Results 51 to 60 of about 3,441,413 (166)
Solving Degree Bounds for Iterated Polynomial Systems
IACR Transactions on Symmetric CryptologyFor Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is ...
Matthias Johann Steiner
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On the first fall degree of summation polynomials
Journal of Mathematical Cryptology, 2019 We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
Kousidis Stavros, Wiemers Andreas
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Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT We study asymptotic dynamics of Kuramoto oscillators with inertia and frustration using the classical perturbation theory of ordinary differential equation systems. Frustration also known as the phase‐lag poses challenges for the mathematical analysis of asymptotic dynamics due to the breakdown of total phase conservation and the gradient ...
Hangjun Cho +2 more
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A Zero-Dimensional Gröbner Basis for AES-128
, 2006 We demonstrate an efficient method for computing a Gröbner basis of a zero-dimensional ideal describing the key-recovery problem from a single plaintext/ciphertext pair for the full AES-128.
Johannes Buchmann +6 more
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An Algebraic Approach to Analyze an MSEIR Epidemic Model
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.This study introduces a fully algorithmic framework for analyzing the dynamics of an MSEIR (Maternal, Susceptible, Exposed, Infectious, Recovered) epidemic model. Unlike traditional approaches that rely on heuristic, model‐specific Lyapunov functions for global stability or manual algebraic manipulations for finding equilibria, we employ computational ...
Adamou Otto +3 more
wiley +1 more source
A fast algorithm for Gröbner basis conversion and its applications [PDF]
, 2000 The Gröbner walk method converts a Gröbner basis by partitioning the computation of the basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of equations.
Quoc-nam Tran, Tran, Quoc-Nam
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Comparing complexities of problems of determining of Grebner’s basis of ideal and solving this ideal
Труды Института системного программирования РАН, 2018 A new method of investigation of ideals in the rings of polynomials was proposed by B. Buchberger in 1965. He proposed to use special basis in such rings named “Gröbner Basis” in the honor of his teacher.
A. V. Shokurov
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Model category structures on truncated multicomplexes for complex geometry
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4163-4177, December 2025.Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to N$N$‐multicomplexes. We present a family of model category structures on the category of N$N$‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism ...
Joana Cirici +2 more
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Polarization and Gorenstein liaison
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen–Macaulay subscheme of Pn$\mathbb {P}^n$ can be G‐linked to a complete intersection. Migliore and Nagel showed that if such a scheme is generically Gorenstein (e.g., reduced), then, after re‐embedding so that it is viewed as a subscheme of Pn ...
Sara Faridi +3 more
wiley +1 more source
Identifikasi Basis Gröbner Dalam Ideal Ring Polinomial [PDF]
, 2015 Dalam suatu ring atau lapangan, dapat didefinisikan suatu polinomial yang koefisien-koefisiennya merupakan elemen dari ring atau lapangan tersebut. [] dan [] merupakan suatu ring yang disebut ring polinomial. Misalkan =〈1,2,…〉⊆[], dengan ≠0 untuk setiap =
Romsery, M. M. (Melky) +2 more
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