Study on Security Analysis of Elliptic and Hyperelliptic Cryptosystems against Weil Descent Attack

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This research is to analyze security of elliptic and hyperelliptic cryptosystems, which are supposed to be the safest cryptosystems, against the recently developed Weil descent GHS attack. In particular, we will show a complete classification of all elliptic and hyperelliptic curved used in the cryptosystems which are weak against the Weil descent GHS attack, find the number and classes of these weak curves and algorithms to test if a random curve is safe or not. These results then provide a full understanding on risk and damage of the cryptosystems again the GHS attack.