Tag
Factor Base
7 resources tagged “Factor Base” across the knowledge library.
7 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 2026Minkowski and Bach BoundsBounds on the norm of ideals needed to generate the class group, and why the conditional bound is what makes computation practical.2 min readRead MoreArticle7 Aug 2026Quadratic Sieve Factor Base SelectionChoosing the factor base for the quadratic sieve, the quadratic residue criterion, and the multiplier.2 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 2026The Continued Fraction Factorisation MethodCFRAC: generating small quadratic residues from the continued fraction expansion, and the congruence-of-squares framework it established.2 min readRead MoreGuide6 Aug 2026Class Group and Unit Computation in General Number FieldsThe general sub-exponential algorithm for class groups and units: factor base selection, ideal reduction, relation collection, the relation matrix and its kernel, and verification against the analytic class number formula.5 min readRead MoreGuide6 Aug 2026The Continued Fraction Factoring MethodCFRAC: generating small residues from the continued fraction expansion of the square root, smoothness testing, the linear algebra step, and its historical role as precursor to the sieves.4 min readRead More