John Friedlander, Carl Pomerance, Igor E. Shparlinski
Abstract
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We show that an algorithm of V. Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important to our proof are estimates for some divisor sums.
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We show that an algorithm of V. Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important to our proof are estimates for some divisor sums.
Key concepts: Mathematics, Schoof's algorithm, Finite field, Elliptic curve, Division polynomials, Divisor (algebraic geometry), Prime (order theory), Supersingular elliptic curve