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Whitehead Problems for Words in [chapter]

Jordi Delgado
2014 Trends in Mathematics  
We solve the Whitehead problem for automorphisms, monomorphisms and endomorphisms in Z mˆF n after giving an explicit description of each of these families of transformations.  ...  Specifically we will write WhPpO, Fq to mean the Whitehead problem with objects in O and transformations in F, i.e. WhPpO, Fq " ¿Dϕ P F such that o 1 ϕ Þ Ñ o 2 ? po 1 ,o 2 in Oq .  ...  These techniques allow the author to solve the Whitehead problem for this kind of groups, in its variant relative to tuples of conjugacy classes and automorphisms.  ... 
doi:10.1007/978-3-319-05488-9_6 fatcat:bfr5akvufzgpfbbzxobagtk5x4

Stream/block ciphers, difference equations and algebraic attacks [article]

Roberto La Scala, Sharwan K. Tiwari
2021 arXiv   pre-print
We illustrate such algebraic attacks in practice by means of the ciphers Bivium and Keeloq.  ...  By using Difference Algebra, that is, the formal theory of difference equations, we can properly define and study important properties of these ciphers, such as their invertibility and periodicity.  ...  We also thank the anonymous referees for the careful reading of the manuscript.  ... 
arXiv:2003.14215v2 fatcat:kesf7divqbh4tdm6u7h6e3lqra

Page 5202 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Each of the classes under consideration is then characterized by means of forbidden partial sublattices.  ...  For a partial algebra, the notions of validity of weak and of strong equations were defined by P. Burmeister [in Algebras and orders (Montreal, PQ, 1991), \-70, Kluwer Acad.  ... 

On Index Calculus Algorithms for Subfield Curves [chapter]

Steven D. Galbraith, Robert Granger, Simon-Philipp Merz, Christophe Petit
2021 Lecture Notes in Computer Science  
of the field F𝑞𝑛 , reducing the number of polynomial systems that need to be solved.  ...  We show how to choose factor bases to achieve this, while simultaneously accelerating the linear algebra step of the index calculus method for Koblitz curves by a factor 𝑛 2 .  ...  Furthermore, we would like to thank the anonymous reviewers for their helpful comments on the submitted manuscript of this paper. Christophe Petit's work was supported by EPSRC grant EP/S01361X/1.  ... 
doi:10.1007/978-3-030-81652-0_5 fatcat:l5lnsyy2r5dfhn452hkxkktch4

On Index Calculus Algorithms for Subfield Curves [article]

Steven D. Galbraith, Robert Granger, Simon-Philipp Merz, Christophe Petit
2020 IACR Cryptology ePrint Archive  
of the field F𝑞𝑛 , reducing the number of polynomial systems that need to be solved.  ...  We show how to choose factor bases to achieve this, while simultaneously accelerating the linear algebra step of the index calculus method for Koblitz curves by a factor 𝑛 2 .  ...  Furthermore, we would like to thank the anonymous reviewers for their helpful comments on the submitted manuscript of this paper. Christophe Petit's work was supported by EPSRC grant EP/S01361X/1.  ... 
dblp:journals/iacr/GalbraithGMP20 fatcat:pavvf2g4crd5tllf3e65vfliqe

Constructing Orthogonal Designs in Powers of Two: Gröbner Bases Meet Equational Unification

Ilias Kotsireas, Temur Kutsia, Dimitris E. Simos, Marc Herbstritt
2015 International Conference on Rewriting Techniques and Applications  
The desired orthogonal designs can be described by a system of equations with the aid of a Gröbner basis computation.  ...  However, the structural properties of the designs make this problem possible to be tackled in terms of rewriting techniques, by equational unification.  ...  The first author is supported by an NSERC Discovery grant. The second author has been supported by the Austrian Science Fund (FWF) under the project SToUT (P 24087-N18).  ... 
doi:10.4230/lipics.rta.2015.241 dblp:conf/rta/KotsireasKS15 fatcat:trcun34wkvhzdc4vkme7j35ndm

Preface to the Special Issue on Deformation Theory and Applications

Abdenacer Makhlouf, Eugen Paal, Alexander Stolin
2011 Journal of Generalized Lie Theory and Applications  
manifold) by a noncommutative one constructed by means of an algebraic formal deformations of the classical algebra.  ...  It turns out that these explicit quantization formulas help to solve the known Kostant problem about description of the algebra of the locally-finite endomorphisms of the highest weight irreducible modules  ...  , by means of homogenous pre-systems.  ... 
doi:10.4303/jglta/g110110 fatcat:6ls5f2ufkje5xaqoqggrlq7ssq

The Jacobian Conjecture, Together with Specht and Burnside-Type Problems [chapter]

Alexei Belov, Leonid Bokut, Louis Rowen, Jie-Tai Yu
2014 Springer Proceedings in Mathematics & Statistics  
We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (19512001)  ...  This approach also indicates some very close connections between mathematical physics, universal algebra and au- tomorphisms of polynomial algebras  ...  Given an algebra A, we define Solv 1 := Solv 1 (A) = {Nilpotent ideals of A}, and inductively, given Solv k , define Solv k+1 by Solv k+1 / Solv k = Solv 1 (A/ Solv k ).  ... 
doi:10.1007/978-3-319-05681-4_15 fatcat:ptdjadsai5efphpojetuqa5km4

Book Review: Double affine Hecke algebras

Eric M. Opdam, Jasper V. Stokman
2008 Bulletin of the American Mathematical Society  
For instance, using the particular solution (2), n-point correlation functions of the associated XXZ spin chain solve such a system of q-difference equations; see [14] .  ...  With given endomorphisms A j (t) of a finite dimensional vector space U , depending meromorphically on t ∈ T , we now associate a system of linear q-difference equations on T by (3) f (τ j t) = A j (t)  ... 
doi:10.1090/s0273-0979-08-01208-1 fatcat:id3myusqvfbwdglvpsuqq7f2jm

On some application of algebraic quasinuclei to the determinant theory

Grazyna Ciecierska
2013 Journal of Applied Mathematics and Computational Mechanics  
In the paper we apply the modified powers of algebraic quasinuclei to construction of determinant systems for quasinuclear perturbations of Fredholm operators.  ...  Given two pairs ( ) Χ Ξ , , ( ) Υ Ω , of conjugate linear spaces, an algebraic quasinucleus ( )  ...  Given [1] [2] [3] for the solution are generalizations of the famous Cramer's rule for solving finite systems of linear equations.  ... 
doi:10.17512/jamcm.2013.3.04 fatcat:rkw3p5k7dbcdtog2o4rgm77gku

An algebraic attack to the Bluetooth stream cipher E0 [article]

Roberto La Scala, Sergio Polese, Sharwan K. Tiwari, Andrea Visconti
2022 arXiv   pre-print
In this paper we study the security of the Bluetooth stream cipher E0 from the viewpoint it is a "difference stream cipher", that is, it is defined by a system of explicit difference equations over the  ...  This approach highlights some issues of the Bluetooth encryption such as the invertibility of its state transition map, a special set of 14 bits of its 132-bit state which when guessed implies linear equations  ...  Indeed, instead of solving equations in the polynomial algebra R B (0 ≤ T ≤ B) we can solve equivalent equations in R B (B = B − T ).  ... 
arXiv:2201.01262v2 fatcat:dbrzitoh3bb2xkw33cbtqkokni

Are Orthogonal Separable Coordinates Really Classified?

Konrad Schöbel
2016 Symmetry, Integrability and Geometry: Methods and Applications  
This leads us to propose a new, algebraic geometric approach to the classification of orthogonal separable coordinates by studying the structure of this variety.  ...  We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group  ...  Acknowledgements This notice is based on a talk held at the workshop "Analytical Mechanics and Differential Geometry" at the Università di Torino on 12th and 13th March 2015 on the occasion of Sergio Benenti's  ... 
doi:10.3842/sigma.2016.041 fatcat:xgxxndnmdbbgtegiuhir3i3xwy

Page 3282 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
An endomorphism of M of order k is a map {:M*-M; the map determines an endomorphism /: M‘ > M* by S( X57 + Xu) = (%25°° +X y, f(%1,°**,X,)).  ...  solved.  ... 

Page 2950 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
Michael (D-HGN; Hagen) Systems of algebraic equations solved by means of endomorphisms.  ...  Summary: “Recently, several authors studied methods based on endomorphisms for localizing and computing the common zeros of systems of polynomial equations fj(x),---,Xn)=0, i=1,---,s, in case the ideal  ... 

Page 66 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
Solving the word problem for congruences motivates term rewriting systems.  ...  Algebraic characterizations of equational and implicational classes of algebras and their theories (Birkhoff-type theorems) are the main topic of Chapter 3.  ... 
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