Constructing linear transformations of MPKC By generalized central symmetric matrices

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.