Abstract
The discrete logarithm problem in a hidden group, which is defined over finite non-commutative associative algebras, represents interest for constructing post-quantum public-key cryptoschemes. The currently known form of the hidden logarithm problem suits well for designing the public-key agreement protocols and public encryption algorithms, but not suits for designing the digital signature algorithms. In the present paper, there are introduced novel forms of defining the hidden discrete logarithm problem, on the base of which two digital signature algorithms are proposed. Two different four-dimensional finite non-commutative associative algebras have been used in the proposed signature algorithms. In one of the proposed algorithms, there are used globally non-invertible vectors that are invertible locally. A large set of the left-side and a large set of the right-side local units relates to some fixed globally non-invertible vector. Several different local units are used to define one of the proposed forms of the hidden logarithm problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sirwan, A., Majeed, N.: New algorithm for wireless network communication security. Int. J. Cryptogr. Inf. Secur. 6(3/4), 1–8 (2016)
Yiteng, F., Guomin, Y., Joseph, K.L.: A new public remote integrity checking scheme with user and data privacy. Int. J. Appl. Cryptography. 3(3), 196–209 (2017)
Chiou, S.Y.: Novel digital signature schemes based on factoring and discrete logarithms. Int. J. Secur. Appl. 10(3), 295–310 (2016)
Poulakis, D.: A Variant of digital signature algorithm. Des. Codes Crypt. 51(1), 99–104 (2009)
Yan, S.Y.: Quantum Computational Number Theory, 252 p. Springer, Berlin (2015)
Yan, S.Y.: Quantum Attacks on Public-Key Cryptosystems, 207 p. Springer, Berlin (2014)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)
Smolin, J.A., Smith, G., Vargo, A.: Oversimplifying quantum factoring. Nature 499(7457), 163–165 (2013)
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
First NIST standardization conference—April 11–13, 2018. http://prometheuscrypt.gforge.inria.fr/2018-04-18.pqc2018.html
Post-Quantum Cryptography. In: 9th International Conference, PQCrypto 2018, Fort Lauderdale, FL, USA, April 9–11, 2018, Proceedings. Lecture Notes in Computer Science Series, vol. 10786. Springer, Berlin (2018)
Proceedings of the 7th International Workshop on Post-Quantum Cryptography, PQCrypto 2016. Fukuoka, Japan, February 24–26, 2016, Lecture Notes in Computer Science (LNCS) Series, vol. 9606, 270 p. Springer, Berlin (2016)
Verma, G.K.: A proxy blind signature scheme over braid groups. Int. J. Netw. Secur. 9(3), 214–217 (2009)
Hiranvanichakorn, P.: Provably authenticated group key agreement based on braid groups—the dynamic case. Int. J. Netw. Secur. 19(4), 517–527 (2017)
Myasnikov, A., Shpilrain, V., Ushakov, A.: A practical attack on a braid group based cryptographic protocol. In: Advances in Cryptology—CRYPTO’05/Lecture Notes in Computer Science, vol. 3621, pp. 86–96. Springer, Berlin (2005)
Chaturvedi, A., Lal, S.: An authenticated key agreement protocol using conjugacy problem in braid groups. Int. J. Netw. Secur. 6(2), 181–184 (2008)
Verma, G.K.: Probable security proof of a blind signature scheme over braid groups. Int. J. Netw. Secur. 12(2), 118–120 (2011)
Moldovyan, D.N.: Non-commutative finite groups as primitive of public-key cryptoschemes. Quasigroups Relat. Syst. 18, 165–176 (2010)
Moldovyan, D.N., Moldovyan, N.A.: Cryptoschemes over hidden conjugacy search problem and attacks using homomorphisms. Quasigroups Relat. Syst. 18, 177–186 (2010)
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)
Schnorr, C.P.: Efficient signature generation by smart cards. J. Cryptol. 4, 161–174 (1991)
Moldovyan, N.A.: Unified method for defining finite associative algebras of arbitrary even dimensions. Quasigroups Relat. Syst. 26(2), 263–270 (2018)Â
Support for Research
This work was partially supported by the Russian Foundation for Basic Research in the framework of the project No. 18-07-00932-a.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Moldovyan, A.A., Moldovyan, N.A., Phieu, N.H., Tran, C.M., Nguyen, H.M. (2020). Digital Signature Algorithms Based on Hidden Discrete Logarithm Problem. In: Satapathy, S., Bhateja, V., Nguyen, B., Nguyen, N., Le, DN. (eds) Frontiers in Intelligent Computing: Theory and Applications. Advances in Intelligent Systems and Computing, vol 1014. Springer, Singapore. https://doi.org/10.1007/978-981-13-9920-6_1
Download citation
DOI: https://doi.org/10.1007/978-981-13-9920-6_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9919-0
Online ISBN: 978-981-13-9920-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)