On Cryptographic Assumptions and Challenges

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2729)


We deal with computational assumptions needed in order to design secure cryptographic schemes. We suggest a classification of such assumptions based on the complexity of falsifying them (in case they happen not to be true) by creating a challenge (competition) to their validity. As an outcome of this classification we propose several open problems regarding cryptographic tasks that currently do not have a good challenge of that sort. The most outstanding one is the design of an efficient block ciphers.


Signature Scheme Block Cipher Random Oracle Blind Signature Weak Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ajtai, M.: Generating Hard Instances of Lattice Problems. In: Proceedings of the 27th ACM Symposium on Theory of Computing, pp. 99–108 (1996)Google Scholar
  2. 2.
    Ajtai, M., Dwork, C.: A Public-Key Cryptosystem with Worst-Case/Average-Case Equivalence. In: Proceedings of the 28th ACM Symposium on Theory of Computing, pp. 284–293 (1997)Google Scholar
  3. 3.
    Anderson, R.: Security Engineering: A guide to Building Dependeable Distributed Systems. Wiley, Chichester (2001)Google Scholar
  4. 4.
    Barak, B.: How to Go Beyond The Black-Box Simulation Barrier. In: Proc. of the 42nd IEEE Symposium on the Foundation of Computer Science (2001)Google Scholar
  5. 5.
    Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among notions of security for public-key encryption schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)Google Scholar
  6. 6.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols Authors. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)Google Scholar
  7. 7.
    Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures - HOw to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Goldwasser, S., Bellare, M.: Lecture Notes on Cryptography (1996), available
  9. 9.
    Boneh, D., Franklin, M.: Identity Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Chaum, D.: Blind signatures for untraceable payments. In: Advances in Cryptology – Proceedings of Crypto 1982, pp. 199–203. Plenum Press, NewYork (1983)Google Scholar
  12. 12.
    Chaum, D., Fiat, A., Naor, M.: Untraceable Electronic Cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)Google Scholar
  13. 13.
    Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Cramer, R., Shoup, V.: Signature Schemes Based on the Strong RSA Assumption. In: ACM Conference on Computer and Communications Security, pp. 46–51 (1999)Google Scholar
  15. 15.
    Diffie, W.: The First Ten Years of Public Key Cryptography. In: Simmons, G.J. (ed.) Contemporary Cryptography The Science of Information Integrity, IEEE Press, Los Alamitos (1992)Google Scholar
  16. 16.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable Cryptography. Siam J. on Computing 30, 391–437 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Dwork, C., Lotspiech, J., Naor, M.: Digital Signets: Self-Enforcing Protection of Digital Information. In: Proceedings of the 27th ACM Symposium on Theory of Computing, pp. 489–498 (1996)Google Scholar
  18. 18.
    Dwork, C., Naor, M.: Pricing via Processing, Or, Combatting Junk Mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993)Google Scholar
  19. 19.
    Dwork, C., Naor, M.: Zaps and their Applications. In: Proceedings of the IEEE 41st Annual Symposium on the Foundations of Computer Science, pp. 283–293 (2000)Google Scholar
  20. 20.
    Dwork, C., Stockmeyer, L.:Google Scholar
  21. 21.
    Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures Without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139 Springer, Heidelberg (1999)Google Scholar
  22. 22.
    Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. JACM 33(4), 792–807 (1986)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Goldwasser, S., Micali, S., Rivest, R.: A secure digital signature scheme. SIAM J. on Computing 17, 281–308 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Goldreich, O.: On the foundations of modern cryptography. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 46–74. Springer, Heidelberg (1997),
  25. 25.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A Pseudorandom Generator from any One-way Function. SIAM J. Computing 28(4), 1364–1396 (1999)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Hada, S., Tanaka, T.: On the Existence of 3-Round Zero-Knowledge Protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998)Google Scholar
  27. 27.
    Impagliazzo, R., Rudich, S.: Limits on the Provable Consequences of One-Way Permutations. In: STOC 1988 (1988)Google Scholar
  28. 28.
    Juels, A., Luby, M., Ostrovsky, R.: Security of Blind Digital Signatures. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997)Google Scholar
  29. 29.
    Kerckhoffs, A.: La Cryptographie Militaire, Journal des Sciences Militaires, pp. 5–38 (1883), Available at
  30. 30.
    Luby, M., Rackoff, C.: How to construct pseudorandom permutations and pseudorandom functions. SIAM J. Computing 17, 373–386 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Naor, M.: Deniable ring authentication. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 481–498. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  32. 32.
    Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. In: Proceedings of the IEEE 38th Symposium on the Foundations of Computer Science, October 1997, pp. 458–467 (1997)Google Scholar
  33. 33.
    Naor, M., Reingold, O.: On the Construction of Pseudo-Random Permutations: Luby- Rackoff Revisited. Journal of Cryptology 12, 29–66 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Naor, M., Reingold, O.: From Unpredictability to Indistinguishability: A Simple Construction of Pseudo-Random Functions from MACs. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 267–282. Springer, Heidelberg (1998)Google Scholar
  35. 35.
    Naor, M., Reingold, O., Rosen, A.: Pseudo-Random Functions and Factoring. Siam J. on Computing 31(5), 1383–1404 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Pinkas, B.: Fair Secure Two-Party. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 87–105. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  37. 37.
    Pointcheval, D., Stern, J.: Security Arguments for Digital Signatures and Blind Signatures. J. of Cryptology 13(3), 361–396 (2000)zbMATHCrossRefGoogle Scholar
  38. 38.
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signature and public key cryptosystems. Communications of the ACM 21, 120–126 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Rivest, R.L., Shamir, A., Tauman, Y.: How to Leak A Secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  40. 40.
    Shamir, A.: Identity-Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Weizmann Institute of ScienceRehovotIsrael

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