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. This article explains Schoof's approach, laying emphasis on the mathematical ideas underlying the structure of the algorithm.
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- software
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- enSchoof'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. This article explains Schoof's approach, laying emphasis on the mathematical ideas underlying the structure of the algorithm.
- Has abstract
- enSchoof'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.
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- Algorithm
- Is primary topic of
- Schoof's algorithm
- Label
- enSchoof's algorithm
- Link from a Wikipage to an external page
- www.mat.uniroma2.it/~schoof/ctg.pdf
- www.mat.uniroma2.it/~schoof/ctpts.pdf
- web.archive.org/web/20121114015633/http:/certivox.com/solutions/miracl-crypto-sdk/
- lecturer.ukdw.ac.id/vmueller/publications.php
- www.math.umn.edu/~musiker/schoof.pdf
- Link from a Wikipage to another Wikipage
- A. O. L. Atkin
- Abelian group
- AGPLv3
- Algebraic closure
- Baby-step giant-step
- C++
- Category:Asymmetric-key algorithms
- Category:Elliptic curve cryptography
- Category:Elliptic curves
- Category:Finite fields
- Category:Group theory
- Category:Number theory
- Chinese remainder theorem
- Chinese Remainder Theorem
- Counting points on elliptic curves
- Discrete logarithm problem
- Division polynomial
- Division polynomials
- Division Polynomials
- Elliptic curve
- Elliptic curve cryptography
- Elliptic curves
- Exponentiation by squaring
- Finite fields
- Frobenius endomorphism
- Generalized Riemann Hypothesis
- Group (mathematics)
- Group morphism
- Hasse's theorem on elliptic curves
- Imaginary hyperelliptic curve
- Las Vegas algorithm
- Modular forms
- Noam Elkies
- Point at infinity
- Prime number theorem
- René Schoof
- Schoof–Elkies–Atkin algorithm
- Torsion subgroup
- SameAs
- 2e26s
- Algorithme de Schoof
- Algorytm Schoofa
- m.09ntdg
- Q2835817
- Schoof's algorithm
- Алгоритм Шуфа
- Алгоритм Шуфа
- Subject
- Category:Asymmetric-key algorithms
- Category:Elliptic curve cryptography
- Category:Elliptic curves
- Category:Finite fields
- Category:Group theory
- Category:Number theory
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- Schoof's algorithm?oldid=931919852&ns=0
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- Wikipage page ID
- 3596006
- Wikipage revision ID
- 931919852
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