On Forging SPHINCS+-Haraka Signatures on a Fault-tolerant Quantum Computer

SPHINCS\(^{+}\) is a state-of-the-art hash based signature scheme, the security of which is either based on SHA-256, SHAKE-256 or on the Haraka hash function. In this work, we perform an in-depth analysis of how the hash functions are embedded into SPHINCS\(^{+}\) and how the quantum pre-image resistance impacts the security of the signature scheme. Subsequently, we evaluate the cost of implementing Grover’s quantum search algorithm to find a pre-image that admits a universal forgery.