Paper 2012/344

Construction of New Classes of Knapsack Type Public Key Cryptosystem Using Uniform Secret Sequence, K(II)$\mathrm{\Sigma }\mathrm{\Pi }$PKC, Constructed Based on Maximum Length Code

Masao KASAHARA

Abstract

In this paper, we present a new class of knapsack type PKC referred to as K(II)$\mathrm{\Sigma }\mathrm{\Pi }$PKC. In K(II)$\mathrm{\Sigma }\mathrm{\Pi }$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 $\rho$ satisfies $0.01<\rho <0.5$. In K(II)$$PKC, no secret sequence such as super-increasing sequence or shifted-odd sequence but the sequence whose component is constructed by a product of the same number of many prime numbers of the same size, is used. We show that K(II)$$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. 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, provided that the conditions given in this paper are strictly observed, without notifying Alice of his secret key through a particular secret channel.