Fast exponentation in cryptography
Purchase on Springer.com
$29.95 / €24.95 / £19.95*
* Final gross prices may vary according to local VAT.
We consider the problem of minimizing the number of multiplications in computing f(x)=x n , where n is an integer and x is an element of any ring. We present new methods which reduce the average number of multiplications comparing with well-known methods, such as the binary method and the q-ary method. We do not compare our approach with algorithms based on addition chains since our approach is intended for cryptosystems with large exponent n and the complexity of constructing the optimal addition chain for such n is too high. We consider the binary representation for the number n and simplify exponentiation by applying ideas close to ideas exploited in data compression. Asymptotical efficiency of the new algorithms is estimated and numerical results are given.
- W. Diffie and M.E. Hellman, New directions in cryptography. IEEE Trans. Inform. Theory, vol. IT-22, pp.644–654, Nov.,1976.
- R.L. Rivest, A. Shamir and L. Adelman,A method of obtaining digital signatures and public-key cryptosystems, Commun. ACM, vol.21,pp.120–126, Feb.,1978
- D.E. Knuth, Seminumrerical algorithms The Art of Computer Programming, vol.2, Addison-Wesley, Reading, Mass., 1969.
- J.Ziv and A.Lempel, Compression of individual sequences via variable rate coding. IEEE Trans. Inform. Theory, V.24, No 5, Sep., 1978.
- Y.Yacobi,Exponentiating faster with addition chains, Proceedings of Eurocrypt'90.
- I.Bocharova and B.Kudryashov, Fast exponentiation based on Lempel-Ziv algorithm, In Proceedings on the 6th joint Swedish-Russian International Workshop on Information Theory, August, 1992, pp.259–263
- T.M.Cover and J.A.Thomas, Elements of information theory. New York: Wiley, 1991.
- F. Jelinek and K.S.Schneider, On variable-length-to-block coding, The structural and distance properties of punctured convolutional codes, IEEE Trans. Inform. Theory, V.18, No 6, Nov., 1982.
- Fast exponentation in cryptography
- Book Title
- Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
- Book Subtitle
- 11th International Symposium, AAECC-11 Paris, France, July 17–22, 1995 Proceedings
- pp 146-157
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Additional Links
- Industry Sectors
- eBook Packages
To view the rest of this content please follow the download PDF link above.