Oblivious transfers and intersecting codes

IEEE Transactions on Information Theory

Volumn 42, Issue 6 PART 1, 1996, Pages 1769-1780

  Brassard, Gilles ^a   Crépeau, Claude ^b,c   Sântha, Miklos ^c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

Author keywords

Algebraic geometric codes; Cryptography; Information theory; Intersecting codes; Oblivious transfer

Indexed keywords

CODES (SYMBOLS); INFORMATION THEORY; SECURITY OF DATA; THEOREM PROVING;

ALGEBRAIC GEOMETRIC CODES; INTERSECTING CODES; OBLIVIOUS TRANSFER;

CRYPTOGRAPHY;

EID: 0030283655     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.556673     Document Type: Article

References (43)

1. D. Beaver, Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority, J. Cryptol, vol. 4, no. 2, pp. 75-122, 1991.
2. M. Bellare and S. Micali, Non-interactive oblivious transfer and applications, in Advances in Cryptology: Crypto '89 Proc. Berlin: Springer-Verlag, 1990, pp. 547-559.
3. C. H. Bennett, G. Brassard, C. Crépeau, and U. M. Maurer, Generalized privacy amplification, IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1915-1923, Nov. 1995.
4. C. H. Bennett, G. Brassard, and J.-M. Robert, Privacy amplification by public discussion, SIAM J. Comput, vol. 17, no. 2, pp. 210-229, Apr. 1988.
5. G. Brassard and C. Crépeau, Oblivious transfers and privacy amplification, unpublished manuscript, 1996.
6. G. Brassard, C. Crépeau, and J.-M. Robert, Information theoretic reductions among disclosure problems, in Proc. 27th Annu. lEEESymp. on Foundations of Computer Science, 1986, pp. 168-173.
7. R. Cleve, Controlled gradual disclosure schemes for random bits and their applications, in Advances in Cryptology: Crypto '89 Proc. Berlin: Springer-Verlag, 1990, pp. 573-588.
8. G. Cohen and A. Lempel, Linear intersecting codes, Discr. Math., vol. 56, pp. 353, 1985.
9. G. Cohen and G. Zémor, Intersecting codes and independent families, IEEE Trans. Inform. Theory, vol. 40, no. 6, pp. 1872-1881, Nov. 1994.
10. C. Crépeau, A zero-knowledge poker protocol that achieves confidentiality of the players' strategy or how to achieve an electronic poker face, in Advances in Cryptology: Crypto '86 Proc. Berlin: SpringerVerlag, 1987, pp. 239-247.
11. Equivalence between two flavors of oblivious transfers (abstract), in Advances in Cryptology: Crypto '87 Proc. Berlin, Germany: Springer-Verlag, 1988, pp. 350-354.
12. Verifiable disclosure of secrets and applications, in Advances in Cryptology: Eurocrypt '89 Proc. Berlin: Springer-Verlag, 1990, pp. 150-154.
13. Correct and private reductions among oblivious transfers, Ph.D. dissertation, Dept. Elec. Engi. and Comput. Sei., MTT, Cambridge, MA, 1990, supervised by S. Micali.
14. Quantum oblivious transfer, J. Mod. Opt., vol. 41, no. 12, pp. 2445-2454, Dec. 1994.
15. C. Crépeau, J. van de Graaf, and A. Tapp, Committed oblivious transfer and private multi-party computations, in Advances in Cryptology: Crypto '95 Proc. Berlin: Springer-Verlag, 1995, pp. 110-123.
16. C. Crépeau and J. Kilian, Achieving oblivious transfer using weakened security assumptions, in Proc. 29th Annu. IEEE Symp. on Foundations of Computer Science 1988, pp. 42-52.
17. C. Crépeau and L. Salvail, Oblivious verification of common string, CWl Quart., vol. 8, no. 2, pp. 97-109, June 1995.
18. C. Crépeau and M. Sântha, On the reversibility of oblivious transfer, in Advances in Cryptology: Eurocrypt '91 Proc. Berlin: Springer-Verlag, 992, pp. 106-113.
19. C. Crépeau and M. Sântha, Efficient reductions among oblivious transfer protocols based on new self-intersecting codes, in Proc. Sequences II: Methods in Communications, Security, and Computer Science. Berlin: Springer-Verlag, 1993, pp. 360-368.
20. S. Even, 0. Goldreich, and A. Lempel, A randomized protocol for signing contracts, in Advances in Cryptology: Proc, Crypto '82. New York: Plenum, 1983, pp. 205-210
21. R. Fagin, M. Naor, and P. Winkler, Comparing common secret information without leaking it, Commun. Assoc. Comput, Mach., vol. 39, no. 5, pp. 77-85, May 1996.
22. G. D. Forney, Concatenated Codes. Cambridge, MA: MIT Press, 1966.
23. O. Goldreich, S. Micali, and A. Wigderson, How to play any mental game, or: A completeness theorem for protocols with honest majority, in Proc. 19th Annual ACM Symp. on Theory of Computing, 1987, pp. 218-229.
24. O. Goldreich and R. Varnish, How to solve any protocol problem-An efficiency improvement, in Advances in Cryptology: Crypto '87 Proc. Berlin: Springer-Verlag, 1988, pp. 73-86.
25. S. Goldwasser and L. Levin, Fair computation of general functions in presence of immoral majority, in Advances in Cryptology: Crypto '90 Proc. Berlin: Springer-Verlag, 1991, pp. 77-93.
26. S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof-systems, SIAM J. Comput., vol. 18, pp. 186-208, 1989.
27. V. D. Goppa, Codes on algebraic curves, Sov. Math.-Dokl, vol. 24, no. 1, pp. 170-172, 1981.
28. G. Katona and J. Srivastava, Minimal 2-coverings of finite affine spaces based on GF(2), J. Statist. Plan. Inference, vol. 8, pp. 375-388, 1983.
29. G. L. Katsman, M. A. Tsfasrnan, and S. G. VläduJ, Modular curves and codes with a polynomial construction, IEEE Trans. Inform. Theory, vol. IT-30, no. 2, pp. 353-355, Mar. 1984.
30. J. Kilian, Founding cryptography on oblivious transfer, in Proc. 20th Annual ACM Symp. on Theory Comp., 1988, pp. 20-31.
31. A general completeness theorem for two-party games, in Proc. 23rd Ann. ACM Symp. on Theory Comp., 1991, pp. 553-560.
32. private communication
33. J. Kilian, S. Micali, and R. Ostrovsky, Minimum resource zero-knowledge proofs, in Proc. 30th Ann. IEEE Symp. on Foundations of Computer Science, 1989, pp. 474-479.
34. F. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
35. Y. I. Manin and S. G. VladuJ, Linear codes and modular curves" Sovr. Prob. Mat., VINITI 1984, in Russian
36. S. Micali and P. Rogaway, Secure computation, IK Advances in Cryptology: Crypto '91 Proc. Berlin: Springer-Verlag, 1992, pp. 392-404.
37. D. Miklos, Linear binary codes with intersecting properties, Discr. Appl. Math., vol. 9, no. 2, pp. 187-196, 1984.
38. H. Nurmi, A. Salomaa, and L. Santean, Secret ballot elections in computer networks, Computers & Security, vol. 10, no. 6, pp. 553-560, 1991.
39. M. O. Rabin, How to exchange secrets by oblivious transfer, Aiken Computation Laboratory, Harvard Univ., Tech. Memo TR-81, 1981.
40. C. T. Retter, Intersecting Goppa codes, IEEE Trans. Inform. Theory, vol. 35, pp. 822-829, 1989.
41. A. De Santis, G. Di Crescenzo, and G. Persiano, Zero-knowledge arguments and public-key cryptography, Inform. Comput., vol. 121, no. 1, pp. 23-40, 1995.
42. N. J. A. Sloane, Covering arrays and intersecting codes, J. Comb. Des., vol. 1, pp. 51-63, 1993.
43. S. Wiesner, Conjugate coding, SigactNews, vol. 15, no. 1, pp. 78-88, 1983. Original manuscript written circa 1970