A tight security reduction in the quantum random oracle model for code-based signature schemes

TL;DR

This paper demonstrates a tight security reduction for code-based signature schemes in the quantum random oracle model, enabling concrete quantum security parameters and analysis of related quantum algorithms.

Contribution

It provides the first tight security reduction for code-based signatures in the QROM and applies it to the SURF scheme with practical parameters.

Findings

Tight security reduction in the QROM for code-based signatures

Concrete parameters for 128-bit quantum security in the QROM

Analysis of quantum algorithms related to code-based assumptions

Abstract

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes.