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An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance

Published:26 August 2022Publication History
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References

  1. [1].D. E. Knuth, The Art of Computer Programming, Vol. II: Seminumerical Algorithms. Reading, MA: Addison-Wesley, 1969.Google ScholarGoogle Scholar
  2. [2].D. E. Knuth, The Art of Computer Programming, Vol. III: Sorting and Searching. Reading, MA: Addison-Wesley, 1973.Google ScholarGoogle Scholar
  3. [3].R. W. Keyes, “Physical limits in digital electronics,” in Proc. IEEE, vol. 63, pp. 740-767, May 1975.Google ScholarGoogle ScholarCross RefCross Ref
  4. [4].R. W. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Develop., vol. 5, pp. 183-191, 1961.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. [5].M. V. Wilkes, Time-Sharing Computer Systems. New York: American Elsevier, 1968.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. [6].A. Evans, W. Kantrowitz, and E. Weiss, “A user authentication scheme not requiring secrecy in the computer,” Comm. ACM, vol. 17, pp. 487-442, Aug. 1974.Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. [7].G. B. Purdy, “A high security log-in procedure,” Comm. of ACM, vol. 17, pp. 442-445, Aug. 1974.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. [8].R. Merkle, “Secure communication over an insecure channel,” submitted to Comm. of ACM. [Subsequently published as R. Merkle, “Secure Communications over Insecure Channels,” Comm. of ACM, vol. 21, pp. 294-299, Apr. 1978. Available online https://www.merkle.com/1974/PuzzlesAsPublished.pdf.]Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. [9].W. Diffie and M. E. Hellman, “New directions in cryptography,” IEEE Trans. Inform Theory, vol. IT-22, pp. 644-654, Nov. 1976. [Now available online http://www-ee.stanford.edu/~hellman/publications/24.pdf.]Google ScholarGoogle Scholar
  10. [10].R. A. Scholtz and L. R. Welch, “Generalized residue sequence,” in Proc. Int. Conf. Comm., Seattle, WA, June 1973.Google ScholarGoogle Scholar
  11. [11].R. Merkle and M. E. Hellman, “Hiding information and receipts in trap door knapsacks,” presented at 1977 IEEE Int. Symp. Information Theory, Ithaca, NY, Oct. 1977. [Subsequently published as IEEE Trans. on Info. Theory, Vol. IT-24, pp. 525-536, Sep. 1978. http://www-ee.stanford.edu/~hellman/publications/30.pdf.]Google ScholarGoogle Scholar
  12. [12].R. G. Archibald, An Introduction to the Theory of Numbers. Columbus, OH: Merrill, 1970.Google ScholarGoogle Scholar
  13. [13].Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, Eds. New York: Dover, 1965.Google ScholarGoogle Scholar
  14. [14].R. L. Rivest, A. Shamir, L. Adleman, “On digital signatures and public-key cryptosystems,” Dep. Elec. Engr. and Comp Sci., M.I.T., Cambridge, MA, Tech. Rep. MIT/LCS/TM-82, Apr. 1977. [Subsequently published in Comm. of ACM, Vol. 21, pp. 120-126, Feb 1978. Now online .]Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. [15].N. J. A. Sloane, A Handbook of Integer Sequences. New York: Academic, 1973.Google ScholarGoogle Scholar

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            cover image ACM Books
            Democratizing Cryptography: The Work of Whitfield Diffie and Martin Hellman
            August 2022
            558 pages
            ISBN:9781450398275
            DOI:10.1145/3549993

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            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 26 August 2022

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