Asymmetric-key algorithms | Finite fields | Group theory | Elliptic curves | Elliptic curve cryptography | Number theory

Schoof's algorithm

Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is important to know the number of points to judge the difficulty of solving the discrete logarithm problem in the group of points on an elliptic curve. The algorithm was published by René Schoof in 1985 and it was a theoretical breakthrough, as it was the first deterministic polynomial time algorithm for counting points on elliptic curves. Before Schoof's algorithm, approaches to counting points on elliptic curves such as the naive and baby-step giant-step algorithms were, for the most part, tedious and had an exponential running time. This article explains Schoof's approach, laying emphasis on the mathematical ideas underlying the structure of the algorithm. (Wikipedia).

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https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Schrodinger's

From playlist Quantum Mechanics

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From playlist The Sato-Tate conjecture for abelian varieties

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From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)

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From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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From playlist Center for Interdisciplinary Research on AIDS

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From playlist Modern Physics

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From playlist Data Structures & Algorithms [2022 Updated]

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From playlist Mathematical Physics II - Youtube

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From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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Las Vegas algorithm | Hasse's theorem on elliptic curves | Torsion subgroup | Prime number theorem | Chinese remainder theorem | Elliptic curve | Division polynomials | Algebraic closure | Counting points on elliptic curves | Exponentiation by squaring | Frobenius endomorphism | Point at infinity | Schoof–Elkies–Atkin algorithm | Baby-step giant-step | Abelian group | Imaginary hyperelliptic curve | Group (mathematics) | A. O. L. Atkin