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108 Chapter 3. Bent functions and algebraic curvesTheorem 3.2.17 ([275, Theorem 4.4.1]). Let H be an imaginary hyperelliptic curve of genus gdefined over F 2 m. There exists an algorithm to compute the cardinality of H inbit operations and O(g 4 m 3 ) memory.O(g 3 m 3 (g 2 + log 2 m log log m) log gm log log gm)A slightly stronger result applies for Artin–Schreier curves.Theorem 3.2.18 ([275, Theorem 4.3.1]). Let H be an Artin–Schreier curve of genus g definedover F 2 m. There exists an algorithm to compute the cardinality of H inbit operations and O(g 3 m 3 ) memory.O(g 3 m 3 (g 2 + log 2 m log log m) log gm log log gm)In particular, the complexities of these algorithms are polynomial in the genus of the curve.