Reliable hash trees for post-quantum stateless cryptographic hash-based signatures

Abstract

The potential advent of quantum computers in coming years has motivated security researchers to start developing resistant systems capable of thwarting future attacks, i.e., developing post-quantum cryptographic approaches. Hash-based, code-based, lattice-based, multivariate-quadratic-equations, and secret-key cryptography are all potential candidates, the merit of which is that they are believed to resist both classical and quantum computers and applying “Shor's algorithm”—the quantum-computer discrete-logarithm algorithm that breaks classical schemes—to them is infeasible. In this paper, we propose reliable and error detection hash trees for stateless hash-based signatures which are believed to be one of the prominent post-quantum schemes, offering security proofs relative to plausible properties of the hash function. We note that this work on the emerging area of reliable, error detection post-quantum cryptography, can be extended and scaled to other approaches as well. We also note that the proposed approaches make such schemes more reliable against natural faults and help protecting them against malicious faults. We propose, benchmark, and discuss fault diagnosis methods for this post-quantum cryptography variant choosing a case study for hash functions, and present the simulations and implementations results to show the applicability of the presented schemes. The presented architectures can be tailored for different reliability objectives based on the resources available, and would initiate the new research area of reliable, error detection postquantum cryptographic architectures.