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On the relation between the MXL family of algorithms and Gröbner basis algorithms

Martin R. Albrecht, Carlos Cid, Jean-Charles Faugère, Ludovic Perret
2012 Journal of symbolic computation  
Using previous results that had shown the relation between the original XL algorithm and F 4 , we conclude that the MXL family of algorithms can be fundamentally reduced to redundant variants of F 4 .  ...  In this work we investigate a recently-proposed strategy, the so-called "Mutant strategy", on which a new family of algorithms is based (MXL, MXL 2 and MXL 3 ).  ...  Based on previous results, which showed the relation between the XL algorithm and F 4 [3] , we conclude that MXL can too be described as a redundant variant of F 4 .  ... 
doi:10.1016/j.jsc.2012.01.002 fatcat:xbskfczfjfdqfkjhwb6cxusaeu

SoK: Gröbner Basis Algorithms for Arithmetization Oriented Ciphers [article]

Jan Ferdinand Sauer, Alan Szepieniec
2021 IACR Cryptology ePrint Archive  
In this paper, we survey the most important algorithms and present them in an intuitive way.  ...  Unfortunately, the literature on Gröbner bases tends to be either purely mathematical, or focused on small fields.  ...  Acknowledgments This work was sponsored by the Ethereum Foundation.  ... 
dblp:journals/iacr/SauerS21 fatcat:k2ymx753lbekjadgs2gvccdtb4

On the complexity of solving generic overdetermined bilinear systems

John B. Baena, Daniel Cabarcas, Javier Verbel
2021 Advances in Mathematics of Communications  
Also, we propose three variations of Gröbner basis algorithms, that only involve multiplication by monomials in the <inline-formula><tex-math id="M8">\begin{document}$ \textbf{y} $\end{document}</tex-math  ...  id="M10">\begin{document}$ \textbf{y} $\end{document}</tex-math></inline-formula>-MXL, based on the mutant XL algorithm, and <inline-formula><tex-math id="M11">\begin{document}$ \textbf{y} $\end{document  ...  The degree of regularity is an important value for measuring the complexity of Gröbner basis algorithms, but it is not the only one.  ... 
doi:10.3934/amc.2021047 fatcat:m5mx5hoscnd4pdsvejuquult6e

On the Complexity of Solving Generic Over-determined Bilinear Systems [article]

John B. Baena and Daniel Cabarcas and Javier Verbel
2020 arXiv   pre-print
Following this observation, we propose three variations of Gröbner basis algorithms, that only involve multiplication by monomials in they-variables, namely, y-XL, based on the XL algorithm, y-MLX, based  ...  on the mutant XL algorithm, and y-HXL, basedon a hybrid approach.  ...  The degree of regularity is an important value for measuring the complexity of Gröbner basis algorithms, but it is not the only one.  ... 
arXiv:2006.09442v1 fatcat:n66sjxqoqfh5blycu7lz6z64qy

Algebraic Cryptanalysis of Deterministic Symmetric Encryption

Petr Sušil
2015
Using these mutants in Gröbner basis computations and SAT solvers reduces the computational cost to solve the system.  ...  The contribution of this thesis is twofold. Firstly, we evaluate the performance of existing algebraic techniques with respect to number of plaintext/ciphertext pairs and their selection.  ...  The XL algorithm and XSL method belong to a wider family of algebraic tools which we will refer to as Gröbner basis techniques.  ... 
doi:10.5075/epfl-thesis-6651 fatcat:hxoqjuppdbbjhnu7yr4sqclkra

Genomic landscape of 261 childhood cancer patient-derived xenograft models [article]

Jo Lynne Rokita, Komal S. Rathi, Maria F. Cardenas, Kristen A. Upton, Joy Jayaseelan, Katherine L. Cross, Jacob Pfeil, Laura E. Ritenour, Apexa Modi, Alvin Farrel, Gregory P. Way, Nathan M. Kendsersky (+55 others)
2019 bioRxiv   pre-print
Accelerating cures for children with cancer remains an immediate challenge due to extensive oncogenic heterogeneity between and within histologies, distinct molecular mechanisms evolving between diagnosis  ...  Here, we genomically characterize 261 PDX models from 29 unique pediatric cancer malignancies and demonstrate faithful recapitulation of histologies, subtypes, and refine our understanding of relapsed  ...  Acknowledgments The authors would like to thank the Alex's Lemonade Stand Foundation for providing the funding for this project. This work was also supported by NIH grants U01 CA199287  ... 
doi:10.1101/566455 fatcat:qklmv6dhyjg7jnvbzhsb23f2e4