English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Algebraic cryptanalysis usually requires to recover the secret key by solvingpolynomial equations. Faugere's F4 is a well-known Grobner bases algorithm tosolve this problem. However, a serious drawback exists in the Grobner basesbased algebraic attacks, namely, any information won't be got if we couldn'twork out the Grobner bases of the polynomial equations system. In this paper,we in-depth research the F4 algorithm over GF(2). By using S-polynomials toreplace critical pairs and computing the normal form of the productions withrespect to the field equations in certain steps, many "redundant" reductors areavoided during the computation process of the F4 algorithm. By slightlymodifying the logic of F4 algorithm, we solve the univariate polynomialsappeared in the algorithm and then back-substitute the values of the solvedvariables at each iteration of the algorithm. We call our improvementsMiddle-Solving F4. The heuristic strategy of Middle-Solving overcomes thedrawback of algebraic attacks and well suits algebraic attacks. It has neverbeen applied to the Grobner bases algorithm before. Experiments to some HiddenField Equation instances and some classical benchmarks (Cyclic 6, Gonnet83)show that Middle-Solving F4 is faster and uses less memory than Faugere's F4.

Middle-Solving F4 to Compute Grobner bases for Cryptanalysis over GF(2)