## 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

**Date: **received 16 Jun 2012

**Contact author: **kasahara at ogu ac jp

**Available format(s): **PDF | BibTeX Citation

**Version: **20120622:195232 (All versions of this report)

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