2003
DOI: 10.1016/s1071-5797(02)00013-8
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Fast computation of canonical lifts of elliptic curves and its application to point counting

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Cited by 29 publications
(50 citation statements)
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“…A more elaborated implementation strategy (with indexes) yields a O(n) time complexity [7]. 2 ) time complexity with space equal to O(nm) with the clever algorithm described in [12].…”
Section: Lifting the Frobeniusmentioning
confidence: 99%
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“…A more elaborated implementation strategy (with indexes) yields a O(n) time complexity [7]. 2 ) time complexity with space equal to O(nm) with the clever algorithm described in [12].…”
Section: Lifting the Frobeniusmentioning
confidence: 99%
“…More specifically, Satoh et al underlined the importance in the so-called SST algorithm to solve this problem when φ is equal to Φ p , the p-th modular polynomial (to compute the j-invariant of the canonical lift) [12], or equal to x p − y (for computing the Teichmüller lift) [14]. Since the idea behind the SST algorithm is to use the Taylor expansion of φ to increment by one the precision of the root of equation (3) computed at the intermediate steps in the algorithm, it is not difficult to generalize it to a more general φ.…”
Section: Lifting Algorithmsmentioning
confidence: 99%
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“…The security of EC depends on the size of the EC order. The common methods for computing order include Schoof's algorithm [5], SEA (Schoof-Elkies-Atkin) algorithm [6], Satoh algorithm [7] and so on.…”
Section: Koblitz Elliptic Curvesmentioning
confidence: 99%