Cascaded Coding Schemes For Public-Key Cryptography

Abstract

1976 Diffic and Hellman introduced the concept of public-key cryptography and in 1978, McEliece introduced the first public-key cryptosystem based on error correcting codes. Since that time, several methods have been proposed to use error correcting codes for cryptography either directly or indirectly. In this work we propose the use of cascaded codes in McEliece algorithm where cascading here means that one code is used after the other. Two or more codes are used in cascade to get high error correcting capabilities even with moderate length codes. This makes the system more useful over noisy channels. The structure of cascaded codes is in itself a good way to secure the data. Binary block codes are only considered in this work although other types of codes can be used. We discuss two different encryption schemes where normal and Tensor products of matrices are used to form the codes. The proposed schemes are more adequate for block encryption. Decoding is also performed in cascade to make use of the existing fast decoding algorithms available for each of the used codes. Therefore, the decryption process will be fast too compared with other schemes based on number theory. The selection of proper code parameters is discussed and the probability of correct recovery of transmitted messages is also found.