Modifying Faugère's F5 algorithm to ensure termination

A Tropical F5 Algorithm

Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gröbner bases taking into account the valuation of K. While generalizing the classical theory of Gröbner bases, it is not clear how modern algorithms for computing Gröbner bases can be adapted to the tropical case. Among them, one of the most efficient is the celebrated F5 Algorithm of Faugère....

Faugere's F5 Algorithm Revisited

Faugère's F5 Algorithm

This report gives pseudocode for an implementation the F5 algorithm, noting errors found both in Faugère's seminal 2002 paper and Stegers' 2006 undergraduate thesis. It also outlines a relatively easy optimization that, in our experience, produces a substiantial improvement to the algorithm's e ciency.

Modifying Boolean Functions to Ensure Maximum Algebraic Immunity

The algebraic immunity of cryptographic Boolean functions is studied in this paper. Proper modifications of functions achieving maximum algebraic immunity are proved, in order to yield new functions of also maximum algebraic immunity. It is shown that the derived results apply to known classes of functions. Moreover, two new efficient algorithms to produce functions of guaranteed maximum algebr...

BTA Algorithms to Ensure Termination of Off-Line Partial Evaluation

A partial evaluator, given a program and a known “static” part of its input data, outputs a residual program in which computations depending only on the static data have been precomputed [3]. The ideal is a “black box” which discovers and performs nontrivial static computations whenever possible, and never fails to terminate. Practical partial evaluators fall short of this goal: they sometimes ...