This paper introduces new p^rq-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
2q_i 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. The case of 8th-power residue symbols is fully detailed along with an
efficient implementation thereof.
Given of their very unique design the proposed signature schemes seem to be overlooked missing species
in the corpus of known signature algorithms