English

Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes

Cryptography and Security 2019-04-29 v2

Abstract

We present here a new family of trapdoor one-way Preimage Sampleable Functions (PSF) based on codes, the Wave-PSF 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)(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-PSF family with ternary generalized (U,U+V)(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 15 thousand bits, the public key size in the order of 4 megabytes, and the rejection rate is limited to one rejection every 10 to 12 signatures.

Keywords

Cite

@article{arxiv.1810.07554,
  title  = {Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes},
  author = {Thomas Debris-Alazard and Nicolas Sendrier and Jean-Pierre Tillich},
  journal= {arXiv preprint arXiv:1810.07554},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1706.08065