A Fast Quantum-safe Asymmetric Cryptosystem Using Extra Superincreasing Sequences

TL;DR

This paper introduces JUOAN2, a fast quantum-safe asymmetric cryptosystem based on extra superincreasing sequences, designed to resist quantum attacks and suitable for secure mobile communications.

Contribution

It proposes a novel cryptosystem using extra superincreasing sequences and analyzes its security against quantum and classical attacks.

Findings

Proves semantic security (IND-CPA) under certain assumptions.

Shows resistance to Shamir minima and LLL lattice attacks.

Potentially resistant to quantum computing attacks.

Abstract

This paper gives the definitions of an extra superincreasing sequence and an anomalous subset sum, and proposes a fast quantum-safe asymmetric cryptosystem called JUOAN2. The new cryptosystem is based on an additive multivariate permutation problem (AMPP) and an anomalous subset sum problem (ASSP) which parallel a multivariate polynomial problem and a shortest vector problem respectively, and composed of a key generator, an encryption algorithm, and a decryption algorithm. The authors analyze the security of the new cryptosystem against the Shamir minima accumulation point attack and the LLL lattice basis reduction attack, and prove it to be semantically secure (namely IND-CPA) on the assumption that AMPP and ASSP have no subexponential time solutions. Particularly, the analysis shows that the new cryptosystem has the potential to be resistant to quantum computing attack, and is especially suitable to the secret communication between two mobile terminals in maneuvering field operations under any weather. At last, an example explaining the correctness of the new cryptosystem is given.