Raphael Overbeck

A Summary of McEliece-Type Cryptosystems and their Security

In this paper we give an overview of some of the cryptographic applications which were derived from the proposal of R. J. McEliece to use error correcting codes for cryptographic purposes. Code based cryptography is an interesting alternative to number theoretic cryptography. Many basic cryptographic functions like encryption, signing, hashing, etc. can be realized using code theoretic concepts. In this paper we briefly show how to correct errors in transmitted data by employing Goppa codes and describe possible applications to public key cryptography. The main focus of this paper is to provide detailed insight into the state of art of cryptanalysis of the McEliece cryptosystem and the effect on different cryptographic applications. We conclude, that for code based cryptography a public key of 88KB offers sufficient security for encryption, while we need a public key of at least 597KB for secure signing.

A new structural attack for GPT and variants

In this paper we look at the Gabidulin version of the McEliece cryptosystem (GPT) and its variants. We propose a new polynomial time attack, which recovers an alternative private key. Our attack is applicable to all variants proposed so far and breaks some of them completely.

Extending gibson's attacks on the GPT cryptosystem

In this paper we look at the Gabidulin version of the McEliece cryptosystem (GPT). In order to avoid Gibsons attacks on GPT, several variants have been proposed. We cryptanalyze the variant with column scrambler and the one using reducible rank codes. Employing Gibsons attacks as a black box, we get an efficient attack for the parameter sets proposed for GPT with column scrambler. As a countermeasure to our attack, we propose a new variant of the GPT cryptosystem.