Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes ★
We present here a new family of trapdoor one-way functions that are Preimage Sampleable on Average (PSA) based on codes, the Wave-PSA family. The trapdoor function is one-way under two computational assumptions: the hardness of generic decoding for high weights and the indistinguishability of generalized $$(U,U+V)$$-codes. Our proof follows the GPV strategy . By including rejection sampling, we ensure the proper distribution for the trapdoor inverse output. The domain sampling property of our family is ensured by using and proving a variant of the left-over hash lemma. We instantiate the new Wave-PSA family with ternary generalized $$(U,U+V)$$-codes to design a “hash-and-sign” signature scheme which achieves existential unforgeability under adaptive chosen message attacks (EUF-CMA) in the random oracle model.