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• W2950487098 abstract "Let g >= 1 and let Q be a monic, squarefree polynomial of degree 2g + 1 in Z[x]. For an odd prime p not dividing the discriminant of Q, let Z_p(T) denote the zeta function of the hyperelliptic curve of genus g over the finite field F_p obtained by reducing the coefficients of the equation y^2 = Q(x) modulo p. We present an explicit deterministic algorithm that given as input Q and a positive integer N, computes Z_p(T) simultaneously for all such primes p < N, whose average complexity per prime is polynomial in g, log N, and the number of bits required to represent Q." @default.
• W2950487098 created "2019-06-27" @default.
• W2950487098 creator A5014621753 @default.
• W2950487098 date "2012-10-31" @default.
• W2950487098 modified "2023-09-27" @default.
• W2950487098 title "Counting points on hyperelliptic curves in average polynomial time" @default.
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