Geodesic
Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 71-78 
N. A. Moldovyan. Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 71-78. http://geodesic.mathdoc.fr/item/BASM_2019_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper considers finite non-commutative associative algebras every of which contains a large set of the global one-sided (right and left) units. Formulas describing all of the global units are derived for each of the algebras. Finite algebras of such type are introduced as carriers of the hidden discrete logarithm problem that is defined in three new forms. One of them is used to design the post-quantum cryptoscheme for public key-distribution. Two others are applied to design the post-quantum digital signature schemes.

[1] Kuzmin A. S., Markov V. T., Mikhalev A. A., Mikhalev A. V., Nechaev A. A., “Cryptographic Algorithms on Groups and Algebras”, Journal of Mathematical Sciences, 223:5 (2017), 629–641 | DOI | MR | Zbl

[2] Moldovyan D. N., “Non-Commutative Finite Groups as Primitive of Public-Key Cryptoschemes”, Quasigroups and Related Systems, 18:2 (2010), 165–176 | MR | Zbl

[3] Moldovyan D. N., Moldovyan N. A., “Cryptoschemes over hidden conjugacy search problem and attacks using homomorphisms”, Quasigroups and Related Systems, 18:2 (2010), 177–186 | MR | Zbl

[4] Post-Quantum Cryptography. 9th International Conference, PQCrypto 2018, Proceedings (Fort Lauderdale, FL, USA, April 9–11, 2018), Lecture Notes in Computer Science series, 10786, Springer

[5] Yan S. Y., Quantum Attacks on Public-Key Cryptosystems, Springer, 2014, 207 pp.

[6] 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

[7] First NIST standardization conference (April 11–13, 2018) http://prometheuscrypt.gforge.inria.fr/2018-04-18.pqc2018.html

[8] Schnorr C. P., “Efficient signature generation by smart cards”, J. Cryptology, 4 (1991), 161–174 | DOI | MR | Zbl