Security of the GPT cryptosystem and its applications to cryptography

Security and Communication Networks

Volumn 4, Issue 8, 2011, Pages 937-946

  Rashwan, Haitham ^a   Gabidulin, Ernst M ^b   Honary, Bahram ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

Author keywords

Code based cryptography; Gabidulin code; Public key cryptosystem; Rank distance codes

Indexed keywords

CODE-BASED CRYPTOGRAPHY; CRYPTOGRAPHIC APPLICATIONS; ERROR CORRECTING CODE; EXTENSION FIELD; GABIDULIN CODE; GPT CRYPTOSYSTEM; MATRIX; PUBLIC KEY CRYPTOSYSTEMS; PUBLIC KEYS; RANK DISTANCE CODES;

PUBLIC KEY CRYPTOGRAPHY;

EID: 79960387857     PISSN: 19390114     EISSN: 19390122     Source Type: Journal    
DOI: 10.1002/sec.228     Document Type: Article

References (21)

1. McEliece RJ. A public key cryptosystem based on algebraic coding theory. In JPL DSN Progress Report 42-44, Pasadena, CA, 1978; 114-116.
2. Niederreiter H. Knapsack-type cryptosystem and algebraic coding theory. Problems of Control and Information Theory 1986; 15: 19-34.
3. Gabidulin EM, Paramonov AV, Tretjakov OV. Ideals over a non-commutative ring and their application in cryptology. In Advances in Cryptology-EUROCRYPT'91, Davies DW (ed.). Lecture Notes in Computer Science, No. 547. Springer-Verlag: Berlin and Heidelberg, 1991; 482-489.
4. Gabidulin EM. Public-key cryptosystems based on linear codes over large alphabets: efficiency and weakness. In Codes and Ciphers, Farrell PG (ed.). Formara Limited: Essex, 1995; 17-32.
5. Gibson JK. Severely denting the Gabidulin version of the McEliece public key cryptosystem. Designs, Codes and Cryptography 1995; 6(1): 37-45.
6. Gibson JK. The security of the Gabidulin public-key cryptosystem. In Advances in Cryptology-EUROCRYPT'96, Maurer UM (ed). LNCS 1070. Springer-Verlag: Berlin, Heidelberg 1996; 212-223.
7. Gabidulin EM, Ourivski AV. Improved GPT public key cryptosystems. In Coding, Communications, and Broadcasting, Farrell P, Darnell M, Honary B (eds). Research Studies Press, London, 2000; 73-102.
8. Ourivski AV, Gabidulin EM. Column scrambler for the GPT cryptosystem. Discrete Applied Mathematics 2003; 128(1): 207-221.
9. Gabidulin EM, Ourivski AV, Honary B, Ammar B. Reducible rank codes and their applications to cryptography. IEEE Transactions on Information Theory 2003; 49(12): 3289-3293.
10. Kshevetskiy AS, Gabidulin EM. High-weight errors in public-key cryptosystems based on reducible rank codes. In Proceedings of ISCTA, 2005.
11. Overbeck R. A new brute-force attack for GPT and variants. In Proceedings of Mycrypt'2005, Vol. 3517 of LNCS. Springer-Verlag, 2005; 5-63.
12. Overbeck R. Brute-force attacks public key cryptosystem based on Gabidulin codes. Journal of Cryptology 2008; 21(2): 280-301.
13. Kshevetskiy AS. Security of GPT-like cryptosystems based on linear rank codes. Signal Design and Its Applications in Communications, 2007. IWSDA 2007. On page(s): 143-147.
14. Gabidulin EM. Attacks and counter-attacks on the GPT public key cryptosystem. Designs, Codes and Cryptography 2008; 48(2): 171-177. DOI 10.1007/s10623-007-9160-8.
15. Gabidulin EM, Rashwan H, Honary B. On improving security of GPT cryptosystems. IEEE International Symposium on Information Theory, 2009.
16. Gabidulin EM. Theory of codes with maximum rank distance. Problems of Information Transmission 1985; 21(1): 1-12.
17. Gabidulin EM. A fast matrix decoding algorithm for rank-error-correcting codes. In Algebraic Coding, Cohen G, Litsyn S, Lobstein A, Zemor G (eds). Lecture Notes in Computer Science No. 573, Springer-Verlag: Berlin, 1992; 126-132.
18. Johansson T, Ourivski AV. New technique for decoding codes in the rank metric and its cryptography applications. Problems of Information Transmission 2002; 38(3): 237-246.
19. Levy-dit-Vehel1 F, Jean-Charles Faug'ere J-Ch, Perret L. Cryptanalysis of MinRank. Advances in Cryptology-CRYPTO 2008, 28th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2008, Proceedings. Series: Lecture Notes in Computer Science. Subseries: Security and Cryptology, Vol. 5157. Wagner, David (Ed.). Springer: Berlin, Heidelberg 2008. 280-296.
20. Bernstein JD, Lange T, Peters C. Attacking and defending the McEliece cryptosystem, Second International Workshop, PQCrypto 2008 Proceedings, Cincinnati, OH, USA, 17-19, 2008.
21. Rivest RL, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 1978; 21: 120-126.