Elliptic Curve Cryptography on Smart Cardswithout Coprocessors

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This contribution describes how an elliptic curve cryptosystem can be implemented on very low cost microprocessors with reasonable performance. They focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other cost sensitive devices. The implementation is based on the use of the finite field GF which is particularly suited for low end 8bit processors. Two advantages of the method are that subfield modular reduction can be performed infrequently, and that an adoption inversion algorithm is used for the group operation. They 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.