Characteristic set algorithms for equation solving in finite fields

DOI10.1016/j.jsc.2011.12.025zbMath1273.11176OpenAlexW2035167209MaRDI QIDQ413410

Xiao-Shan Gao, Zhen Yu Huang

Publication date: 7 May 2012

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.12.025

zbMATH Keywords

finite fieldstream ciphercharacteristic setBoolean polynomialproper triangular setsingle exponential algorithm

Mathematics Subject Classification ID

Related Items (15)

Quantum algorithm for Boolean equation solving and quantum algebraic attack on cryptosystems ⋮ Characteristic sets verses generalized characteristic sets ⋮ A New Method for Solving Polynomial Systems with Noise over $\mathbb{F}_2$ and Its Applications in Cold Boot Key Recovery ⋮ A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity ⋮ Analyzing Boolean functions via solving parametric polynomial systems ⋮ Chordal graphs in triangular decomposition in top-down style ⋮ A note on determine the greatest common subfamily of two NFSRs by Gröbner basis ⋮ Parametric equation solving and quantifier elimination in finite fields with the characteristic set method ⋮ On the efficiency of solving Boolean polynomial systems with the characteristic set method ⋮ Ritt-Wu characteristic set method for Laurent partial differential polynomial systems ⋮ Speeding up the GVW algorithm via a substituting method ⋮ Elimination theory in differential and difference algebra ⋮ Solving polynomial systems with noise over \(\mathbb{F}_2\): revisited ⋮ Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition ⋮ Analyses and implementations of chordality-preserving top-down algorithms for triangular decomposition

Uses Software

• PolyBoRi
• Trivium
• eSTREAM

Cites Work

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• Lifting techniques for triangular decompositions
• Advances in Cryptology - CRYPTO 2003
• Unmixed-dimensional decomposition of a finitely generated perfect differential ideal

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