Paper 2013/180
A New Class of Productsum Type Public Key Cryptosystem,K(V)$\Sigma\Pi$PKC,Constructed Based on Maximum Length Code
Masao KASAHARA
Abstract
The author recently proposed a new class of knapsack type PKC referred to as K(II)$\Sigma\Pi$PKC [1]. In K(II)$\Sigma\Pi$PKC with old algorithm DA[I], 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 $0.01 < \rho < 0.2$. In K(II)$\Sigma\Pi$PKC, no secret sequence such as superincreasing sequence or shiftedodd sequence but the sequence whose components are constructed by a product of the same number of many prime numbers of the same size, is used. In this paper we present a new algorithm, DA(II) for decoding K(II)$\Sigma\Pi$PKC.We show that with new decoding algorithm, DA(II), K(II)$\Sigma\Pi$PKC yields a higher coding rate and a smaller size of public key compared with K(II)$\Sigma\Pi$PKC using old decoding algorithm, DA(I). We further present a generalized version of K(II) $\Sigma\Pi$PKC, referred to as K(\v)$\Sigma\Pi$PKC. We finally present a new decoding algorithm DA(III) and show that, in K(V)$\Sigma\Pi$PKC with DA(III), the relation, $r_F\simeq 0, \rho \simeq \frac{2}{3}$ holds, where $r_F$ is the factor ratio that will be defined in this paper. We show that K(V)$\Sigma\Pi$PKC yields a higher security compared with K(II) $\Sigma\Pi$PKC.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 Publickey cryptosystem(PKC)Productsum type PKCKnapsacktype PKCLLL algorithmPQC.
 Contact author(s)
 kasahara @ ogu ac jp
 History
 20130401: received
 Short URL
 https://ia.cr/2013/180
 License

CC BY
BibTeX
@misc{cryptoeprint:2013/180, author = {Masao KASAHARA}, title = {A New Class of Productsum Type Public Key Cryptosystem,K(V)$\Sigma\Pi$PKC,Constructed Based on Maximum Length Code}, howpublished = {Cryptology ePrint Archive, Paper 2013/180}, year = {2013}, note = {\url{https://eprint.iacr.org/2013/180}}, url = {https://eprint.iacr.org/2013/180} }