The Extended Euclidian Algorithm on Polynomials, and the Computational Efficiency of Hyperelliptic Cryptosystems

After generalising two reduction algorithms tocharacteristic 2, we analyse the average complexity of thearithmetic in hyperelliptic Jacobians over any finite field.To this purpose we determine the exact average number offield operations for computing the greatest common divisor ofpolynomials over a finite field by the extended Euclidianalgorithm.

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