Ehsan Ebrahimi

In this paper, we study the post-quantum security of various threshold symmetric schemes. In a threshold scheme, the secret-key is split among multiple parties in order to protect the key. Our first observation is a security analysis in the superposition-access model might be needed for a multi-party threshold scheme in the post-quantum setting since a corrupt party may deliver its secret key to a quantum adversary. Consequently, the adversary can implement a partial evaluation of the multi-party threshold scheme on his quantum device and this can enforce a superposition access to the underlying primitive. In other words, if the underlying primitive is vulnerable to a superposition attack, then the security of the multi-party threshold scheme might break. For instance, under a reasonable assumption we show that the NPR's threshold pseudorandom function (Naor et al. Eurocrypt 99) is not post-quantum secure if the underlying pseudorandom function family is not secure in the superposition-access model.