Cryptographic Hardware and Embedded Systems - CHES 2002
Lecture Notes in Computer Science, 2003, Volume 2523/2003, 175-192, DOI: 10.1007/3-540-36400-5_28

A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over \mathbbG\mathbbF( 2n ) \mathbb{G}\mathbb{F}\left( {2^n } \right)

M. Ernst, M. Jung, F. Madlener, S. Huss and R. Blümel

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Abstract

The performance of elliptic curve based public key cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. This work describes two generic and scalable architectures of finite field coprocessors, which are implemented within the latest family of Field Programmable System Level Integrated Circuits FPSLIC from Atmel, Inc. The HW architectures are adapted from Karatsuba’s divide and conquer algorithm and allow for a reasonable speedup of the top-level elliptic curve algorithms. The VHDL hardware models are automatically generated based on an eligible operand size, which permits the optimal utilization of a particular FPSLIC device.

Keywords  Elliptic Curve cryptography -  $ \mathbb{G}\mathbb{F}\left( {2^n } \right) $ \mathbb{G}\mathbb{F}\left( {2^n } \right) arithmetic - Karatsuba multiplication - VHDL model generator - coprocessor synthesis - FPGA hardware acceleration - Atmel FPSLIC platform

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