Practical Signatures from the Partial Fourier Recovery Problem

We present PASSSign, a variant of the prior PASS and PASS-2 proposals, as a candidate for a practical post-quantum signature scheme. Its hardness is based on the problem of recovering a ring element with small norm from an incomplete description of its Chinese remainder representation. For our particular instantiation, this corresponds to the recovery of a signal with small infinity norm from a limited set of its Fourier coefficients. The key improvement over previous versions of PASS is the introduction of a rejection sampling technique from Lyubashevsky (2009) which assures that transcript distributions are completely decoupled from the keys that generate them. Although the scheme is not supported by a formal security reduction, we present extensive arguments for its security and derive concrete parameters based on the performance of state of the art lattice reduction and enumeration techniques.