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Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes
Authors: Thomas Debris-Alazard, Nicolas Sendrier, Jean-Pierre TillichAbstract:
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 [GPV08]. 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. For 128 bits of classical security, signature sizes are in the order of 13 thousand bits, the public key size in the order of 3 megabytes, and the rejection rate is below one rejection every 100 signatures.
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