Loading [MathJax]/jax/output/CommonHTML/jax.js
Algebra and Discrete Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra and Discrete Mathematics, 2015, Volume 19, Issue 1, Pages 130–144 (Mi adm512)  

This article is cited in 5 scientific papers (total in 5 papers)

RESEARCH ARTICLE

On the flag geometry of simple group of Lie type and multivariate cryptography

Vasyl Ustimenko

Maria Curie-Sklodowska University, Lublin
Full-text PDF (366 kB) Citations (5)
References:
Abstract: We propose some multivariate cryptosystems based on finite BN-pair G defined over the fields Fq. We convert the adjacency graph for maximal flags of the geometry of group G into a finite Tits automaton by special colouring of arrows and treat the largest Schubert cell Sch isomorphic to vector space over Fq on this variety as a totality of possible initial states and a totality of accepting states at a time. The computation (encryption map) corresponds to some walk in the graph with the starting and ending points in Sch. To make algorithms fast we will use the embedding of geometry for G into Borel subalgebra of corresponding Lie algebra. We also consider the notion of symbolic Tits automata. The symbolic initial state is a string of variables tαFq, where roots α are listed according Bruhat's order, choice of label will be governed by special multivariate expressions in variables tα, where α is a simple root. Deformations of such nonlinear map by two special elements of affine group acting on the plainspace can produce a computable in polynomial time nonlinear transformation. The information on adjacency graph, list of multivariate governing functions will define invertible decomposition of encryption multivariate function. It forms a private key which allows the owner of a public key to decrypt a ciphertext formed by a public user. We also estimate a polynomial time needed for the generation of a public rule.
Keywords: multivariate cryptography, flag variety, geometry of simple group of Lie type, Schubert cell, symbolic walks.
Received: 23.01.2015
Revised: 21.02.2015
Bibliographic databases:
Document Type: Article
Language: English
Citation: Vasyl Ustimenko, “On the flag geometry of simple group of Lie type and multivariate cryptography”, Algebra Discrete Math., 19:1 (2015), 130–144
Citation in format AMSBIB
\Bibitem{Ust15}
\by Vasyl~Ustimenko
\paper On the flag geometry of simple group of Lie type and multivariate cryptography
\jour Algebra Discrete Math.
\yr 2015
\vol 19
\issue 1
\pages 130--144
\mathnet{http://mi.mathnet.ru/adm512}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3376345}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000209846200012}
Linking options:
  • https://www.mathnet.ru/eng/adm512
  • https://www.mathnet.ru/eng/adm/v19/i1/p130
  • This publication is cited in the following 5 articles:
    1. H. Yi, Zh. Nie, “Towards data storage in cryptographic systems: an efficient hardware architecture based on multivariate scheme for secure storage applications”, Cluster Comput., 22:4 (2019), S8639–S8646  crossref  isi  scopus
    2. H. Yi, “Towards wearability in cryptographic systems: a novel architecture based on rainbow scheme for wearable devices”, Wirel. Pers. Commun., 102:2 (2018), 1471–1484  crossref  isi  scopus
    3. V. Ustymenko, A. Wroblewska, U. Romanczuk-Polubiec, E. Zhupa, M. Polak, “On the implementation of new symmetric ciphers based on non-bijective multivariate maps”, Proceedings of the 2018 Federated Conference on Computer Science and Information Systems (FedCSIS), eds. M. Ganzha, L. Maciaszek, M. Paprzycki, IEEE, 2018, 397–405  crossref  isi  scopus
    4. V. A. Ustimenko, “On Schubert cells in Grassmanians and new algorithms of multivariate cryptography”, Tr. In-ta matem., 23:2 (2015), 137–148  mathnet
    5. Vasyl Ustimenko, “On algebraic graph theory and non-bijective multivariate maps in cryptography”, Algebra Discrete Math., 20:1 (2015), 152–170  mathnet  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:206
    Full-text PDF :93
    References:51
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025