Secured Encryption scheme based on the Ree groups

Abstract

An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key recovery attacks. Hence, the complexity of the key recovery attack will be defined by a brute-force attack over the entire group. In this paper, we have proved that to construct secure cryptosystems with group computations over a small finite field, it is needed to use a 3-parametric small Ree group.