Geodesic
New form of the hidden logarithm problem and its algebraic support
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 3-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper introduces a new form of the hidden discrete logarithm problem defined over finite non-commutative associative algebras containing two-sided global unit and sets of local left-sided and right-sided units. The proposed form is characterized in using a new mechanism for masking the finite cyclic group in which the base exponentiation operation is performed. Local units act in frame of subsets of non-invertible vectors and are used as elements of the private key in the proposed post-quantum digital signature scheme. A new 4-dimensional algebra is introduced as algebraic support of the proposed cryptoscheme. Formulas describing units of different types are derived. 
@article{BASM_2020_2_a0,
     author = {D. N. Moldovyan},
     title = {New form of the hidden logarithm problem and its algebraic support},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--10},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2020_2_a0/}
}
TY  - JOUR
AU  - D. N. Moldovyan
TI  - New form of the hidden logarithm problem and its algebraic support
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2020
SP  - 3
EP  - 10
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2020_2_a0/
LA  - en
ID  - BASM_2020_2_a0
ER  - 
%0 Journal Article
%A D. N. Moldovyan
%T New form of the hidden logarithm problem and its algebraic support
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2020
%P 3-10
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2020_2_a0/
%G en
%F BASM_2020_2_a0
D. N. Moldovyan. New form of the hidden logarithm problem and its algebraic support. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 3-10. https://geodesic-test.mathdoc.fr/item/BASM_2020_2_a0/

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

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

[3] Yan S. Y., Quantum Computational Number Theory, Springer, 2015, 252 pp. | MR | Zbl

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

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

[6] 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

[7] Moldovyan A. A., Moldovyan N. A., “Post-quantum signature algorithms based on the hidden discrete logarithm problem”, Computer Science Journal of Moldova, 26:3(78) (2018), 301–313 | MR | Zbl

[8] Moldovyan N. A., Moldovyan A. A., “Finite Non-commutative Associative Algebras as carriers of Hidden Discrete Logarithm Problem”, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming Computer Software (Bulletin SUSU MMCS), 12:1 (2019), 66–81 | Zbl

[9] Moldovyan N. A., “Unified Method for Defining Finite Associative Algebras of Arbitrary Even Dimensions”, Quasigroups and Related Systems, 26:2 (2018), 263–270 | MR | Zbl

[10] Moldovyan N. A., “Finite Non-commutative Associative Algebras for Setting the Hidden Discrete Logarithm Problem and Post-quantum Cryptoschemes on its Base”, Buletinul Academiei de Stiinte a Republicii Moldova, Matematica, 2019, no. 1(89), 71–78 | MR | Zbl