On Division Polynomial PIT and Supersingularity

01/08/2018

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by   Javad Doliskani, et al.

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For an elliptic curve E over a finite field _q, where q is a prime power, we propose new algorithms for testing the supersingularity of E. Our algorithms are based on the Polynomial Identity Testing (PIT) problem for the p-th division polynomial of E. In particular, an efficient algorithm using points of high order on E is given.