Quantum mceliece public-key cryptosystem

Quantum Information and Computation

Volumn 12, Issue 3-4, 2012, Pages 181-202

  Hachiro, Fujita ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

McEliece encryption; Public key cryptosystem; Quantum information

Indexed keywords

EID: 84858035503     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. C. H. Bennett, G. Brassard, C. Cŕepeau, R. Jozsa, A. Peres, and W. K. Wootters (1993), Tele-porting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett., vol. 70, no. 13, pp. 1895-1899.
2. A. Ambainis, M. A. Mosca, A. Tapp, and R. de Wolf (2000), Private quantum channels, in Proc. IEEE Symposium on Foundations of Computer Science, pp. 547-553.
3. P. O. Boykin and V. Roychowdhury (2003), Optimal encryption of quantum bits, Phys. Rev. A, vol. 67, 042317.
4. C. H. Bennett and G. Brassard (1984), Quantum cryptography: public key distribution and coin tossing, in Proc. IEEE International Conference on Computers, Systems, and Signal Processing, pp. 175-179.
5. P. W. Shor and J. Preskill (2000), Simple proof of security of the BB84 quantum key distribution protocol, Phys. Rev. Lett., vol. 85, no. 2, pp. 441-444.
6. T. Okamoto, K. Tanaka, and S. Uchiyama (2000), Quantum public-key cryptosystems, in Advances in Cryptology-CRYPTO 2000 (LNCS 1880), pp. 147-165.
7. A. Kawachi, T. Koshiba, H. Nishimura, and T. Yamakami (2005), Computational indistinguisha-bility between quantum states and its cryptographic application, in Advances in Cryptology-EUROCRYPT 2005 (LNCS 3494), pp. 268-284.
8. G. M. Nikolopoulos (2008), Applications of single-qubit rotations in quantum public-key cryptog-raphy, Phys. Rev. A, vol. 77, 032348.
9. Li Yang, Min Liang, Bao Li, Lei Hu, and Deng-Guo Feng (2010), Quantum public-key cryptosystems based on induced trapdoor one-way transformations, e-print arXiv:1012.5249v1.
10. R. J. McEliece (1978), A public-key cryptosystem based on algebraic coding theory, DSN Progress Report 42-44, pp. 114-116, JPL, Caltech.
11. L. K. Grover (1997), Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett., vol. 79, no. 2, pp. 325-328.
12. Daniel J. Bernstein (2010), Grover vs. McEliece, in PQCrypto 2010 (LNCS 6061), pp.73-80.
13. H. Niederreiter (1986), Knapsack-type cryptosystems and algebraic coding theory, Problems of Control and Information Theory, vol. 15, no. 2, pp. 159-166.
14. D. Engelbert, R. Overbeck, and A. Schmidt (2007), A summary of McEliece-type cryptosystems and their security, J. Math. Crypt., vol. 1, pp. 151-199.
15. R. Overbeck and N. Sendrier (2009), Code-based cryptography, in [41].
16. E. R. Berlekamp, R. J. McEliece, and H. C. van Tilborg (1978), On the inherent intractability of certain coding problems, IEEE Transactions on Information Theory, vol. 24, no. 3, pp. 384-386.
17. Y. X. Li, R. H. Deng, and X. M. Wang (1994), On the equivalence of McEliece's and Niederreiter's public-key cryptosytems, IEEE Transactions on Information Theory, vol. 40, no. 1, pp. 271-273.
18. D. Gottesman (1997), Stabilizer Codes and Quantum Error Correction, Ph.D. thesis, Caltech. Available at http://arxiv.org/abs/quant-ph/9705052.
19. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane (1998), Quantum error correction via codes over GF(4), IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1369-1387.
20. M. A. Nielsen and I. L. Chuang (2000), Quantum Computation and Quantum Information, Cambridge University Press.
21. R. Cleve and D. Gottesman (1997), Efficient computations of encodings for quantum error correction, Phys. Rev. A, vol. 56, 76-82.
22. Min-Hsiu Hsieh and Francois Le Gall (2011), NP-hardness of decoding quantum error correction codes, Phys. Rev. A, vol. 83, 052331.
23. A. R. Calderbank and P. W. Shor (1996), Good quantum error-correcting codes exist, Phys. Rev. A, vol. 54, no. 2, pp. 1098-1105.
24. A. M. Steane (1996), Multiple particle interference and quantum error correction, Proc. Roy. Soc. Lond. A, vol. 452, pp. 2551-2577.
25. M. Grassl, M. Rötteler, and T. Beth (2003), Efficient quantum circuits for non-qubit quantum error-correcting codes, International Journal of Fundations of Computer Science, vol. 14, no. 5, pp. 757-775.
26. E. R. Berlekamp (1968), Algebraic Coding Theory, McGraw-Hill (New York).
27. J. L. Massey (1969), Shift-register synthesis and BCH decoding, IEEE Transactions on Information Theory, vol. 15, no. 1, pp. 122-127.
28. V. M. Sidelnikov and S. O. Shestakov (1992), On insecurity of cryptosystems based on generalized Reed-Solomon codes, Discrete Mathematics and Applications, vol. 2, no. 4, pp. 439-444.
29. T. Berson (1997), Failure of the McEliece public-key cryptosystem under message-resend and related-message attack, in Advances in Cryptology-CRYPTO '97 (LNCS 1294), pp. 213-220.
30. C. Hall, I. Goldberg, and B. Schneier (1999), Reaction attacks against several public-key cryptosys-tems, in Proc. of the 2nd International Conference on Information and Communications Security (LNCS 1726), pp. 2-12.
31. C. M. Adams and H. Meijer (1988), Security-related comments regarding McEliece's public-key cryptosystem, in Advances in Cryptology-CRYPTO '87 (LNCS 293), pp. 224-228.
32. P. J. Lee and E. F. Brickell (1989), An observation on the security of McEliece's public key cryptosystem, in Advances in Cryptology-EUROCRYPT '88 (LNCS 330), pp. 275-280.
33. J. S. Leon (1988), A probabilistic algorithm for computing minimum weights of large error-correcting codes, IEEE Transactions on Information Theory, vol. 34, pp. 1354-1359.
34. J. Stern (1989), A method for finding codewords of small weight, in Coding Theory and Applications (LNCS 388), pp. 106-113.
35. F. Chabaud (1995), on the security of some cryptosystems based on error-correcting codes, in Advances in Cryptology-EUROCRYPT '94 (LNCS 950), pp. 131-139.
36. A. Canteaut and F. Chabaut (1998), 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, vol. 44, no. 1, pp. 367-378.
37. Daniel J. Bernstein, Tanja Lange, Christiane Peters (2008), Attacking and defending the McEliece cryptosystem, in PQCrypto 2008 (LNCS 5299), pp. 31-46.
38. M. Finiasz and N. Sendrier (2009), Security bounds for the design of code-based cryptosystems, in Advances in Cryptology-ASIACRYPT 2009 (LNCS 5912), pp. 88-105.
39. A. Menezes, P. van Oorschot, and S. Vanstone (1996), Handbook of Applied Cryptography, CRC Press.
40. Peter W. Shor (1997), Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing, vol. 26, pp. 1484-1509.
41. Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors) (2009), Post-Quantum Cryptog-raphy, Springer.
42. K. Kobara and H. Imai (2001), Semantically secure McEliece public-key cryptosystems-conversions for McEliece PKC, in Practice and Theory in Public Key Cryptography-PKC '01 (LNCS 1992), pp. 19-35.
43. F. J. MacWilliams and N. J. A. Sloane (1977), The Theory of Error-Correcting Codes, North-Holland.
44. L. Yang (2005), A public-key cryptosystem for quantum message transmission, Proceedings of the SPIE 5631(1), pp. 233-236 and see also e-print arXiv:quant-ph/0310076.
45. M. Grassl, W. Geiselmann, and T. Beth (1999), Quantum Reed-Solomon codes, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (LNCS 1719), pp. 231-244.