On a new fast public key cryptosystem

TL;DR

This paper introduces a new fast public key cryptosystem based on a difficult mathematical function, including a key exchange, encryption, and digital signature algorithms, with security evaluated via reduction to SAT.

Contribution

The paper proposes a novel cryptosystem based on the intractability of a specific modular division function, including new algorithms and security analysis.

Findings

The cryptosystem is computationally efficient.

The hardness of the underlying problem is demonstrated via reduction to SAT.

A new key exchange algorithm, ModDiv2Kex, is introduced.

Abstract

This paper presents a new fast public key cryptosystem namel : a key exchange algorithm, a public key encryption algorithm and a digital signature algorithm, based on the difficulty to invert the following function: $$F(x) =(a\times x)Mod(2^p)Div(2^q).$$ Mod is modulo operation , Div is integer division operation , a , p and q are integers where $( p > q )$. We define p and q values for which ModDiv2Inv can be the hardest. We then present ModDiv2Kex, a new fast key exchange algorithm based on ModDiv2Inv. In this paper we also evaluate the hardness of this problem by reducing it to SAT .