. We show that under this assumption the best attacks on Kyber and Saber can be improved by 1 and 6 bits

Mots clés: Learning with Errors; Lattice; Dual attack; Fast Fourier Transform; Lattice-based Cryptography; Post-quantum Cryptography; Coding theory

Domaines: Informatique [cs]; Mathématiques [math]

Kévin Carrier, Yixin Shen, Jean-Pierre Tillich. Faster Dual Lattice Attacks by Using Coding Theory. 2024. ⟨hal-04519755⟩