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Post-quantum Digital-Signature Algorithms on Finite 6-Dimensional Non-commutative Algebras

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Future Data and Security Engineering (FDSE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12466))

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Abstract

There are introduced three methods for defining finite 6-dimensional associative algebras over the ground finite field GF(p), every one of which contains a set of the global right-sided units. Formulas describing the set of the global units are presented for every of the considered three algebras that contain \(p^s\) global units, where \(s=2,3,4.\) The algebras are used as carriers of the hidden discrete logarithm problem that is used as the base cryptographic primitive of the post-quantum digital signature algorithms.

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References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  2. Yan, S.Y.: Quantum Attacks on Public-Key Cryptosystems, p. 207. Springer, Heidelberg (2014). https://doi.org/10.1007/978-1-4419-7722-9

  3. Smolin, J.A., Smith, G., Vargo, A.: Oversimplifying quantum factoring. Nature 499(7457), 163–165 (2013)

    Article  Google Scholar 

  4. Submission Requirements and Evaluation Criteria for the Post-Quantum Cryptography Standardization Process. NIST PQCrypto project. https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf

  5. First NIST standardization conference - 11–13 April 2018. http://prometheuscrypt.gforge.inria.fr/2018-04-18.pqc2018.html

  6. Takagi, T. (ed.): PQCrypto 2016. LNCS, vol. 9606. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29360-8

    Book  MATH  Google Scholar 

  7. Lange, T., Steinwandt, R. (eds.): PQCrypto 2018. LNCS, vol. 10786. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-79063-3

    Book  Google Scholar 

  8. Moldovyan, N.A.: Unified method for defining finite associative algebras of arbitrary even dimensions. Quasigroups Relat. Syst. 26(2), 263–270 (2018)

    MathSciNet  MATH  Google Scholar 

  9. Sakalauskas, E., Tvarijonas, P., Raulynaitis, A.: Key agreement protocol (KAP) using conjugacy and discrete logarithm problems in group representation level. Informatica 18(1), 115–124 (2007)

    Article  MathSciNet  Google Scholar 

  10. Moldovyan, D.N.: Non-commutative finite groups as primitive of public-key cryptoschemes. Quasigroups Relat. Syst. 18(2), 165–176 (2010)

    MathSciNet  MATH  Google Scholar 

  11. Moldovyan, D.N., Moldovyan, N.A.: Cryptoschemes over hidden conjugacy search problem and attacks using homomorphisms. Quasigroups Relat. Syst. 18(2), 177–186 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Kuzmin, A.S., Markov, V.T., Mikhalev, A.A., Mikhalev, A.V., Nechaev, A.A.: Cryptographic algorithms on groups and algebras. J. Math. Sci. 223(5), 629–641 (2017). https://doi.org/10.1007/s10958-017-3371-y

    Article  MathSciNet  MATH  Google Scholar 

  13. Moldovyan, A.A., Moldovyan, N.A.: Blind signature protocols from digital signature standards. Int. J. Netw. Secur. 13(1), 22–30 (2011)

    MathSciNet  MATH  Google Scholar 

  14. International Standard ISO/IEC 14888–3:2006(E): Information technology - Security techniques - Digital Signatures with appendix - Part 3: Discrete logarithm based mechanisms (2006)

    Google Scholar 

  15. Schnorr, C.P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161–174 (1991). https://doi.org/10.1007/BF00196725

    Article  MATH  Google Scholar 

  16. Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 13, 361–396 (2000)

    Article  Google Scholar 

  17. Koblitz, N., Menezes, A.J.: Another look at “provable security”. J. Cryptol. 20, 3–38 (2007). https://doi.org/10.1007/s00145-005-0432-z

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgement

The reported study was partially funded by the Russian Foundation for Basic Research (project #18-07-00932-a); The Ministry of Science and Technology (MOST) under grant KC.01.22/16-20/.

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Authors and Affiliations

  1. St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, 39, 14th Line, 199178, St. Petersburg, Russia

    Nikolay A. Moldovyan, Dmitriy N. Moldovyan & Alexander A. Moldovyan

  2. Institute of Cryptographic Science and Technology, 105 Nguyen Chi Thanh Street, Hanoi, Vietnam

    Hieu Minh Nguyen

  3. Kien Giang University, 320A Highway 61, Kiengiang, Vietnam

    Le Hoang Tuan Trinh

Authors
  1. Nikolay A. Moldovyan
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  2. Dmitriy N. Moldovyan
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  3. Alexander A. Moldovyan
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  4. Hieu Minh Nguyen
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  5. Le Hoang Tuan Trinh
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Corresponding author

Correspondence to Hieu Minh Nguyen .

Editor information

Editors and Affiliations

  1. Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam

    Tran Khanh Dang

  2. Johannes Kepler University of Linz, Linz, Austria

    Josef Küng

  3. Hosei University, Tokyo, Japan

    Makoto Takizawa

  4. Sungkyunkwan University, Suwon, Korea (Republic of)

    Tai M. Chung

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Moldovyan, N.A., Moldovyan, D.N., Moldovyan, A.A., Nguyen, H.M., Trinh, L.H.T. (2020). Post-quantum Digital-Signature Algorithms on Finite 6-Dimensional Non-commutative Algebras. In: Dang, T.K., Küng, J., Takizawa, M., Chung, T.M. (eds) Future Data and Security Engineering. FDSE 2020. Lecture Notes in Computer Science(), vol 12466. Springer, Cham. https://doi.org/10.1007/978-3-030-63924-2_19

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  • DOI: https://doi.org/10.1007/978-3-030-63924-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63923-5

  • Online ISBN: 978-3-030-63924-2

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