Abstract
The design of a scalable arithmetic unit for operations over elements of GF(2m) represented in normal basis is presented. The unit is applicable in public-key cryptography. It comprises a pipelined Massey-Omura multiplier and a shifter. We equipped the multiplier with additional data paths to enable easy implementation of both multiplication and inversion in a single arithmetic unit. We discuss optimum design of the shifter with respect to the inversion algorithm and multiplier performance. The functionality of the multiplier/inverter has been tested by simulation and implemented in Xilinx Virtex FPGA.We present implementation data for various digit widths which exhibit a time minimum for digit width D = 15.
Highlights
Contemporary cryptographic schemata are frequently based on the Discrete Logarithm Problem (DLP): find integer k such that k å Q = k × P = P (1)for given group elements P and Q.In elliptic curve cryptography (ECC), P and Q are points on a chosen elliptic curve over a finite field
In this work we present a modification of the AMOV multiplier, which allows efficient implementation of both the multiplication and ITT inversion algorithms
We introduce several improvements to this multiplication/inversion unit, which lead to increased performance and a better performance/area ratio
Summary
The DLP in such a group is exponentially hard in comparison with DLP in a multiplicative group over a finite field This means that a 173 bit key provides approximately the same security level as the 1024-bit RSA [7]. This fact is very important in applications such as chip cards, where the size of the hardware and energy consumption is crucial. In algorithms such as the Elliptic Curve Digital Signature Algorithm (ECDSA), k is an m-bit integer, P is a chosen point and Q is computed using Eq 1.
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