Advertisement

Analysis of a Public Key Approach Based on Polynomial Substitution

  • Harriet Fell
  • Whitfield Diffie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 218)

6 Conclusions

We set out to build a public key cryptosystem by repeatedly substituting for variables in multivariate polynomials and simplifying the results to conceal the substitution process. There seems, however, to be no way to build such a system that is both secure and has a public key of practical size when the devices used to limit the number of coefficeints are nilpotence and J-rings. We have only shown, however, that it is impossible to produce such a system if the total degree of the encryption polynomial determines the size of the public key. Perhaps, by properly choosing p 0 and p 1, we can employ the fundamental scheme to produce sparse encrypting polynomials. Then the public key could be kept small while the encrypting polynomial bas large total degree and is difficult to invert.

Keywords

Total Degree Multivariate Polynomial Nilpotent Ideal Polynomial Transformation Fundamental Scheme 
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]
    Don Coppersmith and Edna Grossman, “Generators for Certain Alternating Groups with Applications to Cryptography,” SIAM J. Appl. Math., Vol. 29, No. 4, pp. 624–627, Dec 1975.CrossRefMathSciNetzbMATHGoogle Scholar
  2. [2]
    Whitfield Diffie and Martin E. Hellman, “New Directions in Cryptography,” IEEE Trans. Info. Thy., Vol. IT-22, No. 6, pp. 644–654, November 1976.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Data Encryption Standard, FIPS Pub. No. 46, National Bureau of Standards, 15 January 1977.Google Scholar
  4. [4]
    Solomon W. Golomb, Shift Register Sequences, Holden Day, San Francisco, 1967.zbMATHGoogle Scholar
  5. [5]
    R. McLeice, A Public-Key Cryptosystem Based On Albebraic Coding Theory, DSN Progress Report 42-44, Jet Propulsion Lab, Calif. Inst. of Tech., Pasadina CA, Jan–Feb 1978.Google Scholar
  6. [6]
    R. C. Merkle and M. E. Hellman, “Hiding Information and Signatures in Trapdoor Knapsacks,” IEEE Transactions on Information Theory, Vol. IT-24, No. 5, pp. 525–530, September 1978.CrossRefGoogle Scholar
  7. [7]
    R. L. Rivest, A. Shamir, and L. Adleman, “A Method for Obtaining Digital Signatures and Public Key Cryptosystems,” CACM, Vol. 21, No. 2, pp. 120–126, February 1978.zbMATHMathSciNetGoogle Scholar
  8. [8]
    Gustavus J. Simmons. Personal Communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Harriet Fell
    • 1
  • Whitfield Diffie
    • 2
  1. 1.Northeastern UniversityBoston
  2. 2.Bell-Northern ResearchMountain View

Personalised recommendations