A Fast Asymmetric Cryptosystem Using Extra Superincreasing Sequences

This paper gives the definitions of an extra superincreasing sequence and an anomalous subset sum, and proposes a fast asymmetric cryptosystem (FAC) that is based on an additive multivariate permutation problem (AMPP) and an anomalous subset sum problem (ASSP) which parallels a shortest vector problem, and composed of a key generation algorithm, an encryption algorithm, and a decryption algorithm. The new cryptosystem is analyzed to be resistant to the Shamir minima accumulation point attack and the LLL lattice basis reduction attack, and proved 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 cryptosystem has the potential to be resistant to quantum computing attack. At last, an example of explaining the correctness of the new cryptosystem is given.