A New Class of Product-sum Type Public Key Cryptosystem, K(V)ΣΠPKC, Constructed Based on Maximum Length Code

The author recently proposed a new class of knapsack type PKC referred to as K(II)ΣΠPKC [1]. In K(II)ΣΠPKC with old algorithm DA[I], Bob randomly constructs a very small subset of Alice’s set of public key whose order is very large, under the condition that the coding rate ρ satisfies 0.01 < ρ < 0.2. In K(II)ΣΠPKC, no secret sequence such as super-increasing sequence or shifted-odd sequence but the sequence whose components are constructed by a product of the same number of many prime numbers of the same size, is used. In this paper we present a new algorithm, DA(II) for decoding K(II)ΣΠPKC. We show that with new decoding algorithm, DA(II), K(II)ΣΠPKC yields a higher coding rate and a smaller size of public key compared with K(II)ΣΠPKC using old decoding algorithm, DA(I). We further present a generalized version of K(II)ΣΠPKC, referred to as K(V)ΣΠPKC. We finally present a new decoding algorithm DA(III) and show that, in K(V)ΣΠPKC with DA(III), the relation, rF ∼= 0, ρ ∼= 23 holds, where rF is the factor ratio that will be defined in this paper. We show that K(V)ΣΠPKC yields a higher security compared with K(II)ΣΠPKC. keyword Public-key cryptosystem(PKC), Product-sum type PKC, Knapsack-type PKC, LLL algorithm, PQC.