Engineering↗
Factor Base Selection and Smoothness
Choosing the factor base for class group computation, the smoothness trade-off, and how base size interacts with the linear algebra.
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Factor Base
Every page in the KEVOS library tagged Factor Base. 7 pages.
Engineering↗
Minkowski and Bach Bounds
Bounds on the norm of ideals needed to generate the class group, and why the conditional bound is what makes computation practical.
Engineering↗
Quadratic Sieve Factor Base Selection
Choosing the factor base for the quadratic sieve, the quadratic residue criterion, and the multiplier.
Engineering↗
Smoothness and Sub-exponential Complexity
Smooth numbers, the Dickman function, and how balancing smoothness probability against factor base size produces sub-exponential running times.
Engineering↗
The Continued Fraction Factorisation Method
CFRAC: generating small quadratic residues from the continued fraction expansion, and the congruence-of-squares framework it established.
Engineering↗
Class Group and Unit Computation in General Number Fields
The general sub-exponential algorithm for class groups and units: factor base selection, ideal reduction, relation collection, the relation matrix and its kernel, and verificati…
Engineering↗
The Continued Fraction Factoring Method
CFRAC: 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 t…
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