Constructing linear transformations of MPKC by generalized central symmetric matrices

Authors:
Xin Jiang;Lei Hu;Jintai Ding
Affiliations:
State Key Laboratory of Information Security, Graduate University of the Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Graduate University of the Chinese Academy of Sciences, Beijing, China;Department of Mathematical Sciences, University of Cincinnati, Cincinnati
Venue:
ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
Year:
2009

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Abstract

The multivariate public key cryptosystems (MPKCs) have a bigger scale of private key and public key than conventional number theoretic based public key cryptosystems like RSA, DH, and ECDH. In this paper, we present a method to construct the linear transformations in a private key of MPKC by generalized central symmetric matrices over a finite field of odd characteristic. This method reduces 3/8 of the scale of private key and improves the computation of inverting the linear transformations in decryption or signature generation to 3/4. It also speedups the generation of public and private keys of MPKC. The method can be recursively applied for achieving a further advantage.