Hidden Polynomial(s) Cryptosystems

TL;DR

This paper introduces new public-key cryptosystems based on polynomial equations, utilizing algebraic or differential structures, with protocols for encryption, signature, and signcryption, aiming to enhance cryptographic security.

Contribution

It presents a novel cryptosystem framework where the public key is a system of polynomial equations and the private key is a polynomial or small ideal, along with associated protocols.

Findings

Probabilistic encryption protocols developed

Signature and signcryption protocols established

Potential for increased cryptographic security

Abstract

We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption protocols.