A Public Key Cryptoscheme Using Bit-pairs and Probabilistic Mazes

TL;DR

This paper introduces JUOAN, a novel public key cryptoscheme leveraging bit-pairs and probabilistic mazes, with proven security features and increased efficiency over traditional methods.

Contribution

It proposes a new cryptoscheme based on multivariate permutation and subset product problems, with detailed algorithms, security analysis, and enhanced density and modulus parameters.

Findings

Decryption algorithm is correct.

Probability of nonunique plaintext solutions is nearly zero.

Cryptoscheme is semantically secure with random padding and permutation.

Abstract

This paper gives the definition and property of a bit-pair shadow, and devises the three algorithms of a public key cryptoscheme called JUOAN that is based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far, and regards a bit-pair as a manipulation unit. The authors demonstrate that the decryption algorithm is correct, deduce the probability that a plaintext solution is nonunique is nearly zero, analyze the security of the new cryptoscheme against extracting a private key from a public key and recovering a plaintext from a ciphertext on the assumption that an integer factorization problem, a discrete logarithm problem, and a low-density subset sum problem can be solved efficiently, and prove that the new cryptoscheme using random padding and random permutation is semantically secure. The analysis shows that the bit-pair method increases the density D of a related knapsack to a number more than 1, and decreases the modulus length lgM of the new cryptoscheme to 464, 544, or 640.