A summary of McEliece-type cryptosystems and their security

Journal of Mathematical Cryptology

Volumn 1, Issue 2, 2007, Pages 151-199

  Engelbert, D ^a   Overbeck, R ^a   Schmidt, A ^a  

^a Cryptography and Computer Algebra Group   (Germany)

Author keywords

Code based cryptography; Goppa codes; McEliece cryptosystem; Public key cryptography

Indexed keywords

EID: 84858691417     PISSN: 18622976     EISSN: 18622984     Source Type: Journal    
DOI: 10.1515/JMC.2007.009     Document Type: Article

References (52)

1. A. Kh. Al Jabri, A Statistical Decoding Algorithm for General Linear Block Codes. Cryptography and Coding 2001, LNCS 2260, pp. 1-8. Springer, 2001.
2. M. Alabbadi and S. B. Wicker, Security of Xinmei digital signature scheme, Electronics Letters 29 (1992), pp. 890-891.
3. -, A digital signature scheme based on linear error-correcting block codes. ASI- ACRYPT '94, LNCS 917, pp. 238-248. Springer, 1995.
4. D. Augot, M. Finiasz, and N. Sendrier, A Family of Fast Syndrome Based Cryptographic Hash Functions. Proc. of Mycrypt 2005, LNCS 3715, pp. 64-83, 2005.
5. E. Berlekamp, R. McEliece, and H. van Tilborg, On the inherent intractability of certain coding problems, IEEE Transactions on Information Theory 24 (1978), pp. 384-386. (Pubitemid 8607605)
6. T. Berson, Failure of the McEliece Public-Key Cryptosystem Under Message-Resend and Related-Message Attack. Proceedings of CRYPTO, Lecture Notes in Computer Science 1294, pp. 213-220. Springer, 1997. (Pubitemid 127112554)
7. E. F. Brickell and A. M. Odlyzko, Cryptanalysis: A Survey of Recent Results. Proc. of the IEEE, 76, pp. 578-593, 1988.
8. A. Canteaut and F. Chabaud, Improvements of the attacks on cryptosystems based on error-correcting codes, Rapport interne du Departement Mathematiques et Informatique LIENS-95-21 (1995).
9. A. Canteaut and F. Chabaut, A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH-codes of length 511, IEEE Transactions on Information Theory 44 (1998), pp. 367-378. (Pubitemid 128737912)
10. A. Canteaut and N. Sendrier, Cryptanalysis of the Original McEliece Cryptosystem. Advances in Cryptology - ASIACRYPT '98 Proceedings, pp. 187-199. Springer, 1998. (Pubitemid 128151411)
11. F. Chabaud, On the security of some cryptosystems based on error-correcting codes, Lecture Notes in Computer Science 950 (1995), pp. 131-139.
12. N. Courtois, M. Finiasz, and N. Sendrier, How to achieve a McEliece-based Digital Signature Scheme. Advances in Cryptology - ASIACRYPT 2001, 2248, pp. 157-174. Springer, 2001.
13. F. Levy dit Vehel and S. Litsyn, Parameters of Goppa codes revisited. IEEE Transactions on Information Theory 43 (1997), 1811-1819. (Pubitemid 127826473)
14. J.-B. Fischer and J. Stern, An eficient pseudo-random generator provably as secure as syndrome decoding. Advances in Cryptology - EUROCRYPT '96 (Ueli M. Maurer, ed.), LNCS 1070, pp. 245-255. Springer, 1996. (Pubitemid 126071070)
15. M. Fossorier, H. Imai, and K. Kobara, Modeling Bit Flipping Decoding Based on Non Orthogonal Check Sums and Application to Iterative Decoding Attack of McEliece Crypto-System. Proc. of 2004 International Symposium on Information Theory and its Applications, Parma, Italy (ISITA'04), October 2004.
16. E. Fujisaki and T. Okamoto, Secure Integration of Asymmetric and Symmetric Encryption Schemes. Proc. of CRYPTO, LNCS 547, pp. 535-554. Springer, 1999.
17. E. M. Gabidulin, A. V. Ourivski, B. Honary, and B. Ammar, Reducible rank codes and their applications to cryptography, IEEE Transactions on Information Theory 49 (2003), pp. 3289-3293.
18. E. M. Gabidulin, A. V. Paramonov, and O. V. Tretjakov, Ideals over a Non-Commutative Ring and their Applications to Cryptography. Proc. Eurocrypt '91, LNCS 547. Springer, 1991.
19. P. Gaborit, Shorter keys for code based cryptography. Proc. of WCC 2005, pp. 81-90, 2005.
20. S. Gao and D. Panario, Tests and constructions of irreducible polynomials over finite fields, Foundations of Computational Mathematics (1997), pp. 346-361.
21. K. Gibson, Equivalent Goppa codes and trapdoors to McEliece's public key cryptosystem. Advances in Cryptology - Eurocrypt'91 (D. W. Davies, ed.), LNCS 547, pp. 517-521. Springer, 1991.
22. V. D. Goppa, A New Class of Linear Correcting Codes, Problems of Information Transmission 6 (1970), 207-212.
23. L. Harn and D.-C. Wang, Cryptanalysis and modification of digital signature scheme based on error-correcting codes, Electronics Letters 28 (1992), pp. 157-159.
24. Heise and Quattrocchi, Informations- und Codierungstheorie, 3. edn. Springer, 1995.
25. IEEE 1363-2000 : Standard Specifications For Public Key Cryptography, 2000.
26. H. Janwa and O. Moreno, McEliece Public Key Cryptosystems Using Algebraic-Geometric Codes, Designes, Codes and Cryptography 8 (1996), pp. 293-307. (Pubitemid 126708388)
27. K. Kobara and H. Imai, Semantically Secure McEliece Public-Key Cryptosystems - Conversions for McEliece PKC. Practice and Theory in Public Key Cryptography - PKC '01 Proceedings. Springer, 2001.
28. -, On the One-Wayness Against Chosen-Plaintext Attacks of the Loidreau's modified McEliece PKC. IEEE Transactions on Information Theory 49 (2003), 3160-3168.
29. J. C. Lagarias and A. M. Odlyzko, Solving Low-Density Subset Sum Problems, J. ACM 32 (1985), pp. 229-246. (Pubitemid 15599042)
30. P. J. Lee and E. F. Brickell, An observation on the security of McEliece's public key cryptosystem. Advances in Cryptology-EUROCRYPT'88, LNCS 330, pp. 275-280. Springer, 1989, http://dsns.csie.nctu.edu.tw/research/crypto/ HTML/PDF/E88/275.PDF.
31. A. K. Lenstra and E. R. Verheul, Selecting Cryptographic Key Sizes, Journal of Cryptology: the journal of the International Association for Cryptologic Research 14 (2001), pp. 255-293. (Pubitemid 33770276)
32. J. S. Leon, A probabilistic algorithm for computing minimum weights of large error-correcting codes, IEEE Transactions on Information Theory 34 (1988), pp. 1354-1359.
33. Y. X. Li, R. H. Deng, and X. M. Wang, the Equivalence of McEliece's and Niederreiter's Public-Key Cryptosystems, IEEE Transactions on Information Theory 40 (1994), pp. 271-273.
34. R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, 2. edn. Cambridge University Press, 1986.
35. P. Loidreau and N. Sendrier, Weak keys in the McEliece public-key cryptosystem, IEEE Transactions on Information Theory 47 (2001), pp. 1207-1211. (Pubitemid 32425453)
36. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correctiong Codes, 7. edn. North-Holland Amsterdam, 1992.
37. R. J. McEliece, A public key cryptosystem based on algebraic coding theory, DSN progress report 42-44 (1978), pp. 114-116.
38. T. Okamoto, K. Tanaka, and S. Uchiyama, Quantum Public Key Cryptosystems. Proc. Of CRYPTO 2000, LNCS, 1880, pp. 147-165, 2000, Springer.
39. R. Overbeck, A new structural attack for GPT and variants. Proc. of Mycrypt 2005, LNCS 3715, pp. 50-63. Springer, 2005.
40. -, Statistical Decoding revisited. Proc. of ACISP 2006, LNCS 4058, pp. 283-294. Springer, 2006. (Pubitemid 44121001)
41. N. Patterson, Algebraic Decoding of Goppa Codes, IEEE Trans. Info. Theory 21 (1975), pp. 203-207.
42. D. Pointcheval, Chosen-Ciphertext Security for any One-Way Cryptosystem. Proc. of PKC, LNCS 1751, pp. 129-146. Springer, 2000.
43. V. C. Jr. Rocha, V. C. JR Da Rocha, and D. L. Macedo, Cryptanalysis of Krouk's public-key cipher, Electronics Letters 32 (1996), 1279-1280. (Pubitemid 126511297)
44. N. Sendrier, On the dimension of the hull, SIAM Journal on Discrete Mathematics 10 (1997), pp. 282-293. (Pubitemid 127577165)
45. -, Finding the permutation between equivalent linear codes: the support splitting algorithm, IEEE Transactions on Information Theory 46 (2000), 1193-1203.
46. -, On the security of the McEliece public-key cryptosystem. Proceedings of Workshop honoring Prof. Bob McEliece on his 60th birthday (M. Blaum, P. G. Farrell, and H. van Tilborg, eds.), pp. 141-163. Kluwer, 2002.
47. V. M. Sidelnikov, A Public-Key Cryptosystem Based on Binary Reed-Muller Codes, Discrete Mathematics and Applications 4 (1994).
48. V. M. Sidelnikov and S. O. Shestakov, On insecurity of cryptosystems based on generalized Reed-Solomon codes, Discrete Mathematics and Applications 2 (1992), 439-444.
49. J. Stern, A method for finding codewords of small weight, Coding Theory and Applications 388 (1989), pp. 106-133.
50. -, A new identification scheme based on syndrome decoding. Advances in Cryptology - CRYPTO'93, LNCS 773. Springer, 1994.
51. -, Can one design a signature scheme based on error-correcting codes. ASIACRYPT '94, LNCS 917, pp. 424-426, 1995.
52. W. Xinmei, Digital signature scheme based on error-correcting codes, Electronics Letters 26 (1990), pp. 898-899. (Pubitemid 20709324)