Architectural Extensions for Elliptic Curve Cryptography over GF(2^m ) on 8-bit Microprocessors

Authors:
Hans Eberle;Arvinderpal Wander;Nils Gura;Sheueling Chang-Shantz;Vipul Gupta
Affiliations:
Sun Microsystems Laboratories Menlo Park, California, USA;Sun Microsystems Laboratories Menlo Park, California, USA;Sun Microsystems Laboratories Menlo Park, California, USA;Sun Microsystems Laboratories Menlo Park, California, USA;Sun Microsystems Laboratories Menlo Park, California, USA
Venue:
ASAP '05 Proceedings of the 2005 IEEE International Conference on Application-Specific Systems, Architecture Processors
Year:
2005

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Abstract

We describe and analyze architectural extensions to accelerate the public-key cryptosystem Elliptic Curve Cryptography (ECC) on 8-bit microprocessors. We show that simple extensions of the data path suffice to efficiently support ECC over GF(2^m). These extensions include an extended multiplier that generates results for both integer multiplications and multiplications in fields GF(2^m) and a multiply-accumulate instruction for efficiently performing multiple-precision multiplications. To our knowledge, this is the first paper that quantifies performance of standard NIST and SECG elliptic curves over GF(2^m) on an 8-bit microprocessor equipped with a dual-?eld multiplier. On the ATmega128 microprocessor running at 8 MHz we measured an execution time of 0.29 s for a 163-bit ECC point multiplication over GF(2^m), 0.81 s for a 160-bit ECC point multiplication over GF(p), and 11 s for a 1024-bit RSA private-key operation - the chosen key sizes provide equivalent security strength.