Efficient One-Time Signatures from Quasi-Cyclic Codes: A Full Treatment

Edoardo Persichetti

doi:10.3390/cryptography2040030

Abstract

The design of a practical code-based signature scheme is an open problem in post-quantum cryptography. This paper is the full version of a work appeared at SIN’18 as a short paper, which introduced a simple and efficient one-time secure signature scheme based on quasi-cyclic codes. As such, this paper features, in a fully self-contained way, an accurate description of the scheme setting and related previous work, a detailed security analysis, and an extensive comparison and performance discussion.

Highlights

Digital signatures are a very important cryptographic primitive in the modern world
Its elliptic curves version (ECDSA), all included in the FIPS standard 186-3 [1]
Many schemes based on coding theory have been proposed over the years that either follow a “direct” hash-and-sign approach like the Courtois-Finiasz-Sendrier scheme (CFS) [2] and the Kabatianskii-Krouk-Smeets scheme (KKS) [3], or rely on the Fiat–Shamir transform [4] to convert an identification scheme into a signature scheme

Summary

Introduction

Digital signatures are a very important cryptographic primitive in the modern world. Among the most popular, there are, for instance, schemes based on the RSA assumptions, discrete logarithm (DSA). Many of the various proposals have been broken, and all those that are still considered secure suffer from one or more flaws, be that a huge public key, a large signature or a slow signing algorithm, which make them highly inefficient in practical situations This is evident in the identification schemes, where it is usually necessary to repeat the protocol many times in order to guarantee correctness or security. Choosing quasi-cyclic codes allows for taking advantage of the innate ring metric and makes the scheme viable in practice This full version features a detailed security analysis, including a proof of security that guarantees one-time existential unforgeability against chosen-message attacks, i.e., 1-EUF-CMA.

Coding Theory

Identification Schemes and Signatures

Number Theory and Lattices

A Coding Theory Scenario

The New Scheme

Security

Performance and Comparison

Existing Code-Based Solutions

Identification Schemes

Comparison

Implementation

Conclusions