A Public Key Cryptoscheme Using Bit-pairs and Probabilistic Mazes
This work addresses cryptographic security for data encryption, but appears incremental as it builds on existing knapsack and permutation problems with specific parameter improvements.
The paper tackles the problem of designing a secure public key cryptoscheme by introducing JUOAN, based on multivariate permutation and anomalous subset product problems, resulting in a modulus length reduced to 464, 544, or 640 bits and increased knapsack density above 1.
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.