Geodesic
Candidate for practical post-quantum signature scheme
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 4, pp. 455-461
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new criterion of post-quantum security is used to design a practical signature scheme based on the computational complexity of the hidden discrete logarithm problem. A $4$-dimensional finite non-commutative associative algebra is applied as algebraic support of the cryptoscheme. The criterion is formulated as computational intractability of the task of constructing a periodic function containing a period depending on the discrete logarithm value. To meet the criterion, the hidden commutative group possessing the $2$-dimensional cyclicity is exploited in the developed signature scheme. The public-key elements are computed depending on two vectors that are generators of two different cyclic groups contained in the hidden group. When computing the public key two types of masking operations are used: $i)$ possessing the property of mutual commutativity with the exponentiation operation and $ii)$ being free of such property. The signature represents two integers and one vector $S$ used as a multiplier in the verification equation. To prevent attacks using the value $S$ as a fitting element the signature verification equation is doubled.
Keywords: digital signature, post-quantum cryptoscheme, public key, hidden logarithm problem, finite non-commutative algebra, associative algebra. 
@article{VSPUI_2020_16_4_a9,
     author = {N. A. Moldovyan and A. A. Moldovyan},
     title = {Candidate for practical post-quantum signature scheme},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {455--461},
     year = {2020},
     volume = {16},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a9/}
}
TY  - JOUR
AU  - N. A. Moldovyan
AU  - A. A. Moldovyan
TI  - Candidate for practical post-quantum signature scheme
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 455
EP  - 461
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a9/
LA  - en
ID  - VSPUI_2020_16_4_a9
ER  - 
%0 Journal Article
%A N. A. Moldovyan
%A A. A. Moldovyan
%T Candidate for practical post-quantum signature scheme
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2020
%P 455-461
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a9/
%G en
%F VSPUI_2020_16_4_a9
N. A. Moldovyan; A. A. Moldovyan. Candidate for practical post-quantum signature scheme. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 4, pp. 455-461. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a9/

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

[2] S. Y. Yan, Quantum attacks on public-key cryptosystems, Springer Publ, Boston, 2013, 207 pp. | Zbl

[3] 9th International Conference, PQCrypto 2018 Proceedings (Fort Lauderdale, FL, USA, April 9–11, 2018), Lecture Notes in Computer Science, 10786, 2018 | Zbl

[4] 10th International Conference, PQCrypto 2019 Proceedings (Chongqing, China, May 8–10, 2019), Lecture Notes in Computer Science, 11505, 2019 | Zbl

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

[6] A. A. Moldovyan, N. A. Moldovyan, “Finite non-commutative associative algebras as carriers of hidden discrete logarithm problem”, Bulletin of the South Ural State University. Series Mathematical Modelling, Programming Computer Software, 12:1 (2019), 66–81 | Zbl

[7] N. A. Moldovyan, “Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base”, Bulletin of Academy of Sciences of Moldova. Mathematics, 2019, no. 1 (89), 71–78 | MR | Zbl

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

[9] N. A. Moldovyan, “Fast signatures based on non-cyclic finite groups”, Quasigroups and Related Systems, 18:1 (2010), 83–94 | MR | Zbl