##  [Number Field Sieve](/number-field-sieve) 

  ##  [Number Field Sieve](https://puremath.quantumdictionary.io/number-field-sieve-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The asymptotically fastest known classical integer factorization algorithm for very large integers, which uses algebraic number fields, polynomial selection, sieving of norms and large-scale linear algebra to produce relations that yield congruences of squares modulo n.