## Cryptology ePrint Archive: Report 2012/344

Construction of New Classes of Knapsack Type Public Key Cryptosystem Using Uniform Secret Sequence, K(II)$\Sigma\Pi$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)$\Sigma\Pi$PKC. In K(II)$\Sigma\Pi$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)$\Sigma\Pi$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)$\Sigma\Pi$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)$\Sigma\Pi$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.

Category / Keywords: public-key cryptography / Public-key cryptosystem(PKC), Knapsack-type PKC, Product-sum type PKC, LLL algorithm, PQC

Publication Info: Graduate School of Osaka Gakuin University