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This thesis describes how an elliptic curve cryptosystem can be implemented on low cost microprocessors without coprocessors with reasonable performance. We focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other cost-sensitive devices, and on the Motorola Dragonball, found in the Palm Computing Platform. | Efficient Algorithms for Elliptic Curve Cryptosystems on Embedded Systems by Adam D. Woodbury A Thesis submitted to the Faculty of the Worcester Polytechnic Institute In partial fulfillment of the requirements for the Degree of Master of Science in Electrical Engineering by September 2001 Approved Dr. Christof Paar Thesis Advisor ECE Department Dr. Berk Sunar Thesis Committee ECE Department Dr. William Martin Thesis Committee Mathematical Sciences Department Dr. John Orr Department Head ECE Department ii Abstract This thesis describes how an elliptic curve cryptosystem can be implemented on low cost microprocessors without coprocessors with reasonable performance. We focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other cost-sensitive devices and on the Motorola Dragonball found in the Palm Computing Platform. The implementation is based on the use of the Optimal Extension Fields GF 28 17 17 for low end 8-bit processors and GF 213 1 13 for 16-bit processors. Two advantages of our method are that subfield modular reduction can be performed infrequently and that an adaption of Itoh and Tsujii s inversion algorithm may be used for the group operation. We show that an elliptic curve scalar multiplication with a fixed point which is the core operation for a signature generation can be performed in a group of order approximately 2134 in less than 2 seconds on an 8-bit smart card. On a 16-bit microcontroller signature generation in a group of order approximately 2169 can be performed in under 700 milliseconds. Unlike other implementations we do not make use of curve parameters defined over a subfield such as Koblitz curves. iii Preface This work details the research I conducted at Worcester Polytechnic Institute in pursuit of my Master s degree. I would first like to thank Prof. Christof Paar who has been my advisor mentor and friend since I began my studies with him. Working with Prof. Paar has taken me to foreign lands .
