{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:16:04Z","timestamp":1772266564610,"version":"3.50.1"},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["527814"],"award-info":[{"award-number":["527814"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009432","name":"Government Council on Grants, Russian Federation","doi-asserted-by":"publisher","award":["N14.W03.31.0030"],"award-info":[{"award-number":["N14.W03.31.0030"]}],"id":[{"id":"10.13039\/501100009432","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["16-11-10075"],"award-info":[{"award-number":["16-11-10075"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We suggest several automaton groups as platforms for Anshel\u2013Anshel\u2013Goldfeld key agreement metascheme.\nThey include Grigorchuk and universal Grigorchuk groups, Hanoi 3-towers group, the Basilica group and a subgroup of the affine group <jats:inline-formula id=\"j_gcc-2019-2012_ineq_9999_w2aab3b7e1481b1b6b1aab1c14b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>Aff<\/m:mi>\n                                 <m:mn>4<\/m:mn>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\u2124<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gcc-2019-2012_eq_0064.png\"\/>\n                        <jats:tex-math>{\\mathrm{Aff}_{4}(\\mathbb{Z})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1515\/gcc-2019-2012","type":"journal-article","created":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T15:14:06Z","timestamp":1571930046000},"page":"77-81","source":"Crossref","is-referenced-by-count":3,"title":["Key agreement based on automaton groups"],"prefix":"10.1515","volume":"11","author":[{"given":"Rostislav","family":"Grigorchuk","sequence":"first","affiliation":[{"name":"Mathematics Department , Texas A & M University , College Station , TX 77843-3368 , USA"}]},{"given":"Dima","family":"Grigoriev","sequence":"additional","affiliation":[{"name":"CNRS , Math\u00e9matiques , Universit\u00e9 de Lille , Villeneuve d\u2019Ascq , 59655 , France"}]}],"member":"374","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"2021021300491644546_j_gcc-2019-2012_ref_001_w2aab3b7e1481b1b6b1ab2ab1Aa","unstructured":"I.  Anshel, M.  Anshel and D.  Goldfeld,\nAn algebraic method for public-key cryptography,\nMath. Res. Lett. 6 (1999), no. 3\u20134, 287\u2013291."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_002_w2aab3b7e1481b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"L.  Bartholdi, R. I.  Grigorchuk and Z.  \u0160uni\u1e31,\nBranch Groups,\nHandbook of Algebra, Vol. 3,\nElsevier, Amsterdam (2003), 989\u20131112.","DOI":"10.1016\/S1570-7954(03)80078-5"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_003_w2aab3b7e1481b1b6b1ab2ab3Aa","unstructured":"M. G.  Benli, R.  Grigorchuk and T.  Nagnibeda,\nUniversal groups of intermediate growth and their invariant random subgroups,\nFunct. Anal. Appl. 49 (2015), no. 3, 159\u2013174."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_004_w2aab3b7e1481b1b6b1ab2ab4Aa","unstructured":"O.  Bogopolski, A.  Martino and E.  Ventura,\nOrbit decidability and the conjugacy problem for some extensions of groups,\nTrans. Amer. Math. Soc. 362 (2010), no. 4, 2003\u20132036."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_005_w2aab3b7e1481b1b6b1ab2ab5Aa","unstructured":"I.  Bondarenko,\nThe word problem in Hanoi Towers groups,\nAlgebra Discrete Math. 17 (2014), no. 2, 248\u2013255."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_006_w2aab3b7e1481b1b6b1ab2ab6Aa","unstructured":"I. V.  Bondarenko, N. V.  Bondarenko, S. N.  Sidki and F. R.  Zapata,\nOn the conjugacy problem for finite-state automorphisms of regular rooted trees,\nGroups Geom. Dyn. 7 (2013), no. 2, 323\u2013355."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_007_w2aab3b7e1481b1b6b1ab2ab7Aa","unstructured":"M.  Garzon and Y.  Zalcstein,\nThe complexity of Grigorchuk groups with application to cryptography,\nTheoret. Comput. Sci. 88 (1991), no. 1, 83\u201398."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_008_w2aab3b7e1481b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"R.  Grigorchuk,\nSolved and unsolved problems around one group,\nInfinite Groups: Geometric, Combinatorial and Dynamical Aspects,\nProgr. Math. 248,\nBirkh\u00e4user, Basel (2005), 117\u2013218.","DOI":"10.1007\/3-7643-7447-0_5"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_009_w2aab3b7e1481b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"R.  Grigorchuk and Z.  \u0160uni\u0107,\nSchreier spectrum of the Hanoi Towers group on three pegs,\nAnalysis on Graphs and its Applications,\nProc. Sympos. Pure Math. 77,\nAmerican Mathematical Society, Providence (2008), 183\u2013198.","DOI":"10.1090\/pspum\/077\/2459869"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_010_w2aab3b7e1481b1b6b1ab2ac10Aa","unstructured":"R.  Grigorchuk and Z.  \u0160uni\u1e31,\nAsymptotic aspects of Schreier graphs and Hanoi Towers groups,\nC. R. Math. Acad. Sci. Paris 342 (2006), no. 8, 545\u2013550."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_011_w2aab3b7e1481b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"R. I.  Grigorchuk,\nDegrees of growth of finitely generated groups and the theory of invariant means,\nMath. USSR Izv. 25 (1985), 939\u2013985.","DOI":"10.1070\/IM1985v025n02ABEH001281"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_012_w2aab3b7e1481b1b6b1ab2ac12Aa","unstructured":"R. I.  Grigorchuk, V. V.  Nekrashevich and V. I.  Sushchanski\u012d,\nAutomata, dynamical systems, and groups,\nProc. Steklov Inst. Math. 231 (2000), 128\u2013203."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_013_w2aab3b7e1481b1b6b1ab2ac13Aa","unstructured":"R. I.  Grigorchuk and J. S.  Wilson,\nThe conjugacy problem for certain branch groups,\nProc. Steklov Inst. Math. 231 (2000), 204\u2013219."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_014_w2aab3b7e1481b1b6b1ab2ac14Aa","unstructured":"R.  Grigorchuk and A.  Zuk,\nOn a torsion-free weakly branch group defined by a three state automaton,\nInternat. J. Algebra Comput. 12 (2002), no. 1\u20132, 223\u2013246."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_015_w2aab3b7e1481b1b6b1ab2ac15Aa","doi-asserted-by":"crossref","unstructured":"R. I.  Grigorchuk and A.  \u017buk,\nSpectral properties of a torsion-free weakly branch group defined by a three state automaton,\nComputational and Statistical Group Theory,\nContemp. Math. 298,\nAmerican Mathematical Society, Providence (2002), 57\u201382.","DOI":"10.1090\/conm\/298\/05114"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_016_w2aab3b7e1481b1b6b1ab2ac16Aa","doi-asserted-by":"crossref","unstructured":"D.  Grigoriev and I.  Ponomarenko,\nConstructions in public-key cryptography over matrix groups,\nAlgebraic Methods in Cryptography,\nContemp. Math. 418,\nAmerican Mathematical Society, Providence (2006), 103\u2013119.","DOI":"10.1090\/conm\/418\/07949"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_017_w2aab3b7e1481b1b6b1ab2ac17Aa","unstructured":"D.  Grigoriev and V.  Shpilrain,\nAuthentication from matrix conjugation,\nGroups Complex. Cryptol. 1 (2009), no. 2, 199\u2013205."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_018_w2aab3b7e1481b1b6b1ab2ac18Aa","unstructured":"M.  Habeeb, D.  Kahrobaei, C.  Koupparis and V.  Shpilrain,\nPublic key exchange using semidirect product of (semi)groups,\nApplied Cryptography and Network Security,\nLecture Notes in Comput. Sci. 7954,\nSpringer, Berlin (2013), 475\u2013486."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_019_w2aab3b7e1481b1b6b1ab2ac19Aa","unstructured":"Y. G.  Leonov,\nThe conjugacy problem in a class of 2-groups,\nMat. Zametki 64 (1998), no. 4, 573\u2013583."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_020_w2aab3b7e1481b1b6b1ab2ac20Aa","unstructured":"I.  Lysenok, A.  Myasnikov and A.  Ushakov,\nThe conjugacy problem in the Grigorchuk group is polynomial time decidable,\nGroups Geom. Dyn. 4 (2010), no. 4, 813\u2013833."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_021_w2aab3b7e1481b1b6b1ab2ac21Aa","unstructured":"A. J.  Menezes, P. C.  van Oorschot and S. A.  Vanstone,\nHandbook of Applied Cryptography,\nCRC Press, Boca Raton, 1997."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_022_w2aab3b7e1481b1b6b1ab2ac22Aa","unstructured":"A.  Myasnikov, V.  Shpilrain and A.  Ushakov,\nGroup-based Cryptography,\nAdv. Courses Math. CRM Barcelona,\nBirkh\u00e4user, Basel, 2008."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_023_w2aab3b7e1481b1b6b1ab2ac23Aa","unstructured":"A. D.  Myasnikov and A.  Ushakov,\nCryptanalysis of the Anshel\u2013Anshel\u2013Goldfeld\u2013Lemieux key agreement protocol,\nGroups Complex. Cryptol. 1 (2009), no. 1, 63\u201375."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_024_w2aab3b7e1481b1b6b1ab2ac24Aa","unstructured":"G.  Petrides,\nCryptanalysis of the public key cryptosystem based on the word problem on the Grigorchuk groups,\nCryptography and Coding,\nLecture Notes in Comput. Sci. 2898,\nSpringer, Berlin (2003), 234\u2013244."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_025_w2aab3b7e1481b1b6b1ab2ac25Aa","unstructured":"A. V.  Rozhkov,\nThe conjugacy problem in an automorphism group of an infinite tree,\nMat. Zametki 64 (1998), no. 4, 592\u2013597."},{"key":"2021021300491644546_j_gcc-2019-2012_ref_026_w2aab3b7e1481b1b6b1ab2ac26Aa","doi-asserted-by":"crossref","unstructured":"Z.  \u0160uni\u0107 and E.  Ventura,\nThe conjugacy problem in automaton groups is not solvable,\nJ. Algebra 364 (2012), 148\u2013154.","DOI":"10.1016\/j.jalgebra.2012.04.014"},{"key":"2021021300491644546_j_gcc-2019-2012_ref_027_w2aab3b7e1481b1b6b1ab2ac27Aa","unstructured":"J. S.  Wilson and P. A.  Zalesskii,\nConjugacy separability of certain torsion groups,\nArch. Math. (Basel) 68 (1997), no. 6, 441\u2013449."}],"container-title":["Groups Complexity Cryptology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/gcc.2019.11.issue-2\/gcc-2019-2012\/gcc-2019-2012.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gcc-2019-2012\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gcc-2019-2012\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T03:08:58Z","timestamp":1614395338000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gcc-2019-2012\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,24]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,10,24]]},"published-print":{"date-parts":[[2019,11,1]]}},"alternative-id":["10.1515\/gcc-2019-2012"],"URL":"https:\/\/doi.org\/10.1515\/gcc-2019-2012","relation":{},"ISSN":["1869-6104","1867-1144"],"issn-type":[{"value":"1869-6104","type":"electronic"},{"value":"1867-1144","type":"print"}],"subject":[],"published":{"date-parts":[[2019,10,24]]}}}