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
Download
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:

Links

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. https://www.researchgate.net/publication/243776483_Knapsack_Type_Cryptosystems_and_Algebraic_Coding_Theory

1995. J. K. Gibson. “Severely denting the Gabidulin version of the McEliece public key cryptosystem.” Designs, Codes and Cryptography 6, 37–45. MR 1334199. http://www.springerlink.com/index/G980X82N7045L487.pdf

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. http://ieeexplore.ieee.org/iel1/18/6734/00272496.pdf?arnumber=272496