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The performance of elliptic curve (EC) cryptosystems depends essentially on efficient arithmetic in the underlying finite field. Binary finite fields GF(2m) have the advantage of "carry-free" addition. Multiplication, on the other hand, is rather costly since polynomial arithmetic is not supported by general-purpose processors. We propose a combined hardware/software approach to overcome this problem. First, we outline that multiplication of binary polynomials can be easily integrated into a multiplier datapath for integers without significant additional hardware. Then, we present new algorithms for multiple-precision arithmetic in GF(2m) based on the availability of an instruction for single-precision multiplication of binary polynomials. The proposed hardware/software approach is considerably faster than a "conventional" software implementation and well suited for constrained devices like smart cards. Our experimental results show that an enhanced 16 bit RISC processor is able to generate a 191 bit ECDSA signature in less than 650 msec when the core is clocked at 5 MHz.