We study the complexity of arithmetic in finite fields of characteristic two, \F_{2^n}.
We concentrate on the following two problems:
Iterated Multiplication: Given \alpha_1, \alpha_2,..., \alpha_t \in \F_{2^n}, compute \alpha_1 \cdot \alpha_2 \cdots \alpha_t \in \F_{2^n}.
Exponentiation: Given \alpha \in \F_{2^n} and a t-bit integer k, compute \alpha^k \in \F_{2^n}.
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