A tight security reduction in the quantum random oracle model for code-based signature schemes
This work addresses the problem of quantum-safe cryptography for secure digital signatures, providing incremental improvements in security reductions for code-based schemes.
The paper tackles the challenge of achieving concrete quantum security for signature schemes in the Quantum Random Oracle Model (QROM) by demonstrating tight security reductions for code-based schemes, specifically applying this to the SURF signature scheme with parameters for 128 bits of quantum security that are competitive with other quantum-secure schemes.
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.