New number-theoretic cryptographic primitives

Éric Brier, Houda Ferradi, Marc Joye, David Naccache
2019 Journal of Mathematical Cryptology  
This paper introduces new {p^{r}q} -based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat–Shamir transform. In the basic signature scheme, the signer generates multiple RSA-like moduli {n_{i}={p_{i}}^{2}q_{i}} and keeps their factors secret. The signature is a bounded-size prime whose Jacobi symbols with respect to the
more » ... 's match the message digest. The generalized signature schemes replace the Jacobi symbol with higher-power residue symbols. Given of their very unique design, the proposed signature schemes seem to be overlooked "missing species" in the corpus of known signature algorithms.
doi:10.1515/jmc-2019-0035 fatcat:4qn7el77gnbh5kdfhm3bfpakji