Welcome to the resource topic for 2012/344
Title:
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
Authors: 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.
ePrint: https://eprint.iacr.org/2012/344
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