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Lecture Notes in Computer Science
The use of elliptic and hyperelliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test whether the Jacobian -over a finite field Fq -of a hyperelliptic curve of the form Y 2 = X 5 + aX 3 + bX (with a, b ∈ F * q ) has a large prime factor. His approach is to obtain candidates for the zeta function of the Jacobian over F * q from its zeta function over an extension field wheredoi:10.1007/978-3-642-36334-4_16 fatcat:cdp3jvavxfhr3h37fmz4c5pjvi