Integration, the VLSI
Journal, Vol. 37, No. 2, pages 103-120, May 2004.
Scalable VLSI Architecture for Montgomery
Inversion in GF(p)
Gutuba,* and Alexandre Ferreira Tencab
Computer Engineering Department, King Fahd
University of Petrolium & Minerals, Dhahran 31261,
Electrical and Computer Engineering Department,
Oregon State University, Corvallis, Oregon 97331 USA.
The multiplicative inversion operation
is a fundamental computation in several cryptographic applications. In this
work, we propose a scalable VLSI hardware to compute the Montgomery modular inverse in GF(p). We
suggest a new correction phase for a previously proposed almost Montgomery inverse
algorithm to calculate the inversion in hardware. We also propose an efficient
hardware algorithm to compute the inverse by multi-bit shifting method. The
intended VLSI hardware is scalable, which means that a fixed-area module can
handle operands of any size. The word-size, which the module operates, can be
selected based on the area and performance requirements. The upper limit on the
operand precision is dictated only by the available memory to store the
operands and internal results. The scalable module is in principle capable of
performing infinite-precision Montgomery
inverse computation of an integer, modulo a prime number.
This scalable hardware is compared with a previously proposed fixed (fully
parallel) design showing very attractive results.
inverse, Elliptic curve cryptography, Scalable hardware design