Hidden Polynomial(s) Cryptosystems

TL;DR

This paper introduces new variants of hidden polynomial cryptosystems designed to resist known attacks, utilizing identities based on bivariate polynomials and extending to digital signatures and various field types.

Contribution

It presents novel cryptosystem variants resistant to existing attacks, employing polynomial identities and extending applicability to digital signatures and different field types.

Findings

Cryptosystems resistant to all known attacks.

Extension to digital signature algorithms.

Works on differential fields of positive characteristic.

Abstract

We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can be replaced by a ``small'' ideal, as well. Throughout, we set up probabilistic encryption protocols, too. The same ideas extend to digital signature algorithms, as well. Our schemes work as well on differential fields of positive characteristic, and elsewhere.