Code-based public-key cryptosystems evolution

System Year Codes Metric Ciphertext Attack
McEliece system Download Paper 1978 Goppa codes Hamming metric  c=mGpub 1991 by Sidelnikov & Shestakov
Niederreiter system Download Paper 1986 Reed-Solomon code Hamming metric  c=Gpubm 1994 by Sidelnikov & Shestakov Download
GPT system Download Paper 1991 Gabidulin code with min rank distance Rank metric ROW4 COL6

Original McEliece system by Robert J. McEliece. Published in 1978: McEliece-Cryptosystem-Download. Cracked in 1991 by Sidelnikov & Shestakov: McElilece-Cryptoanalysis-Download. Goppa codes. Hamming metric. Ciphertext:

Original Niederreiter system by Harald Niederreiter. Published in 1986: Niederreiter-Cryptosystem-Link . Cracked in 1994 by Sidelnikov: Niederreiter-Cryptoanalysis-Download ; equivalence to McEliece stand for Sidelnikov & Shestakov attack is applicable. Reed-Solomon code. Hamming metric. Ciphertext:

Original GPT system by Ernst M. Gabidulin, A. V. Paramonov, O. V. Tretjakov. Published in 1991: GPT-Cryptosystem-Download. Cracked in 1995 by Gibson: GPT-Cryptoanalysis-Link . Gabidulin code with maximum rank distance. Rank metric. Ciphertext:

Sidelnikov system by Vladimir Sidelnikov. Published in 1994: Sidelnikov-Cryptosystem-Download. Cracked in 2007 by Minder&Shokrollahi: Sidelnikov-Cryptoanalysis-Download. Reed-Muller codes. Hamming metric. Ciphertext:

LDPC McEliece by C. Monico, J. Rosenthal and A. Shokrollahi. Published in 2000:  Low-Density-Parity-Check-Codes-in-the-McEliece-Download. Cracked in 2007 by Marco Baldi: LDPC-McEliece-attacks-Download. Low Density Parity Check codes. Hamming metric. Ciphertext:

GPT Modification I by E. Gabidulin and Ourivski. Published in 2001. Cracked in (?). Gabidulin code. Rank metric. Ciphertext with right scrambler:

Gabidulin&Obernikhin system. Published in 2002. Reed-Solomon code. Vandermond matrix based metric. Ciphertext:

GPT Modification II by E. Gabidulin and Ourivski. Published in 2003. Cracked in 2008 by Overbeck. Gabidulin code. Rank Metric. Ciphertext with column scrambler:

Modification proposed by T. Berger and P. Loidreau. Published in 2004: Berger-Loidreau-Cryptosystem-Download. (attacks?). Reducible Rank code. Rank metric. Ciphertext:

Cryptosystem by Gabidulin & Samokhina (Churusova). Published in 2005:  The-modified-Niederreiter-cryptosystem-based-on-new-metric-Download. Modified Gabidulin code. F-metric associated with Frobenius matrix. Ciphertext:

McEliece modification with increased public key security by Marco Baldi, Marco Bianchi, Franco Chiaraluce, Joachim Rosenthal and Davide Schipani. Published in 2011: McEliece-cryptosystem-with-increased-public-key-security-Download . (attacks?). Gabidulin code with hight rank gen matrix. Hamming metric. Ciphertext:

McEliece system modification by Gerhard Hoffman and Stephan Heyse. Published in 2011: McEliece-system-on-quasi-dyadic-Goppa-codes-Download. (attacks?). McEliece system modification with quasi-dyadic Goppa codes. Hamming metric. Ciphertext:

MDPC McEliece by Misoczki, Tillich, Sendrier, Barreto. Published in 2013: MDPC-McEliece-Download. Moderate Density Parity Check codes. Hamming metric. Ciphertext:

Third modification of GPT. Published in 2014. (attacks?). Reducible Rank code. Rank metric. Ciphertext:


1986. Harald Niederreiter. “Knapsack-type cryptosystems and algebraic coding theory.” Problems of Control and Information Theory 15, 19–34. Problemy Upravlenija i Teorii Informacii 15, 159–166.

1995. J. K. Gibson. “Severely denting the Gabidulin version of the McEliece public key cryptosystem.” Designs, Codes and Cryptography 6, 37–45. MR 1334199.

1994. Yuan Xing Li, Robert H. Deng, Xin Mei Wang. “On the equivalence of McEliece’s and Niederreiter’s public-key cryptosystems.” IEEE Transactions on Information Theory 40, 271–273. MR 1281932.

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