A correlation cryptographic scheme

Abstract

In [1] McEliece introduced a public key cryptosystem using error correcting codes. The message is coded into codewords by using a public generator matrix G. The key to the system is an error vector of weight smaller than the error capacity which is added to the coded information vector. Polynomial time attacks have been devised against this scheme.

In this work we introduce a secret key coding scheme which relies on a subset S of a particular set of random codes of known minimum distance and for which a decoding algorithm is known. The cryptogram vector is this case too made of the sum of a codeword and a noise vector. However, the vector containing information is the “noise” vector and the masking vector is the “codeword”. The code itself is randomly chosen at each message in the corresponding set.

The robustness of the system is studied and, in particular, the attacks on the McEliece scheme [2] do not hold in this scheme, as well as the attacks that succeed when the set of codes is reduced to exactly one code.

This cryptosystem has the property that, if a set of matrices can be put in a tamper proof environment, then a user does not need to know any secret information to operate the system.

A conventional public key version of the cryptosystem, which needs more on line redundancy to achieve the same level of secrecy, will be given in a forthcoming paper.

As it is the case for the McEliece cryptosystem the new system introduces redundancy. These redundancy requirements are also studied.