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A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms

Part of the Lecture Notes in Computer Science book series (LNCS,volume 196)


A new signature scheme is proposed together with an implementation of the Diffie - Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.


  • Signature Scheme
  • Discrete Logarithm
  • Distribution Scheme
  • Discrete Logarithm Problem
  • Cipher Text

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.

This work was supported by the NSF under contract ECS83 07741 while the author was at the information systems laboratory. Stanford University.


  1. L. Adleman, A Subexponential Algorithm for the Discrete Logarithm Problem with Applications to Cryptography, Proc. 20th IEEE Foundations of Computer Science Symposium (1979). 55–50.

    Google Scholar 

  2. D. Coppersmith. Fast Evaluation of Logarithms in Fields of Characteristic two, IEEE Transactions on Information Theory IT-30 (1964), 587–594.

    MathSciNet  Google Scholar 

  3. W. Diffie and M. Hellman. New Directions in Cryptography, IEEE Transactions on Information Theory, IT-22 (1976). 472–492.

    MathSciNet  Google Scholar 

  4. T. ElGamal. A Subexponential-Time Algorithm for Computing Discrete Logarithms over GF(p 2). submitted to IEEE Transactions on Information Theory.

    Google Scholar 

  5. A. Odlyzko. Discrete Logarithms in Finite Fields and Their Cryptographic Significance. to appear in Proceedings of Eurocrypt’ 84.

    Google Scholar 

  6. H. Ong and C. Schnorr, Signatures Through Approximate Representations by Quadratic Forms, to be published.

    Google Scholar 

  7. H. Ong, C. Schnorr, and A. Shamir, An efficient Signature Scheme Based on Quadratic Forms, pp 208–216 in Proceedings of 16th ACM Symposium on Theoretical Computer Science, 1984.

    Google Scholar 

  8. S. Pohlig and M. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Transactions on Information Theory It-24 (1978). 106–110

    CrossRef  MathSciNet  Google Scholar 

  9. R. Rivest, A. Shamir, and L. Adleman, A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM. Feb 1978, volume 21. number 2. 120–128.

    MATH  CrossRef  MathSciNet  Google Scholar 

  10. C. Schnorr and H. W. Lenstra Jr.. A Monte Carlo Factoring Algorithm with Finite Storage. to appear in Mathematics of Computation.

    Google Scholar 

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© 1985 Springer-Verlag Berlin Heidelberg

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ElGamal, T. (1985). A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In: Blakley, G.R., Chaum, D. (eds) Advances in Cryptology. CRYPTO 1984. Lecture Notes in Computer Science, vol 196. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-540-15658-1

  • Online ISBN: 978-3-540-39568-3

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