Advertisement

Non-interactive Public-Key Cryptography

  • Ueli M. Maurer
  • Yacov Yacobi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)

Abstract

An identity-based non-interactive public key distribution system is presented that is based on a novel trapdoor one-way function allowing a trusted authority to compute the discrete logarithm of a given number modulo a publicly known composite number m while this is infeasible for an adversary not knowing the factorization of m. Without interaction with a key distribution center or with the recipient of a given message a user can generate a mutual secure cipher key based solely on the recipient’s identity and his own secret key and send the message, encrypted with the generated cipher key using a conventional cipher, over an insecure channel to the recipient. Unlike in previously proposed identity-based systems, no public keys, certificates for public keys or other information need to be exchanged and thus the system is suitable for many applications such as electronic mail that do not allow for interaction.

Keywords

Signature Scheme Discrete Logarithm Discrete Logarithm Problem Decimal Digit Large Prime Factor 
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.

References

  1. [1]
    D. Coppersmith, A.M. Odlyzko and R. Schroeppel, Discrete Logarithms in GF(p), Algorithmica, vol. 1, pp. 1–15, 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    W. Diffie and M.E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, vol. IT-22, pp. 664–654, Nov. 1976.MathSciNetGoogle Scholar
  3. [3]
    T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, vol. IT-31, pp. 469–472, July 1985.CrossRefMathSciNetGoogle Scholar
  4. [4]
    M. Girault, Self-certified public keys, these proceedings.Google Scholar
  5. [5]
    C.G. Günther, An identity-based key-exchange protocol, Advances in Cryptology-EUROCRYPT’ 89, Lecture Notes in Computer Science, vol. 434, Berlin: Springer Verlag, pp. 29–37, 1990.Google Scholar
  6. [6]
    L. Kohnfelder, Towards a practical public-key cryptosystem, B.S. Thesis, MIT, 1979.Google Scholar
  7. [7]
    K. Koyama and K. Ohta, Identity-based conference key distribution systems, Advances in Cryptology-CRYPTO’ 87, Lecture Notes in Computer Science, vol. 293, Berlin: Springer Verlag, pp. 175–184, 1988.Google Scholar
  8. [8]
    A.K. Lenstra, personal communication, 1991.Google Scholar
  9. [9]
    A.K. Lenstra and M.S. Manasse, Factoring with two large primes, Advances in Cryptology-EUROCRYPT’ 90, Lecture Notes in Computer Science, vol. 473, Berlin: Springer Verlag, pp. 69–80, 1991.Google Scholar
  10. [10]
    H.W. Lenstra, Factoring integers with elliptic curves, Annals of Mathematics, vol. 126, pp. 649–673, 1987.CrossRefMathSciNetGoogle Scholar
  11. [11]
    A.K. Lenstra, H.W. Lenstra, M.S. Manasse and J.M. Pollard, The number field sieve, to appear.Google Scholar
  12. [12]
    A.K. Lenstra and M.S. Manasse, Factoring with electronic mail, Advances in Cryptology-EUROCRYPT’ 89, Lecture Notes in Computer Science, vol. 434, Berlin: Springer Verlag, pp. 355–371, 1990.Google Scholar
  13. [13]
    T. Matsumoto and H. Imai, On the key predistribution system: a practical solution to the key distribution problem, Advances in Cryptology-CRYPTO’ 87, Lecture Notes in Computer Science, vol. 293, Berlin: Springer Verlag, pp. 185–193, 1988.Google Scholar
  14. [14]
    U.M. Maurer, Fast generation of secure RSA-moduli with almost maximal diversity, Advances in Cryptology-EUROCRYPT’ 89, Lecture Notes in Computer Science, vol. 434, Berlin: Springer Verlag, pp. 636–647, 1990.Google Scholar
  15. [15]
    K.S. McCurley, A key distribution system equivalent to factoring, Journal of Cryptology, vol. 1, no. 2, pp. 95–106, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    G.L. Miller, Riemann’s hypothesis and tests for primality, Journal of Computer and System Sciences, vol. 13, pp. 300–317, 1976.zbMATHMathSciNetGoogle Scholar
  17. [17]
    Y. Murakami and M. Kasahara, An ID-based key distribution system, Proc. of ISEC90, pp. 33–40, 1990 (in Japanese).Google Scholar
  18. [18]
    A.M. Odlyzko, personal communications, 1990–91.Google Scholar
  19. [19]
    T. Okamoto and K. Ohta, How to utilize the randomness of zero-knowledge proofs, presented at CRYPTO’90 (to appear in the proceedings), Santa Barbara, CA, Aug. 11–15, 1990.Google Scholar
  20. [20]
    E. Okamoto and K. Tanaka, Key distribution based on identification information, IEEE Journal on Selected Areas in Communications, vol. 7, no. 4, pp. 481–485, May 1989.CrossRefGoogle Scholar
  21. [21]
    S.C. Pohlig and M.E. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Transactions on Information Theory, vol IT-24, pp. 106–110, Jan. 1978.CrossRefMathSciNetGoogle Scholar
  22. [22]
    J.M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Society, vol. 76, pp. 521–528, 1974.zbMATHMathSciNetCrossRefGoogle Scholar
  23. [23]
    R.L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, vol. 21, pp. 120–126, 1978.zbMATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    R.J. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Mathematics of Computation, vol. 44, pp. 483–494, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  25. [25]
    A. Shamir, Identity-based cryptosystems and signature schemes, Advances in Cryptology-CRYPTO’ 84, Lecture Notes in Computer Science, vol. 196, Berlin: Springer Verlag, pp. 47–53, 1985.Google Scholar
  26. [26]
    Z. Shmuely, Composite Diffie-Hellman public-key generating systems are hard to break, TR 356, CS Dept., Technion, Feb. 1985.Google Scholar
  27. [27]
    S. Tsujii and T. Itoh, An ID-based cryptosystem based on the discrete logarithm problem, IEEE Journal on Selected Areas in Communications, vol. 7, no. 4, pp. 467–473, May 1989.CrossRefGoogle Scholar
  28. [28]
    Y. Yacobi, A key distribution “paradox”, presented at CRYPTO’90 (to appear in the proceedings), Santa Barbara, CA, Aug. 11–15, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ueli M. Maurer
    • 1
  • Yacov Yacobi
    • 2
  1. 1.Dept. of Computer SciencePrinceton UniversityPrinceton
  2. 2.BellcoreMorristown

Personalised recommendations