Current paradigms for construction of lattice-based digital signature schemes

A. G. Leevik ; E. S. Malygina ; E. M. Melnichuk ; D. A. Nabokov

Prikladnaâ diskretnaâ matematika, no. 1 (2025), pp. 36-69

Résumé

With the advent of quantum computing, research into post-quantum cryptography has gained significant attention. This is a novel branch of cryptography that utilizes algorithms and protocols designed to withstand attacks from quantum computers. Lattice theory represents a promising area within post-quantum cryptographic research. Two early examples of lattice-based cryptosystems are the GGH and NTRU schemes. These schemes are based on the challenge of finding the closest vector in a lattice and differ primarily in the type of lattice used. The NTRUSign protocol was developed by combining the strengths of both schemes. In 2008, another approach to lattice signatures was introduced by a group of authors. It is based on the hash-and-sign paradigm, in which a signature for a message is generated using a trapdoor. A year later, V. Lyubashevsky proposed another method for constructing lattice-based signatures that utilizes the Fiat — Shamir transform. However, due to the nature of the underlying lattice structure, the algorithm for signature generation produces a correct signature only with a certain probability. This is due to the use of a rejection sampling for security purposes. This paper presents an overview of existing lattice-based signature construction approaches and cryptographic schemes that are based on these approaches. A comparative analysis was conducted on these schemes, identifying the advantages and disadvantages of each method. Based on the results, optimal conditions for the application of each approach have been determined.

Détail

Keywords: post-quantum cryptography, lattice theory, lattice-based signature.