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This contribution describes a methodology used to efficiently implement elliptic curves (EC) over GF(p) on the 16-bit TI MSP430x33x family of low-cost microcontrollers. We show that it is possible to implement EC cryptosystems in highly constrained embedded systems and still obtain acceptable performance at low cost. We modified the EC point addition and doubling formulae to reduce the number of intermediate variables while at the same time allowingfor flexibility. We used a Generalized-Mersenne prime to implement the arithmetic in the underlying field. We take advantage of the special form of the moduli to minimize the number of precomputations needed to implement inversion via Fermat's Little theorem and the k-ary method of exponentiation. We apply these ideas to an implementation of an elliptic curve system over GF(p), where p = 2128 - 297 - 1. We show that a scalar point multiplication can be achieved in 3.4 seconds without any stored/precomputed values and the processor clocked at 1 MHz.

Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP430x33x Family of Microcontrollers