A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security

The authors give the definition and property of a bit-pair shadow, and design the algorithms of a public key cryptoscheme 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 an operation unit. Further, 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 scheme 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 new scheme using random padding and permutation is semantically secure. The analysis shows that the bit-pair method increases the density D of a related knapsack to 1+, and decreases the modulus length \( \left\lceil {\lg M} \right\rceil \) of the new scheme to 464, 544, or 640.

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