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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board Member: Blackburn, Simon R. / Blundo, Prof. / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Prof. / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lange, Prof. / Lauter, Prof. / Menezes, Alfred / Nguyen, Phong Q. / Rötteler, Martin / Pieprzyk, Josef / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Prof. / Williams, Hugh C. / Yung, Moti

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A Summary of McEliece-Type Cryptosystems and their Security

D. Engelbert1 / R. Overbeck3 / A. Schmidt5

1TU Darmstadt, Department of Computer Science, Cryptography and Computer Algebra Group Hochschulstraße 10, 64298 Darmstadt, Germany.

2Email:

3TU Darmstadt, GK Electronic Commerce, Department of Computer Science, Cryptography and Computer Algebra Group Hochschulstraße 10, 64298 Darmstadt, Germany.

4Email:

5TU Darmstadt, Department of Computer Science, Cryptography and Computer Algebra Group Hochschulstraße 10, 64298 Darmstadt, Germany.

6Email:

Citation Information: Journal of Mathematical Cryptology JMC. Volume 1, Issue 2, Pages 151–199, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: 10.1515/JMC.2007.009, May 2007

Publication History

Published Online:
2007-05-21

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.

Key Words: McEliece cryptosystem,; public key cryptography,; code based cryptography,; Goppa codes.

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