Construction of New Classes of Product-sum Type Public Key Cryptosystem, K(II)∑∏PKC, Constructed Based on the Maximum Length Code - A Possibility of Opening Up a New Field of Applications of Cryptosystem

摘要

In this paper, we present a new class of knapsack type PKC referred to as K(I)∑∏PKC. In K(II)∑∏PKC, 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 < 0.5. In K(I) ∑∏PKC, no secret sequence such as super-increasing sequence or shifted-odd sequence but the sequence whose component is constructed by a product of the same number of many prime numbers of the same size, is used. We show that K(I)∑∏PKC is secure against the attacks such as LLL algorithm, Shamir's attack etc., because a subset of Alice's public keys is chosen entirely in a probabilistic manner at the sending end, say, by Bob. We also show that K(II) ∑∏PKC can be used as a member of the class of common key cryptosystems because the list of the subset randomly chosen by Bob can be used as a common key between Bob and Alice, for a certain short period, without notifying Alice of his secret key through a particular secret channel.