Geodesic
Signature schemes on algebras, satisfying enhanced criterion of post-quantum security
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 62-67.

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

The paper introduces an enhanced criterion of the post-quantum security for designing post-quantum digital signature schemes based on the hidden discrete logarithm problem. The proposed criterion requires that it is computationally impossible to construct a periodic function containing a period whose length depends on the value of a discrete logarithm in a hidden cyclic group when using public parameters of the signature scheme. A practical post-quantum signature scheme which satisfies the criterion is proposed. 
@article{BASM_2020_2_a5,
     author = {N. A. Moldovyan},
     title = {Signature schemes on algebras, satisfying enhanced criterion of post-quantum security},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {62--67},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2020_2_a5/}
}
TY  - JOUR
AU  - N. A. Moldovyan
TI  - Signature schemes on algebras, satisfying enhanced criterion of post-quantum security
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2020
SP  - 62
EP  - 67
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2020_2_a5/
LA  - en
ID  - BASM_2020_2_a5
ER  - 
%0 Journal Article
%A N. A. Moldovyan
%T Signature schemes on algebras, satisfying enhanced criterion of post-quantum security
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2020
%P 62-67
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2020_2_a5/
%G en
%F BASM_2020_2_a5
N. A. Moldovyan. Signature schemes on algebras, satisfying enhanced criterion of post-quantum security. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 62-67. http://geodesic.mathdoc.fr/item/BASM_2020_2_a5/

[1] Post-Quantum Cryptography. 9th International Conference (Fort Lauderdale, FL, USA, April 9-11, 2018), LNCS, 10786, Springer Verlag, 2018 | Zbl

[2] PQCrypto 2019, Proceedings of the 10th International Conference (Chongqing, China, May 8-10, 2019), LNCS, 11505, Springer Verlag, 2019 | Zbl

[3] Shor P. W., “Polynomial-time algorithms for prime factorization and discrete logarithms on quantum computer”, SIAM Journal of Computing, 26 (1997), 1484–1509 | DOI | MR | Zbl

[4] Smolin J. A., Smith G., Vargo A., “Oversimplifying quantum factoring”, Nature, 499:7457 (2013), 163–165 | DOI

[5] A. Ekert, R. Jozsa, “Quantum computation and Shorś factoring algorithm”, Rev. Mod. Phys., 68 (1996), 733 | DOI | MR

[6] Jozsa R., “Quantum algorithms and the Fourier transform”, Proc. Roy. Soc. London Ser A, 454 (1998), 323–337 | DOI | MR | Zbl

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

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

[9] 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

[10] 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, 12:1 (2019), 66–81 | Zbl

[11] 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

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

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

[14] Moldovyan N. A., Abrosimov I. K., “Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 15:2 (2019), 212–220 | DOI | MR

[15] D. N. Moldovyan, “New Form of the Hidden Logarithm Problem and Its Algebraic Support”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2020, no. 2 (93), 3–10 | MR | Zbl

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

[17] 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