Amount of Key Information Contained in Plain and Encrypted Text Sets of the Symmetric Randomized McEliece Cryptosystem

Abstract

A symmetric code cryptosystem, which is similar to the randomized (asymmetric) McEliece encryption scheme, is considered. An expression for the amount of information on the private key, which can be extracted from public and respective encrypted messages of the cryptosystem, is obtained. It is shown that with this information, the security of the symmetric cryptosystem against attacks based on the known ciphertext coincides with the security of its asymmetric counterpart.