منابع مشابه
Background on Weil Descent
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We propose an improved implementation of modified Weil pairings. By reduction of operations in the extension field to those in the base field, we can save some operations in the extension field when computing a modified Weil pairing. In particular, computing e`(P, φ(P )) is the same as computing the Tate pairing without the final powering. So we can save about 50% of time for computing e`(P, φ(...
متن کاملA Novel Proof on Weil Pairing
In this paper we will prove a basic property of weil pairing which helps in evaluating its value. We will show that the weil pairing value as computed from the definition is equivalent with the ratio formula based on the miller function. We prove a novel theorem (Theorem 2) and use it to establish the equivalence. We further validate our claims with actual random examples.
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For K3 surfaces, we derive some conditions the characteristic polynomial of the Frobenius on the étale cohomology must satisfy. These conditions may be used to speed up the computation of Picard numbers and the decision of the sign in the functional equation∗∗. Our investigations are based on the Artin-Tate formula.
متن کاملOn Polynomial Systems Arising from a Weil Descent (Extended version)
In the last two decades, many computational problems arising in cryptography have been successfully reduced to various systems of polynomial equations. In this paper, we revisit a class of polynomial systems introduced by Faugère, Perret, Petit and Renault. Based on new experimental results and heuristic evidence, we conjecture that their degrees of regularity are only slightly larger than the ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2009
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-09-01270-1