Secure Cryptographic Scheme based on Modified Reed Muller Codes

It is devised a new cryptosystem based on modified Reed Muller codes RM(r, m). The new cryptosystem is a modified version of Sidel'nikov's one. This allows to increase the security of the public key, and to reconsider Reed Muller codes as good candidates for using in secure encryption scheme. An efficient decoding with the Reed Muller decoding algorithm RM(r, m) and an increased level of security against attacks of the Sidel'nikov's crypto-system due to Minder and Shokrolahi are the main advantages of the modified version. Adding new columns implies longer codes, but this would not be a problem for decoding or deciphering because in decode one has only to deal with the words of the secret code belonging to the Reed Muller code RM(r, m). So the decoding phase would not suffer from this modification.