Verifiable Obtained Random Subsets for Improving SPHINCS+

SPHINCS+ is a stateless hash-based digital signature scheme and an alternate candidate in round 3 of the NIST Post-Quantum Cryptography standardization competition. Although not considered as a finalist because of its performance, SPHINCS(+)may be considered for standardization by NIST after another round of evaluations. In this paper, we propose a Verifiable Obtained Random Subsets (v-ORS) generation mechanism which with one extra hash computation binds the message with the signing FORS instance (the underlying few-time signature algorithm). This enables SPHINCS+ to offer more security against generic attacks because the proposed modification restricts the ORS generation to use a hash key from the utilized signing FORS instance. Consequently, such a modification enables the exploration of different parameter sets for FORS to achieve better performance at the same security level. For instance, when using v-ORS, one parameter set for SPHINCS+-256s provides 82.9% reduction in the computation cost of FORS which leads to around 27% reduction in the number of hash calls of the signing procedure. Given that NIST has identified the performance of SPHINCS+ as its main drawback, these results are a step forward in the path to standardization.