New number-theoretic cryptographic primitives

Abstract

This paper introduces new prq-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 ni = pi2qi and keeps their factors secret. The signature is a bounded-size prime whose Jacobi symbols with respect to the ni’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.

Keywords

• r-th power residue symbol
• r-th order imprint
• prq moduli
• number theory
• one-way functions
• digital signatures
• cryptographic primitives
• 94a60
• 11t71
• 11a15
• 11r18