High Performance Elliptic Curve Cryptographic Co-processor

Electrical & Computer Engineering;elliptic curve co-processor;cryptography;koblitz curves;FPGA;hardware

Lutz, Jonathan

University of Waterloo

关键词: Electrical & Computer Engineering;    elliptic curve co-processor;    cryptography;    koblitz curves;    FPGA;    hardware;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/855/1/jlutz2003.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In FIPS 186-2, NIST recommends several finite fields to be used in theelliptic curve digital signature algorithm (ECDSA). Of the tenrecommended finite fields, five are binary extension fields withdegrees ranging from 163 to 571. The fundamental building block of theECDSA, like any ECC based protocol, is elliptic curve scalarmultiplication. This operation is also the most computationallyintensive. In many situations it may be desirable to accelerate theelliptic curve scalar multiplication with specialized hardware.In this thesis a high performance elliptic curve processor isdeveloped which is optimized for the NIST binary fields. Thearchitecture is built from the bottom up starting with the fieldarithmetic units. The architecture uses a field multiplier capable ofperforming a field multiplication over the extension field with degree163 in 0.060 microseconds. Architectures for squaring and inversion arealso presented. The co-processor uses Lopez and Dahab;;s projectivecoordinate system and is optimized specifically for Koblitz curves. Aprototype of the processor has been implemented for the binaryextension field with degree 163 on a Xilinx XCV2000E FPGA. Theprototype runs at 66 MHz and performs an elliptic curve scalarmultiplication in 0.233 msec on a generic curve and 0.075 msec on aKoblitz curve.