On the solvability of the discrete logarithm problem in residue classes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 647-653.

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The article is devoted to solvability of the discrete logarithm problem modulo composite number. Two theorems are proved, giving necessary and sufficient conditions for solvability in some cases. Also one method is suggested for proving solvability, analogous to the Pohlig–Hellman algorithm for solving the discrete logarithm problem.
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O. N. Vasilenko. On the solvability of the discrete logarithm problem in residue classes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 647-653. http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a1/

[1] Cohen H., A course in computational algebraic number theory, Springer-Verlag, Berlin, 1993 | MR

[2] McCurley K., “The discrete logarithm problem”, Proc. of Symp. in Appl. Mat., 42 (1990), 49–74 | MR | Zbl

[3] Odlyzko A., “Discrete logarithms in finite fields and their cryptographic significance”, Lect. Notes in Comput. Sci., 209, 1985, 224–314 | MR | Zbl

[4] Pohlig S. C., Hellman M., “An improved algorithm for computing logarithms over $\mathrm{GF}(p)$ and its cryptographic significance”, IEEE Trans. Inf. Theory, 24 (1978), 106–110 | DOI | MR | Zbl

[5] Riesel H., “Some soluble cases of the discrete logarithm problem”, BIT, 28 (1998), 839–851 | DOI | MR

[6] Schirokauer O., Weber D., Denny T., “Discrete logarithms: the effectiveness of the index calculus method”, Lect. Notes in Comput. Sci., 1122, 1996, 337–362 | MR

[7] Vinogradov I. M., Osnovy teorii chisel, Nauka, M., 1972 | MR