Geodesic
An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues
Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 603-612 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the context of the study of pseudorandom sequences that use quadratic residues modulo the prime $p$, the constructive description of the set of prime moduli for which given integers are quadratic residues is considered. Using the Gauss Lemma, we prove a criterion of combinatorial nature for a given integer $a$ to be a quadratic residue prime modulo $p$. It is shown how to apply this criterion to the problem of effective description of the prime moduli $p$ satisfying the equation $\bigl(\frac ap\bigr)=1$ for each $p$ from a given finite set $M$. 
@article{MZM_2003_73_4_a11,
     author = {V. E. Tarakanov},
     title = {An {Application} of the {Gauss} {Lemma} to the {Study} of {Pseudorandom} {Sequences} {Based} on {Quadratic} {Residues}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {603--612},
     year = {2003},
     volume = {73},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a11/}
}
TY  - JOUR
AU  - V. E. Tarakanov
TI  - An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues
JO  - Matematičeskie zametki
PY  - 2003
SP  - 603
EP  - 612
VL  - 73
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a11/
LA  - ru
ID  - MZM_2003_73_4_a11
ER  - 
%0 Journal Article
%A V. E. Tarakanov
%T An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues
%J Matematičeskie zametki
%D 2003
%P 603-612
%V 73
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a11/
%G ru
%F MZM_2003_73_4_a11
V. E. Tarakanov. An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues. Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 603-612. http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a11/

[1] Koblits N., Kurs teorii chisel i kriptografii, TVP, M., 2001

[2] Brands S. A., Gill R. D., “Cryptography, statistics, and pseudorandomness, I”, Probab. Math. Statist., 15 (1995), 101–114 | MR | Zbl

[3] Brands S. A., Gill R. D., “Cryptography, statistics, and pseudorandomness, II”, Probab. Math. Statist., 16 (1995), 1–17 | MR

[4] Anchel M., Goldfeld D., “Zeta functions, one-way functions, and pseudorandom number generators”, Duke Math. J., 88 (1997), 371–390 | DOI | MR

[5] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1964

[6] Khasse G., Lektsii po teorii chisel, IL, M., 1953