Last update: Fri Jul 22 08:02:48 MDT 2022
Volume 1, Number 1, 2009Dima Grigoriev and Edward A. Hirsch and Konstantin Pervyshev A complete public-key cryptosystem . . . 1--12 Alex D. Myasnikov Generic case complexity and one-way functions . . . . . . . . . . . . . . . 13--31 Vladimir Shpilrain and Gabriel Zapata Using decision problems in public key cryptography . . . . . . . . . . . . . . 33--49 Benjamin Fine and Alexei Myasnikov and Gerhard Rosenberger Generic subgroups of group amalgams . . 51--61 Alex D. Myasnikov and Alexander Ushakov Cryptanalysis of the Anshel--Anshel--Goldfeld--Lemieux key agreement protocol . . . . . . . . . . . 63--75 Llu\'ìs Bacardit and Warren Dicks Actions of the braid group, and new algebraic proofs of results of Dehornoy and Larue . . . . . . . . . . . . . . . 77--129 Fabienne Chouraqui Rewriting systems and embedding of monoids in groups . . . . . . . . . . . 131--140
Gerhard Rosenberger A short biography of Ben Fine . . . . . 141--142 Daniella Bak Shnaps The word and conjugacy problem for shuffle groups . . . . . . . . . . . . . 143--164 Anthony E. Clement Torsion-free abelian factor groups of the Baumslag--Solitar groups and subgroups of the additive group of the rational numbers . . . . . . . . . . . . 165--168 Margaret H. Dean Metabelian product of a free nilpotent group with a free abelian group . . . . 169--180 Anthony M. Gaglione and Seymour Lipschutz and Dennis Spellman Almost locally free groups and a theorem of Magnus: some questions . . . . . . . 181--198 Dima Grigoriev and Vladimir Shpilrain Authentication from matrix conjugation 199--205 Volkmar große Rebel and Miriam Hahn and Gerhard Rosenberger The Tits alternative for Tsaranov's generalized tetrahedron groups . . . . . 207--216 Delaram Kahrobaei and Michael Anshel Decision and search in non-abelian Cramer--Shoup public key cryptosystem 217--225 Arkadius Kalka and Eran Liberman and Mina Teicher A note on the shifted conjugacy problem in braid groups . . . . . . . . . . . . 227--230 Martin Kreuzer Algebraic attacks galore! . . . . . . . 231--259 Stephen R. Lakin and Richard M. Thomas Space complexity and word problems of groups . . . . . . . . . . . . . . . . . 261--273 Jonathan Longrigg and Alexander Ushakov A practical attack on a certain braid group based shifted conjugacy authentication protocol . . . . . . . . 275--286 C. Maclachlan Existence and non-existence of torsion in maximal arithmetic Fuchsian groups 287--295 Stephen Majewicz and Marcos Zyman Power-commutative nilpotent $R$-powered groups . . . . . . . . . . . . . . . . . 297--309 D. Osin On the universal theory of torsion and lacunary hyperbolic groups . . . . . . . 311--319
Uri Weiss On Shephard groups with large triangles 1--34 Marston Conder An update on Hurwitz groups . . . . . . 35--49 Martin Kassabov Presentations of matrix rings . . . . . 51--57 Gideon Amir and Ori Gurel-Gurevich The diameter of a random Cayley graph of $ \mathbb {Z}_q $ . . . . . . . . . . . 59--65 Gilbert Baumslag and Yegor Bryukhov and Benjamin Fine and Douglas Troeger Challenge response password security using combinatorial group theory . . . . 67--81 Ayan Mahalanobis The discrete logarithm problem in the group of non-singular circulant matrices 83--89 A. Shevlyakov Algebraic geometry over natural numbers. The classification of coordinate monoids 91--111
Celine Carstensen and Benjamin Fine and Gerhard Rosenberger On asymptotic densities and generic properties in finitely generated groups 113--121 Tetsuya Ito On finite Thurston-type orderings of braid groups . . . . . . . . . . . . . . 123--155 Arkadius Kalka and Eran Liberman and Mina Teicher Subgroup conjugacy problem for Garside subgroups of Garside groups . . . . . . 157--174 Chi Sing Chum and Xiaowen Zhang The latin squares and the secret sharing schemes . . . . . . . . . . . . . . . . 175--202 Matthias Neumann-Brosig and Gerhard Rosenberger A note on the homology of hyperbolic groups . . . . . . . . . . . . . . . . . 203--212 Bernhard Krön Cutting up graphs revisited --- a short proof of Stallings' structure theorem 213--221 Murray Elder and Andrew Rechnitzer Some geodesic problems in groups . . . . 223--229 Vladimir Shpilrain Search and witness problems in group theory . . . . . . . . . . . . . . . . . 231--246 Philipp Jovanovic and Martin Kreuzer Algebraic attacks using SAT-solvers . . 247--259
Lisa Carbone and Leigh Cobbs and Gabriel Rosenberg Tree lattice subgroups . . . . . . . . . 1--23 Russell Miller An introduction to computable model theory on groups and fields . . . . . . 25--45 Murray R. Bremner How to compute the Wedderburn decomposition of a finite-dimensional associative algebra . . . . . . . . . . 47--66 Natalia Mosina and Alexander Ushakov Strong law of large numbers on graphs and groups . . . . . . . . . . . . . . . 67--103 Svetla Vassileva Polynomial time conjugacy in wreath products and free solvable groups . . . 105--120 Alexei Myasnikov and Alexander Ushakov Random van Kampen diagrams and algorithmic problems in groups . . . . . 121--185
Llu\'ìs Bacardit and Warren Dicks The Zieschang--McCool method for generating algebraic mapping-class groups . . . . . . . . . . . . . . . . . 187--220 Jennifer Seberry and Vinhbuu To and Dongvu Tonien A new generic digital signature algorithm . . . . . . . . . . . . . . . 221--237 Bronlyn Wassink Subgroups of R. Thompson's group $F$ that are isomorphic to $F$ . . . . . . . 239--256 Robert H. Gilman and Alexei Myasnikov and Vitali\u\i Roman'kov Random equations in free groups . . . . 257--284 Kenneth J. Falconer and Benjamin Fine and Delaram Kahrobaei Growth rate of an endomorphism of a group . . . . . . . . . . . . . . . . . 285--300 Yago Antol\'ìn On Cayley graphs of virtually free groups . . . . . . . . . . . . . . . . . 301--327 Marianna Bonanome and Stephen Majewicz Quantum algorithms for fixed points and invariant subgroups . . . . . . . . . . 329--348 Benjamin Fine and Gerhard Rosenberger A note on faithful representations of limit groups . . . . . . . . . . . . . . 349--355
Kashi Neupane Two-party key establishment: from passive to active security without introducing new assumptions . . . . . . 1--17 Dima Grigoriev and Sergey Nikolenko Continuous hard-to-invert functions and biometric authentication . . . . . . . . 19--32 James B. Wilson Existence, algorithms, and asymptotics of direct product decompositions, I . . 33--72 Mark L. Lewis and James B. Wilson Isomorphism in expanding families of indistinguishable groups . . . . . . . . 73--110 Ivo Hedtke and Sandeep Murthy Search and test algorithms for triple product property triples . . . . . . . . 111--133 Matthew J. Craven and Henri C. Jimbo Evolutionary algorithm solution of the multiple conjugacy search problem in groups, and its applications to cryptography . . . . . . . . . . . . . . 135--165 Mohammad Eftekhari A Diffie--Hellman key exchange protocol using matrices over noncommutative rings 167--176 Dima Grigoriev and Vladimir Shpilrain No-leak authentication by the Sherlock Holmes method . . . . . . . . . . . . . 177--189
Vitali\u\i Roman'kov Equations over groups . . . . . . . . . 191--239 Markus Lohrey Algorithms on SLP-compressed strings: a survey . . . . . . . . . . . . . . . . . 241--299 Murray Elder and Andrew Rechnitzer and Thomas Wong On the cogrowth of Thompson's group $F$ 301--320 Volker Diekert and Andrew Duncan and Alexei G. Myasnikov Cyclic rewriting and conjugacy problems 321--355 Fedaa Ibrahim Cylinders, multi-cylinders and the induced action of $ {\rm Aut}(F_n) $ . . 357--375 Delaram Kahrobaei and Charalambos Koupparis Non-commutative digital signatures . . . 377--384
Derek F. Holt and Sarah Rees Shortlex automaticity and geodesic regularity in Artin groups . . . . . . . 1--23 Alexander Rybalov Generic complexity of the Diophantine problem . . . . . . . . . . . . . . . . 25--30 Dima Grigoriev and Vladimir Shpilrain Secrecy without one-way functions . . . 31--52 Mikhail Anokhin Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption . . . . . . . . . . . . . . . 53--74 Thomas Connor and Dimitri Leemans A new algorithm to find apartments in coset geometries . . . . . . . . . . . . 75--89 Benjamin Fine and Gerhard Rosenberger Faithful representations of limit groups II . . . . . . . . . . . . . . . . . . . 91--96 Delaram Kahrobaei and Charalambos Koupparis and Vladimir Shpilrain Public key exchange using matrices over group rings . . . . . . . . . . . . . . 97--115
Neal Koblitz and Alfred Menezes Another look at non-uniformity . . . . . 117--139 Daan Krammer An asymmetric generalisation of Artin monoids . . . . . . . . . . . . . . . . 141--167 Arkadius Kalka and Mina Teicher Non-associative key establishment for left distributive systems . . . . . . . 169--191 Maggie Habeeb and Delaram Kahrobaei On the dimension of matrix representations of finitely generated torsion free nilpotent groups . . . . . 193--209 Amnon Rosenmann On the intersection of subgroups in free groups: echelon subgroups are inert . . 211--221 Benjamin Fine and Anja I. S. Moldenhauer and Gerhard Rosenberger A secret sharing scheme based on the closest vector theorem and a modification to a private key cryptosystem . . . . . . . . . . . . . . 223--238
Maurice Chiodo On torsion in finitely presented groups 1--8 Tara Brough Groups with poly-context-free word problem . . . . . . . . . . . . . . . . 9--29 Alexey D. Myasnikov and Alexander Ushakov Quantum algorithm for discrete logarithm problem for matrices over finite group rings . . . . . . . . . . . . . . . . . 31--36 Liljana Babinkostova and Kevin W. Bombardier and Matthew C. Cole and Thomas A. Morrell and Cory B. Scott Algebraic properties of generalized Rijndael-like ciphers . . . . . . . . . 37--54 Olga Kharlampovich and Alexei Myasnikov and Denis Serbin Infinite words and universal free actions . . . . . . . . . . . . . . . . 55--69
Charles F. Miller, III Friends and relatives of $ \rm B S(1, 2) $ . . . . . . . . . . . . . . . . . . . 73--80 Benjamin Fine and Anthony Gaglione and Gerhard Rosenberger and Dennis Spellman Reflections on some aspects of infinite groups . . . . . . . . . . . . . . . . . 81--91 Robert H. Gilman Generalized small cancellation presentations for automatic groups . . . 93--101 Alexei Myasnikov and Vitalii Roman'kov Diophantine cryptography in free metabelian groups: theoretical base . . 103--120 Tim R. Riley and Andrew W. Sale Palindromic width of wreath products, metabelian groups, and max-$n$ solvable groups . . . . . . . . . . . . . . . . . 121--132 Enric Ventura Group-theoretic orbit decidability . . . 133--148 Vladimir Shpilrain Decoy-based information security . . . . 149--155
Andreas Distler and Bettina Eick Group extensions with special properties 1--10 Benjamin Atchison and Edward C. Turner Symmetries of finite graphs and homology 11--30 Sarah Hart and Ivo Hedtke and Matthias Müller-Hannemann and Sandeep Murthy A fast search algorithm for $ \langle m, m, m \rangle $ triple product property triples and an application for $ 5 \times 5 $ matrix multiplication . . . . 31--46 Manik Lal Das Key-escrow free multi-signature scheme using bilinear pairings . . . . . . . . 47--57 Anthony M. Gaglione and Seymour Lipschutz and Dennis Spellman An application of elementary real analysis to a metabelian group admitting integral polynomial exponents . . . . . 59--68 Jordan Sahattchieve On convex hulls and the quasiconvex subgroups of $ F_m \times \mathbb {Z}^n $ . . . . . . . . . . . . . . . . . . . 69--80 Alexei Myasnikov and Vitali\u\i Roman'kov A linear decomposition attack . . . . . 81--94
Llu\'ìs Bacardit A combinatorial algorithm to compute presentations of mapping class groups of orientable surfaces with one boundary component . . . . . . . . . . . . . . . 95--115 Evgeni Begelfor and Stephen D. Miller and Ramarathnam Venkatesan Non-abelian analogs of lattice rounding 117--133 Jennifer Taback and Sharif Younes Tree-based language complexity of Thompson's group $F$ . . . . . . . . . . 135--152 Vitalii A. Roman'kov New probabilistic public-key encryption based on the RSA cryptosystem . . . . . 153--156 Stepan Yu. Orevkov Algorithmic recognition of quasipositive $4$-braids of algebraic length three . . 157--173 Chris Monico and Mara D. Neusel Cryptanalysis of a system using matrices over group rings . . . . . . . . . . . . 175--182 Artyom S. Ivachev On transitive differentiable modulo $ p^n $ functions . . . . . . . . . . . . 183--190 Alexander Rybalov On the generic complexity of the searching graph isomorphism problem . . 191--193 Jean-Marie Chauvet and Eric Mahé Key agreement under tropical parallels 195--198
Iris Anshel and Derek Atkins and Dorian Goldfeld and Paul E. Gunnells A class of hash functions based on the algebraic eraser\TM . . . . . . . . . . 1--7 Gennady A. Noskov and Alexander N. Rybalov Generic case complexity of the graph isomorphism problem . . . . . . . . . . 9--20 Murray Elder and Jennifer Taback Thompson's group $F$ is $1$-counter graph automatic . . . . . . . . . . . . 21--33 Bettina Eick The automorphism group of a finitely generated virtually abelian group . . . 35--45 Omar Akchiche and Omar Khadir Factoring multi-power RSA moduli with primes sharing least or most significant bits . . . . . . . . . . . . . . . . . . 47--54 Emmanuel Fouotsa and Abdoul Aziz Ciss Faster Ate pairing computation on Selmer's model of elliptic curves . . . 55--67 Kenneth R. Blaney and Andrey Nikolaev A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups . . . . . . . . . . . 69--74 Sylvain Duquesne and Loubna Ghammam Memory-saving computation of the pairing final exponentiation on BN curves . . . 75--90
Christian Schridde Computing discrete logarithms using $ \mathscr {O}((\log q)^2) $ operations from $ \{ +, -, \times, \div, & \} $ . . 91--107 Matthew J. Craven and Daniel Robertz A parallel evolutionary approach to solving systems of equations in polycyclic groups . . . . . . . . . . . 109--125 Alexander Ushakov Authenticated commutator key agreement protocol . . . . . . . . . . . . . . . . 127--133 Luise-Charlotte Kappe and Daniela Nikolova-Popova and Eric Swartz On the covering number of small symmetric groups and some sporadic simple groups . . . . . . . . . . . . . 135--154 Vladimir Shpilrain and Bianca Sosnovski Compositions of linear functions and applications to hashing . . . . . . . . 155--161 Kristen Pueschel Hydra group doubles are not residually finite . . . . . . . . . . . . . . . . . 163--170 Jonathan Gryak and Delaram Kahrobaei The status of polycyclic group-based cryptography: a survey and open problems 171--186 Artem N. Shevlyakov On irreducible algebraic sets over linearly ordered semilattices . . . . . 187--195 Vitali\uì Roman'kov A nonlinear decomposition attack . . . . 197--207
Anonymous Frontmatter . . . . . . . . . . . . . . i Mikhail Anokhin Pseudo-free families of finite computational elementary abelian $p$-groups . . . . . . . . . . . . . . . 1 Jean-Marie Chauvet and Eric Mahé Cryptography from the tropical Hessian pencil . . . . . . . . . . . . . . . . . 19 Franti\vsek Marko and Alexandr N. Zubkov and Martin Jurá\vs Public-key cryptosystem based on invariants of diagonalizable groups . . 31 Bettina Eick and Ann-Kristin Engel The isomorphism problem for torsion free nilpotent groups of Hirsch length at most $5$ . . . . . . . . . . . . . . . . 55 Alexei Miasnikov and Svetla Vassileva Log-space conjugacy problem in the Grigorchuk group . . . . . . . . . . . . 77 Alexei Mishchenko and Alexander Treier Knapsack problem for nilpotent groups 87
Anonymous Front matter . . . . . . . . . . . . . . i--i Albert Garreta and Alexei Miasnikov and Denis Ovchinnikov Random nilpotent groups, polycyclic presentations, and Diophantine problems 99 Stefan Friedl An elementary proof of the group law for elliptic curves . . . . . . . . . . . . 117 Vitali\uì Roman'kov Cryptanalysis of a combinatorial public key cryptosystem . . . . . . . . . . . . 125 Jack O. Button Free by cyclic groups and linear groups with restricted unipotent elements . . . 137 Alexander Rybalov Generic hardness of the Boolean satisfiability problem . . . . . . . . . 151 Evgeny I. Timoshenko A remark on spherical equations in free metabelian groups . . . . . . . . . . . 155 Mohammad Shahryari and Artem Shevlyakov Direct products, varieties, and compactness conditions . . . . . . . . . 159
Anonymous Frontmatter . . . . . . . . . . . . . . i Matvei Kotov and Dmitry Panteleev and Alexander Ushakov Analysis of secret sharing schemes based on Nielsen transformations . . . . . . . 1 Meng-Che Ho The word problem of Z n is a multiple context-free language . . . . . . . . . 9 Alexey Gribov and Delaram Kahrobaei and Vladimir Shpilrain Practical private-key fully homomorphic encryption in rings . . . . . . . . . . 17 Mohammad Hossein Ghaffari and Zohreh Mostaghim More secure version of a Cayley hash function . . . . . . . . . . . . . . . . 29 Marek Kaluba and Piotr W. Nowak Certifying numerical estimates of spectral gaps . . . . . . . . . . . . . 33 Benjamin Fine and Anthony Gaglione and Gerhard Rosenberger and Dennis Spellman Orderable groups, elementary theory, and the Kaplansky conjecture . . . . . . . . 43
Anonymous Front matter . . . . . . . . . . . . . . i--iv Robert H. Gilman and Robert P. Kropholler and Saul Schleimer Groups whose word problems are not semilinear . . . . . . . . . . . . . . . 53 Pedro V. Silva and Alexander Zakharov On finitely generated submonoids of virtually free groups . . . . . . . . . 63 Vitaly Roman'kov Two general schemes of algebraic cryptography . . . . . . . . . . . . . . 83 Mikhail Anokhin A certain family of subgroups of $ \mathbb {Z} n \star $ is weakly pseudo-free under the general integer factoring intractability assumption . . 99 Alireza Khalili Asboei Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order . . . . . . . . . . . . . . . . . 111
Anonymous Frontmatter . . . . . . . . . . . . . . i Robert P. Kropholler and Davide Spriano Closure properties in the class of multiple context-free groups . . . . . . 1 Chris Monico Cryptanalysis of a hash function, and the modular subset sum problem . . . . . 17 Delaram Kahrobaei and Keivan Mallahi-Karai Some applications of arithmetic groups in cryptography . . . . . . . . . . . . 25 Vitali\uì Roman'kov An improved version of the AAG cryptographic protocol . . . . . . . . . 35 Dmitry Panteleev and Alexander Ushakov Conjugacy search problem and the Andrews--Curtis conjecture . . . . . . . 43
Anonymous Frontmatter . . . . . . . . . . . . . . i--iv Anonymous Frontmatter . . . . . . . . . . . . . . i--iv Saul Schleimer and Bert Wiest Garside theory and subsurfaces: Some examples in braid groups . . . . . . . . 61--75 Rostislav Grigorchuk and Dima Grigoriev Key agreement based on automaton groups 77--81 Olga Kharlampovich and Alexei Myasnikov and Alexander Taam Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups . . 83--101 Jyotirmoy Pramanik and Avishek Adhikari Ramp secret sharing with cheater identification in presence of rushing cheaters . . . . . . . . . . . . . . . . 103--113 Artem N. Shevlyakov On group automorphisms in universal algebraic geometry . . . . . . . . . . . 115--121 Mohammad Reza Mirzaee Shamsabad and Seyed Mojtaba Dehnavi and Akbar Mahmoodi Rishakani Randomized nonlinear software-oriented MDS diffusion layers . . . . . . . . . . 123--131 Mikhail Anokhin Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption . . . . . . . . . . . . . . . 133--134