Advertisement

SAFECOMP ’93 pp 341-348 | Cite as

MRSA — a new public key encryption method

  • Reinhard Posch
Conference paper

Abstract

This paper focuses on the key generation problem for a modified RSA public key cryptographic system based on the RNS arithmetic. The RNS based modification of the well known RSA algorithm uses highly parallel computation with the restriction that only a subset of key triples (D,ekey,dkey) of a conventional RSA system can be adopted. These restrictions result from the choice of base elements used. The present work shows that the remaining set of possible keys is still large enough to be used in a realistic cryptographic system. The encryption machine under discussion can use parallelism and thus high speed. A rather straight forward algorithm for the generation of keys can be given. The resulting key space can be viewed as satisfactory. The method gives an additional degree of freedom for the implementation on parallel systems avoiding all conversions between number systems.

Keywords

Base Extension Residue Number System Modulo Reduction Cryptographic System Modulo Multiplication 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference List

  1. 1.
    Cooper R.H., Patterson W.: RSA as a Benchmark for Multiprocessor Machines; Proc. “Advances in Cryptology — AUSCRYPT ’90” LNCS, Springer 1990, pp. 356–359Google Scholar
  2. 2.
    Montgomery L.: Modular Multiplication Without Trial Division; Mathematics of Computation, Vol. 44, No. 170, April 1985, pp. 519–521.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Posch K.C., Posch R.: Approaching encryption at ISDN speed using partial parallel modulus multiplication; Microprocessing and Microprogramming, North-Holland, 29, (1990), pp. 177–184.CrossRefGoogle Scholar
  4. 4.
    Beeth Th. et al.; Public key Cryptography, State of the Art and Future Directions; LNCS 578, Springer 1992Google Scholar
  5. 5.
    Ivey P.A., Walker S.N., Stern J.M., Davidson S.: An Ultra-High Speed Public Key Encryption Processor; IEEE Custom Integrated Circuits Conference, 1992, pp. 19.6.1–19.6.4Google Scholar
  6. 6.
    Lippitsch P., Posch K.C., Posch R., Schindler V.: A scalable RSA design with encryption rates from 200 Kbit/sec to 1,5 Mbit/sec; Poster at CRYPTO ’92Google Scholar
  7. 7.
    Posch R.: A Parallel Approach to Long Integer Register Oriented Arithmetic; Fifth International Conference on Parallel and Distributed Computing and Systems; Oct 1.–3. 1992, Pittsburgh, PA.Google Scholar
  8. 8.
    Schoenfeld L.: Sharper bounds for the Chebychev functions Θ(x) ans Ψ(x); II, Math. Comp. 30, (1976), pp 337–360.MathSciNetGoogle Scholar
  9. 9.
    Rivest R., Shamir A., Adlemann L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems; Comm. of the ACM (Feb. 1978),pp. 120–126.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Knuth D.E.: The Art of Computer Programming, Vol 2, Addison Wesley, Reading, Mass., 1969zbMATHGoogle Scholar
  11. 11.
    Wallace C.S.: A suggestion for a fast multiplier; IEEE Transaction on Electronic Computers, Vol. EC-13, Feb. 1964, pp. 14–17.CrossRefGoogle Scholar
  12. 12.
    Lüneburg, H.: Vorlesungen über Zahlentheorie; Elemente der Mathematik vom höheren Standpunkt aus, Band VII, ed. by E. Trost, BirkhäuserVerlag, (basel, 1978).Google Scholar
  13. 13.
    Denning D.E.: Cryptography and data security; Addison Wesley, Reading, Mass., 1983zbMATHGoogle Scholar
  14. 14.
    Posch K.C, Posch R.: Residue number systems a key to parallelism in public key cryptography; Fourth IEEE Symposium on Parallel and Distributed Processing; Dec. 1.–4. 1992, Dallas.Google Scholar

Copyright information

© Springer-Verlag London Limited 1993

Authors and Affiliations

  • Reinhard Posch
    • 1
  1. 1.Institute for Applied Information Processin GrazUniversity of TechnologyGrazAustria

Personalised recommendations