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## Filters

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Whitehead Problems for Words in
[chapter]

2014
*
Trends in Mathematics
*

We

doi:10.1007/978-3-319-05488-9_6
fatcat:bfr5akvufzgpfbbzxobagtk5x4
*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. ...##
###
Stream/block ciphers, difference equations and algebraic attacks
[article]

2021
*
arXiv
*
pre-print

We illustrate such

arXiv:2003.14215v2
fatcat:kesf7divqbh4tdm6u7h6e3lqra
*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. ...##
###
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. ...##
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On Index Calculus Algorithms for Subfield Curves
[chapter]

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. ...

##
###
On Index Calculus Algorithms for Subfield Curves
[article]

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. ...

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

2015
*
International Conference on Rewriting Techniques and Applications
*

The desired orthogonal designs can be described

doi:10.4230/lipics.rta.2015.241
dblp:conf/rta/KotsireasKS15
fatcat:trcun34wkvhzdc4vkme7j35ndm
*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). ...##
###
Preface to the Special Issue on Deformation Theory and Applications

2011
*
Journal of Generalized Lie Theory and Applications
*

manifold)

doi:10.4303/jglta/g110110
fatcat:6ls5f2ufkje5xaqoqggrlq7ssq
*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*. ...##
###
The Jacobian Conjecture, Together with Specht and Burnside-Type Problems
[chapter]

2014
*
Springer Proceedings in Mathematics & Statistics
*

We explore an (unpublished) approach to the famous Jacobian Conjecture

doi:10.1007/978-3-319-05681-4_15
fatcat:ptdjadsai5efphpojetuqa5km4
*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 ). ...##
###
Book Review: Double affine Hecke algebras

2008
*
Bulletin of the American Mathematical Society
*

For instance, using the particular solution (2), n-point correlation functions

doi:10.1090/s0273-0979-08-01208-1
fatcat:id3myusqvfbwdglvpsuqq7f2jm
*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) ...##
###
On some application of algebraic quasinuclei to the determinant theory

2013
*
Journal of Applied Mathematics and Computational Mechanics
*

In the paper we apply the modified powers

doi:10.17512/jamcm.2013.3.04
fatcat:rkw3p5k7dbcdtog2o4rgm77gku
*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*. ...##
###
An algebraic attack to the Bluetooth stream cipher E0
[article]

2022
*
arXiv
*
pre-print

In this paper we study the security

arXiv:2201.01262v2
fatcat:dbrzitoh3bb2xkw33cbtqkokni
*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 ). ...##
###
Are Orthogonal Separable Coordinates Really Classified?

2016
*
Symmetry, Integrability and Geometry: Methods and Applications
*

This leads us to propose a new,

doi:10.3842/sigma.2016.041
fatcat:xgxxndnmdbbgtegiuhir3i3xwy
*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 ...##
###
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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