An FPGA Implementation of a Montgomery Multiplier Over GF(2^m)


  • Nele Mentens
  • Siddika Berna Ors
  • Bart Preneel
  • Joos Vandewalle


Elliptic curve cryptosystems, FPGA, Montgomery´s multiplication method, systolic array


This paper describes an efficient FPGA implementation for modular multiplication in the finite field GF(2^m) that is suitable for implementing Elliptic Curve Cryptosystems. We have developed a systolic array implementation of a~Montgomery modular multiplication. Our solution is efficient for large finite fields (m=160-193), that offer a high security level, and it can be scaled easily to larger values of m. The clock frequency of the implementation is independent of the field size. In contrast to earlier work, the design is not restricted to field representations using irreducible trinomials, all one polynomials or equally spaced polynomials.


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How to Cite

Mentens, N., Ors, S. B., Preneel, B., & Vandewalle, J. (2012). An FPGA Implementation of a Montgomery Multiplier Over GF(2^m). COMPUTING AND INFORMATICS, 23(5-6), 487–499. Retrieved from