Frequency characteristics of sequences generated by the stream encryption algorithm GEA-1
Matematičeskie voprosy kriptografii, Tome 15 (2024), pp. 67-82.

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

We consider frequencies and cross-correlation coefficients for sequences generated by the stream encryption algorithm GEA-1. Results are obtained by means of well-known estimates for exponential sums from linear recurrent sequences.
@article{MVK_2024_15_a3,
     author = {O. V. Kamlovskii and V. V. Mizerov},
     title = {Frequency characteristics of sequences generated by the stream encryption algorithm {GEA-1}},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {67--82},
     publisher = {mathdoc},
     volume = {15},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2024_15_a3/}
}
TY  - JOUR
AU  - O. V. Kamlovskii
AU  - V. V. Mizerov
TI  - Frequency characteristics of sequences generated by the stream encryption algorithm GEA-1
JO  - Matematičeskie voprosy kriptografii
PY  - 2024
SP  - 67
EP  - 82
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2024_15_a3/
LA  - ru
ID  - MVK_2024_15_a3
ER  - 
%0 Journal Article
%A O. V. Kamlovskii
%A V. V. Mizerov
%T Frequency characteristics of sequences generated by the stream encryption algorithm GEA-1
%J Matematičeskie voprosy kriptografii
%D 2024
%P 67-82
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2024_15_a3/
%G ru
%F MVK_2024_15_a3
O. V. Kamlovskii; V. V. Mizerov. Frequency characteristics of sequences generated by the stream encryption algorithm GEA-1. Matematičeskie voprosy kriptografii, Tome 15 (2024), pp. 67-82. http://geodesic.mathdoc.fr/item/MVK_2024_15_a3/

[1] Lidl R., Niderraiter G., Konechnye polya, v. 1, 2, Mir, M., 1988, 822 pp.

[2] Kuzmin A.S., Kurakin V.L., Nechaev A.A., “Psevdosluchainye i polilineinye posledovatelnosti”, Trudy po diskretnoi matematike, 1, 1997, 139–202 | MR | Zbl

[3] Korobov N.M., “Raspredelenie nevychetov i pervoobraznykh kornei v rekurrentnykh ryadakh”, Doklady Akademii nauk SSSR, 88:4 (1953), 603–606 | Zbl

[4] Nechaev V.I., “Raspredelenie znakov v posledovatelnosti pryamougolnykh matrits nad konechnym polem”, Trudy MIAN im. V.A. Steklova, 218, 1997, 335–342 | Zbl

[5] Shparlinskii I.E., “O raspredelenii znachenii rekurrentnykh posledovatelnostei”, Problemy peredachi informatsii, 25:2 (1989), 46–53 | MR | Zbl

[6] Sarwate D.V., “An upper bound on the aperiodic autocorrelation function for a maximal-length sequence”, IEEE Trans. Inf. Theory, 30:4 (1984), 685–687 | DOI | MR | Zbl

[7] Niederreiter H., “Distribution properties of feedback shift register sequences”, Probl. Contr. Inform. Theory, 15:1 (1986), 19–34 | MR | Zbl

[8] Kamlovskii O.V., “Kolichestvo poyavlenii elementov v vykhodnykh posledovatelnostyakh filtruyuschikh generatorov”, Prikladnaya diskretnaya matematika, 2013, no. 3(21), 11–25 | Zbl

[9] Beierle C., Derbez P., Leander G., Leurent G., Raddum H., Rotella Y., Rupprecht D., Stennes L., “Cryptanalysis of the GPRS encryption algorithms GEA-1 and GEA-2”, Lect. Notes Comput. Science, 12697, 2021, 155–183 | DOI | MR | Zbl

[10] Gill A., Lineinye posledovatelnye mashiny, Mir, M., 1974, 288 pp.

[11] Shnaier B., Prikladnaya kriptografiya. Protokoly, algoritmy, iskhodnye teksty na yazyke Si, Triumf, M., 2003, 816 pp.

[12] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yaschenko V.V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2012, 584 pp.

[13] Kamlovskii O.V., “Svoistva raspredelenii strok i stolbtsov dlya matrichnykh lineinykh rekurrentnykh posledovatelnostei pervogo poryadka”, Matematicheskie voprosy kriptografii, 6:4 (2015), 65–76 | DOI | MR | Zbl

[14] Glukhov M.M., Elizarov V.P., Nechaev A.A., Algebra, Uchebnik, v. 2, Gelios ARV, M., 2003, 416 pp.

[15] Laksov D., “Lineinye rekurrentnye posledovatelnosti nad konechnymi polyami”, Matematika. Sb. perev., 11:6 (1967), 145–158

[16] Tsirler N., “Lineinye vozvratnye posledovatelnosti”, Kiberneticheskii sbornik, 1963, no. 6, 55–79

[17] Kamlovskii O.V., “Otsenki chisla poyavlenii vektorov na tsiklakh lineinykh rekurrentnykh posledovatelnostei nad konechnym polem”, Diskretnaya matematika, 20:4 (2008), 102–112 | DOI | MR | Zbl

[18] Bilyak I.B., Kamlovskii O.V., “Chastotnye kharakteristiki tsiklov vykhodnykh posledovatelnostei kombiniruyuschikh generatorov nad polem iz dvukh elementov”, Prikladnaya diskretnaya matematika, 2015, no. 3(29), 17–31

[19] Cochran T., “On a trigonometric inequality of Vinogradov”, J. Number Theory, 27:1 (1987), 9–16 | DOI | MR | Zbl

[20] Golomb S.W., Gong G., Signal design for good correlation, Cambridge, 2005, 438 pp. | MR | Zbl

[21] Vinogradov I.M., Osnovy teorii chisel, Nauka, M., 1965, 172 pp. | MR