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FPGA implementation of modular exponentiation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1586))

Abstract

An efficient implementations of the main building block in the RSA cryptographic scheme is achieved by mapping a bit-level systolic array for modular exponentiation onto Xilinx FPGAs. One XC6000 chip, or 4 Kgates accommodates 132-bit long integers. 16 Kgates is required for modular exponentiation of 512 bit keys, with the estimated bit rate 800 Kb/sec.

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References

  1. K. Iwamura, T. Matsumoto and H. Imai, Modular Exponentiation Using Montgomery Method and the Systolic Array, IEICE Technical Report, vol. 92, no. 134, ISEC92-7, 1992, pp. 49–54.

    Google Scholar 

  2. P. L. Montgomery, Modular multiplication without trial division. Mathematics of Computations, 1985 (44) 519–521.

    Article  MATH  Google Scholar 

  3. H. Orup, E. Svendsen, E. And, VICTOR an efficient RSA hardware implementation. In: Eurocrypt 90, LNCS, vol. 473 (1991) 245–252

    Google Scholar 

  4. J. Sauerbrey, A Modular Exponentiation Unit Based on Systolic Arrays, in Advances in Cryptology—AUSCRYPT’93, Springer-Verlag, LNCS, vol. 718 (1993) 505–516.

    Google Scholar 

  5. M. Shand, J. Vuillemin, Fast Implementation of of RSA Cryptography. In Proc. of the 11th IEEE Symposium on Computer Arithmetics, 1993. pp. 252–259.

    Google Scholar 

  6. A. A. Tiountchik, Systolic modular exponentiation via Montgomery algorithm. J. Electronics Letters, 1998 (34).

    Google Scholar 

  7. C. D. Walter, Systolic Modular Multiplication. IEEE Trans. on Comput., 1993 (42) 376–378.

    Article  Google Scholar 

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José Rolim Frank Mueller Albert Y. Zomaya Fikret Ercal Stephan Olariu Binoy Ravindran Jan Gustafsson Hiroaki Takada Ron Olsson Laxmikant V. Kale Pete Beckman Matthew Haines Hossam ElGindy Denis Caromel Serge Chaumette Geoffrey Fox Yi Pan Keqin Li Tao Yang G. Chiola G. Conte L. V. Mancini Domenique Méry Beverly Sanders Devesh Bhatt Viktor Prasanna

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© 1999 Springer-Verlag

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Tiountchik, A., Trichina, E. (1999). FPGA implementation of modular exponentiation. In: Rolim, J., et al. Parallel and Distributed Processing. IPPS 1999. Lecture Notes in Computer Science, vol 1586. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097960

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  • DOI: https://doi.org/10.1007/BFb0097960

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65831-3

  • Online ISBN: 978-3-540-48932-0

  • eBook Packages: Springer Book Archive

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