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A redundant binary algorithm for RSA


The normal form and modified normal form for binary redundant representation are defined. A redundant binary algorithm to compute modular exponentiation for very large integers is proposed. It is shown that the proposed algorithm requires the minimum number of basic operations (modular multiplications) among all possible binary redundant representations.

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  1. [1]

    Rviest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystem.Communication of the ACM, 1978, 21(2): 120–126.

  2. [2]

    Knuth D E. Seminumerical Algorithm—The Art of Computer Programming. Vol.2, Chapter 4, Addison-Wesley, Reading, MA, 1981.

  3. [3]

    Selby A, Mitchell C. Algorithms for software implementations of RSA.IEE, Part E., 1989, 136(3): 166–170.

  4. [4]

    Yun D Y Y, Zhang C N. A fast carry-free algorithm and hardware design for extended integer GCD computation. InInternational ACM Conference on Symbolic and Algebra Computation, Waterloo, Canada, July 1986, pp.82–84.

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Author information

Correspondence to Ronghua Shi.

Additional information

Shi Ronghua received his B.S. degree in computer software from Changsha Railway University in 1986, and his M.S. degree in computer science from Central South University of Technology in 1989. He has been working in the Changsha Railway University since 1989, and is currently a Lecturer of the Department of Electronic Engineering. His current research interests include computer networks, algorithm and system, broadband ISDN.

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Shi, R. A redundant binary algorithm for RSA. J. of Comput. Sci. & Technol. 11, 416–420 (1996).

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  • Redundant binary representation
  • redundant binary algorithm
  • RSA