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@article{DM_2014_26_1_a10, author = {S. A. Stepanov}, title = {On the discrete logarithm problem}, journal = {Diskretnaya Matematika}, pages = {133--142}, publisher = {mathdoc}, volume = {26}, number = {1}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/DM_2014_26_1_a10/} }
S. A. Stepanov. On the discrete logarithm problem. Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 133-142. http://geodesic.mathdoc.fr/item/DM_2014_26_1_a10/
[1] Adleman L. M., “A sub-exponential algorithm for the discrete logarithm problem with applications”, Proc. 20-th Annual IEEEE Symp. on the Found. Comp. Sci., 1979, 55–60
[2] Diffie W., Hellman M., “New directions in cryptography”, IEEE Trans. Inf. Theory, 22 (1976), 644–654 | DOI | MR | Zbl
[3] Coppersmith D., “Fast evaluation of discrete logarithms in fields of characteristic 2”, IEEE Trans. Inf. Theory, 30 (1984), 587–594 | DOI | MR | Zbl
[4] Coppersmith D., Odlyzko A. M., Schroeppel R., “Discrete logarithms in $GF(p)$”, Algoritmica, 1 (1986), 1–15 | DOI | MR | Zbl
[5] ElGamal T., “A public key cryptosystem and a signature scheme based on discrete logarithms”, IEEE Trans. Inf. Theory, 31:4 (1985), 469–472 | MR | Zbl
[6] ElGamal T., “Computing logarithms over finite fields”, Lect. Notes in Comp. Sci., 218, 1986, 396–402 | DOI | MR
[7] Hellman M. E., Reyneri J. M., “Fast computation of discrete logarithms in $GF(q)$”, Proc. of Cripto' 82, Plenum, 1983, 3–13
[8] Koblitz N., A Course in Number Theory and Cryptography, Springer-Verlag, New York, 1987 | MR | Zbl
[9] LaMacchia B. A., Odlyzko A. M., “Computation of discrete logarithms in prime fields”, Designs, Codes and Cryptography, 1:1 (1991), 47–62 | DOI | MR | Zbl
[10] Lidl R., Niederreiter G. L., Finite Fields, Addison-Wesley, Reading, MA, 1983 | Zbl
[11] Massey J. L., “Logarithms in finite cyclic groups – cryptographic issues”, Proc. 4-th Benelux Symp. on Inf. Theory, 1983, 17–25
[12] McCurley K. S., “The discrete logarithm problem”, Proc. Symp. in Appl. Math., 42 (1990), 49–74 | MR | Zbl
[13] McCurley K. S., “Cryptographic key distribution and computation in class groups”, Proc. of the NATO Advanced Study Inst. on Number Theory and Appl., Kluwer, Boston, 1989, 459–479 | MR
[14] Menezes A., Okamoto T., Vanstone S., “Reducing elliptic curve logarithms to logarithms in a finite field”, Proc. 22-th Annual ACM Symp. on Theory of Comp., 1991, 80–89
[15] Odlyzko A. M., “Discrete logarithms in finite fields and their cryptographic significance”, Proc. of Eurocrypt 84, Springer-Verlag, New York, 1985, 224–314 | MR
[16] Pohlig S., Hellman M., “An improved algorithm for computing logarithms over $GF(p)$ and its cryptographic significance”, IEEE Trans. Inf. Theory, 24:1 (1978), 106–110 | DOI | MR | Zbl
[17] Pollard J. M., “Monte Carlo methods for index computation mod $p$”, Math. Comp., 32 (1978), 918–924 | MR | Zbl
[18] Pomerance C., “Fast, rigorous factorization and discrete logarithm algorithms”, Discrete Algorithms and Complexity, Academic Press, Orlando, Japan, 1987, 119–143 | DOI | MR
[19] Semaev I. A., “Computation of discrete logarithms in an arbitrary finite field”, Discrete Math. Appl., 5:2 (1995), 107–116 | DOI | MR | Zbl
[20] Shanks D., “Class number, a theory of factorization and genera”, Proc. Symp. in Pure Math., AMS, Providence, 1971, 415–440 | MR
[21] Shparlinski I. E., Computational and algorithmic problems in finite fields, Kluwer Acad. Publ., Dordrecht, 1992 | MR | Zbl
[22] Stepanov S. A., Arithmetic of algebraic curves, Plenum, New York–London, 1994 | MR | Zbl
[23] Van de Woestijne C., “Deterministic equation solving over finite fields”, ISSAC' 05, China, 2005
[24] Von zur Gathen J., Gerhard J., Modern computer algebra, second ed., Cambridge University Press, 2003 | MR | Zbl
[25] Washington L., Elliptic curves: number theory and cryptography, Chapman Hall/CRC Press, 2003 | MR | Zbl