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This paper gives the definitions of an extra superincreasing sequence and ananomalous subset sum, and proposes a fast quantum-safe asymmetric cryptosystemcalled JUOAN2. The new cryptosystem is based on an additive multivariatepermutation problem (AMPP) and an anomalous subset sum problem (ASSP) whichparallel a multivariate polynomial problem and a shortest vector problemrespectively, and composed of a key generator, an encryption algorithm, and adecryption algorithm. The authors analyze the security of the new cryptosystemagainst the Shamir minima accumulation point attack and the LLL lattice basisreduction attack, and prove it to be semantically secure (namely IND-CPA) onthe assumption that AMPP and ASSP have no subexponential time solutions.Particularly, the analysis shows that the new cryptosystem has the potential tobe resistant to quantum computing attack, and is especially suitable to thesecret communication between two mobile terminals in maneuvering fieldoperations under any weather. At last, an example explaining the correctness ofthe new cryptosystem is given.

A Fast Quantum-safe Asymmetric Cryptosystem Using Extra Superincreasing Sequences