A new analysis of the McEliece cryptosystem based on QC-LDPC codes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5229 LNCS, Issue , 2008, Pages 246-262

  Baldi, Marco ^a   Bodrato, Marco ^b   Chiaraluce, Franco ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Cryptanalysis; McEliece cryptosystem; QC LDPC codes; Toom Cook; Winograd

Indexed keywords

CHLORINE COMPOUNDS; CODES (STANDARDS); CODES (SYMBOLS); CONVOLUTIONAL CODES; MATRIX ALGEBRA; QUANTUM CHEMISTRY; QUANTUM THEORY;

CIRCULANT MATRICES; CRYPTANALYSIS; CRYPTO SYSTEMS; EFFICIENT ALGORITHMS; ENCRYPTION AND DECRYPTION; GOPPA CODES; INTERNATIONAL CONFERENCES; MCELIECE CRYPTOSYSTEM; PRIVATE KEYS; QC-LDPC CODES; SECURITY LEVELS; SPEED UPS; SYSTEM PARAMETERS; TOOM-COOK; TRANSMISSION RATES; WINOGRAD;

CRYPTOGRAPHY;

EID: 52149114896     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85855-3_17     Document Type: Conference Paper

References (29)

1. McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report, 114-116 (1978)
2. Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theory 24, 384-386 (1978)
3. Lee, P., Brickell, E.: An observation on the security of McEliece's public-key cryptosystem. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 275-280. Springer, Heidelberg (1988)
4. Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: application to McEliece's cryptosystem and to narrow-sense BCH codes of length 511. IEEE Trans. Inform. Theory 44, 367-378 (1998)
5. Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Probl. Contr. and Inform. Theory 15, 159-166 (1986)
6. Li, Y.X., Deng, R., Wang, X.M.: On the equivalence of McEliece's and Niederreiter's public-key cryptosystems. IEEE Trans. Inform. Theory 40, 271-273 (1994)
7. Riek, J.: Observations on the application of error correcting codes to public key encryption. In: Proc. IEEE International Carnahan Conference on Security Technology. Crime Countermeasures, Lexington, KY, USA, October 1990, pp. 15-18 (1990)
8. Richardson, T., Urbanke, R.: The capacity of low-density parity-check codes under message-passing decoding. IEEE Trans. Inform. Theory 47, 599-618 (2001)
9. Baldi, M., Chiaraluce, F.: Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC codes. In: Proc. IEEE ISIT 2007, Nice, France, June 2007, pp. 2591-2595 (2007)
10. Monico, C., Rosenthal, J., Shokrollahi, A.: Using low density parity check codes in the McEliece cryptosystem. In: Proc. IEEE ISIT 2000, Sorrento, Italy, June 2000, p. 215 (2000)
11. Otmani, A., Tillich, J.P., Dallot, L.: Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes. In: Proc. First International Conference on Symbolic Computation and Cryptography (SCC 2008), Beijing, China (April 2008)
12. Gaborit, P.: Shorter keys for code based cryptography. In: Proc. Int. Workshop on Coding and Cryptography (WCC 2005), Bergen, Norway, March 2005, pp. 81-90 (2005)
13. Richardson, T., Urbanke, R.: Efficient encoding of low-density parity-check codes. IEEE Trans. Inform. Theory 47, 638-656 (2001)
14. Neal, R.M.: Faster encoding for low-density parity check codes using sparse matrix methods (1999), http://www.cs.toronto.edu/∼radford/ftp/ima- part1.pdf.
15. Stern, J.: A method for finding codewords of small weight. In: Wolfmann, J., Cohen, G. (eds.) Coding Theory 1988. LNCS, vol. 388, pp. 106-113. Springer, Heidelberg (1989)
16. Baldi, M., Chiaraluce, F.: LDPC Codes in the McEliece Cryptosystem (September 2007), http://arxiv.org/abs/0710.0142
17. Karatsuba, A.A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics Doklady 7, 595-596 (1963)
18. Toom, A.L.: The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady 3, 714-716 (1963)
19. Cook, S.A.: On the minimum computation time of functions. PhD thesis, Dept. of Mathematics, Harvard University (1966)
20. Bodrato, M., Zanoni, A.: Integer and polynomial multiplication: Towards optimal Toom-Cook matrices. In: Brown, C.W. (ed.) Proceedings of the ISSAC 2007 Conference, July 2007, pp. 17-24. ACM Press, New York (2007)
21. Cantor, D.G.: On arithmetical algorithms over finite fields. Journal of Combinatorial Theory A 50, 285-300 (1989)
22. Schönhage, A.: Schnelle Multiplikation von Polynomen über Körpern der Charak-teristik 2. Acta Informatica 7, 395-398 (1977)
23. Brent, R.P., Zimmermann, P., Gaudry, P., Thomé, E.: Faster multiplication in GF(2)[x]. In: van der Poorten, A.J., Stein, A. (eds.) ANTS-VIII 2008. LNCS, vol. 5011, pp. 153-166. Springer, Heidelberg (2008)
24. Bodrato, M.: Towards optimal Toom-Cook multiplication for univariate and mul-tivariate polynomials in characteristic 2 and 0. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 116-133. Springer, Heidelberg (2007)
25. Jebelean, T.: An algorithm for exact division. Journal of Symbolic Computation 15, 169-180 (1993)
26. Winograd, S.: Arithmetic Complexity of Computations. CBMS-NSF Regional Conference Series in Mathematics, vol. 33. SIAM, Philadelphia (1980)
27. Micciancio, D.: Generalized compact knapsacks, cyclic lattices and efficient oneway functions. Computational Complexity 16, 365-411 (2007)
28. Silverman, J.H.: High-speed multiplication of (truncated) polynomials. Technical Report 10, NTRU CryptoLab (January 1999)
29. Weimerskirch, A., Stebila, D., Shantz, S.C.: Generic GF(2) arithmetic in software and its application to ECC. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 79-92. Springer, Heidelberg (2003)