Acta Applicandae Mathematica

, Volume 93, Issue 1–3, pp 279–297 | Cite as

On the Design of Cryptographic Primitives

Article

Abstract

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed.

Mathematics Subject Classifications (2000)

94A60 11T99 14G50 11T71 

Key words

cryptography secure communications finite fields discrete mathematics 

References

  1. 1.
    Abadi, M., Needham, R.: Prudent engineering practice for cryptographic protocols. IEEE Trans. Softw. Eng. 22(1), 6–15 (1996)CrossRefGoogle Scholar
  2. 2.
    Beaver, D., Goldwasser, S.: Multiparty computation with faulty majority. Advances in Cryptology. In: Proceedings of Crypto ’89. Lecture Notes in Computer Science 435, pp. 589–590. Springer, Berlin Heidelberg New York (1989)Google Scholar
  3. 3.
    Blum, M.: Coin Flipping by Telephone: a Protocol for Solving Impossible Problems. IEEE Computer Conference, pp. 133–137 (1982)Google Scholar
  4. 4.
    Blum, M., Vazirani, U.V., Vazirani, V.V.: Reducibility among protocols. Advances in Cryptology. In: Proceedings of Crypto ’83, pp. 137–146. Plenum (1984)Google Scholar
  5. 5.
    Burrows, M., Abadi, M., Needham, R.: A logic of authentication. ACM Trans. Comput. Syst. 1(8), 18–36 (1990)CrossRefGoogle Scholar
  6. 6.
    Caballero, P., Hernández, C.: Strong solutions to the identification problem. Proceedings of the 7th Annual International Computing and Combinatorics Conference COCOON ’01. Lecture Notes in Computer Science 2108, pp. 257–261. Springer, Berlin Heidelberg New York (2001)Google Scholar
  7. 7.
    Clark, S., Millen, J., Freedman, S.: The interrogator: protocol security analysis. IEEE Trans. Softw. Eng. 13(2), 274–288 (1987)Google Scholar
  8. 8.
    Crepeau, C.: Equivalence between two flavours of oblivious transfers. Advances in Cryptology. In: Proceedings of Crypto ’87. Lecture Notes in Computer Science 293, pp. 350–354. Springer, Berlin Heidelberg New York (1987)Google Scholar
  9. 9.
    Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inform. Theory IT-22, 644–654 (1976)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dolev, D., Yao, A.: On the security of public key protocols. IEEE Trans. Inform. Theory 29(2), 198–208 (1983)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Even, S.: A protocol for signing contracts. Advances in Cryptology. In: Proceedings of Crypto ’81. Lecture Notes in Computer Science, pp. 148–153. Springer, Berlin Heidelberg New York (1982)Google Scholar
  12. 12.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts (extended abstract). Advances in Cryptology. In: Proceedings of Crypto ’82, pp. 205–210. Plenum (1982)Google Scholar
  13. 13.
    Even, S., Yacobi, Y.: Relations among public-key signature systems, TR-175, Computer Science Dept., Technion, Israel (1980)Google Scholar
  14. 14.
    Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identity. J. Cryptology 1, 77–95 (1988)MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Fortnow, L.: The complexity of perfect zero-knowledge. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing STOC ’87, pp. 204–209 (1987)Google Scholar
  16. 16.
    Goldreich, O., Micali, S., Wigderson, A.: How to Solve any Protocol Problem. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing STOC ’87, pp. 218–229 (1987)Google Scholar
  17. 17.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing STOC ’85, pp. 291–304 (1985)Google Scholar
  18. 18.
    Gong, L., Syverson, P.: Fail-stop protocols: A new approach to designing secure protocols. In: Proceedings of the 5th International Working Conference on Dependable Computing for Critical Applications, pp. 44–55 (1995)Google Scholar
  19. 19.
    Heintze, N., Tygar, J.: A model for secure protocols and their compositions. In: Proceedings of the IEEE, Symposium on Research in Security and Privacy, pp. 2–13 (1994)Google Scholar
  20. 20.
    Impagliazzo, R., Yung, M.: Direct minimum knowledge computations. Advances in Cryptology – Crypto’87. Lecture Notes in Computer Science 293, pp. 40–51. Springer, Berlin Heidelberg New York (1987)Google Scholar
  21. 21.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of 20th ACM Symposium on Theory of Computing, STOC ’88, pp. 20–31 (1988)Google Scholar
  22. 22.
    Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press (1986)Google Scholar
  23. 23.
    Nao, M., Fagin, R., Winkler, P.: Comparing information without leaking it. Commun. ACM 39(5), 77–85 (1996)CrossRefGoogle Scholar
  24. 24.
    Odlyzko, A.M.: Discrete logarithms in finite fields and their cryptographic significance. Advances in Cryptology. In: Proceedings of Eurocrypt ’84, Lecture Notes in Computer Science 209, pp. 224–314. Springer, Berlin Heidelberg New York (1985)Google Scholar
  25. 25.
    Rabin, M.O.: How to Exchange Secrets by Oblivious Transfer. Tech. Report TR-81, Harvard Aitken Computation Laboratory (1981)Google Scholar
  26. 26.
    Shostak, R., Lamport, L., Pease, M.: The byzantine generals problem. ACM Trans. Program. Lang. Syst. 4, 382–401 (1982)MATHCrossRefGoogle Scholar
  27. 27.
    Yao, A.: Protocols for secure computations. Proceedings of Foundations of Computer Science FOCS’82, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Departamento de Estadistica, Investigacion Operativa y ComputacionUniversity of La LagunaLa LagunaSpain
  2. 2.Institute of Applied PhysicsMadridSpain

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