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** [[Special number field sieve]]
** [[Trial division]]
* [[Lenstra–Lenstra–Lovász lattice basis reduction algorithm|Lenstra–Lenstra–Lovász algorithm]] (also known as LLL algorithm): find a short, nearly orthogonal [[Lattice (group)|lattice]] [[Basis (linear algebra)|basis]] in polynomial time▼
* [[Modular square root]]: computing square roots modulo a prime number
** [[Berlekamp's root finding algorithm]]
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** [[Toom–Cook multiplication]]
* [[Odlyzko–Schönhage algorithm]]: calculates nontrivial zeroes of the [[Riemann zeta function]]
▲* [[Lenstra–Lenstra–Lovász lattice basis reduction algorithm|Lenstra–Lenstra–Lovász algorithm]] (also known as LLL algorithm): find a short, nearly orthogonal [[Lattice (group)|lattice]] [[Basis (linear algebra)|basis]] in polynomial time
* [[Primality test]]s: determining whether a given number is [[prime number|prime]]
** [[AKS primality test]]
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