International Association
for Cryptologic Research

SPHINCS$^+$ is a stateless hash-based signature scheme that has been selected for standardization as part of the NIST post-quantum cryptography (PQC) standardization process. Its security proof relies on the distinct-function multi-target second-preimage resistance (DM-SPR) of the underlying keyed hash function. The SPHINCS$^+$ submission offered several instantiations of this keyed hash function, including one based on SHA-256. A recent observation by Sydney Antonov on the PQC mailing list demonstrated that the construction based on SHA-256 did not have DM-SPR at NIST category five, for several of the parameter sets submitted to NIST; however, it remained an open question whether this observation leads to a forgery attack. We answer this question in the affirmative by giving a complete forgery attack that reduces the concrete classical security of these parameter sets by approximately 40 bits of security.

Our attack works by applying Antonov's technique to the {WOTS$^+$} public keys in {\SPHINCS}, leading to a new one-time key that can sign a very limited set of hash values. From that key, we construct a slightly altered version of the original hypertree with which we can sign arbitrary messages, yielding signatures that appear valid.