Tag
smoothness
5 resources tagged “smoothness” across the knowledge library.
5 items
Article7 Aug 2026Factor Base Selection and SmoothnessChoosing the factor base for class group computation, the smoothness trade-off, and how base size interacts with the linear algebra.2 min readRead MoreArticle7 Aug 2026Number Field Sieve: Polynomial Selection and StructureHow the number field sieve achieves its complexity, why polynomial selection matters so much, and the role of number field arithmetic.3 min readRead MoreArticle7 Aug 2026Smoothness and Sub-exponential ComplexitySmooth numbers, the Dickman function, and how balancing smoothness probability against factor base size produces sub-exponential running times.2 min readRead MoreArticle7 Aug 2026Sub-exponential Class Group Computation for Quadratic FieldsSub-exponential class group and regulator computation for quadratic fields by relation collection over a factor base.2 min readRead MoreArticle7 Aug 2026The Pollard p-1 MethodPollard's p-1 method, its dependence on the smoothness of the group order, and why that dependence is its fatal limitation.2 min readRead More