Keywords: Discrete logarithm; polynomial approximation; character sums
@article{ARM_2006_42_1_a4,
author = {Brandst\"atter, Nina and Winterhof, Arne},
title = {Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials},
journal = {Archivum mathematicum},
pages = {43--50},
year = {2006},
volume = {42},
number = {1},
mrnumber = {2227111},
zbl = {1164.11073},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a4/}
}
TY - JOUR AU - Brandstätter, Nina AU - Winterhof, Arne TI - Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials JO - Archivum mathematicum PY - 2006 SP - 43 EP - 50 VL - 42 IS - 1 UR - http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a4/ LA - en ID - ARM_2006_42_1_a4 ER -
Brandstätter, Nina; Winterhof, Arne. Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials. Archivum mathematicum, Tome 42 (2006) no. 1, pp. 43-50. http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a4/
[1] Cochrane T.: On a trigonometric inequality of Vinogradov. J. Number Theory 27 (1987), 9–16. | MR | Zbl
[2] Coppersmith D., Shparlinski I.: On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping. J. Cryptology 13 (2000), 339–360. | MR | Zbl
[3] Ding C., Helleseth T.: On cyclotomic generator of order $r$. Inform. Process. Lett. 66 (1998), 21–25. | MR | Zbl
[4] Kiltz E., Winterhof A.: Polynomial interpolation of cryptographic functions related to Diffie-Hellman and discrete logarithm problem. Discrete Appl. Math. 154 (2006), 326–336. | MR | Zbl
[5] Konyagin S., Lange T., Shparlinski I.: Linear complexity of the discrete logarithm. Des. Codes Cryptogr. 28 (2003), 135–146. | MR | Zbl
[6] Lange T., Winterhof A.: Polynomial interpolation of the elliptic curve and XTR discrete logarithm. Lecture Notes in Comput. Sci. 2387 (2002), 137–143. | MR | Zbl
[7] Lange T., Winterhof A.: Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions. Acta Arith. 101 (2002), 223–229. | MR | Zbl
[8] Lange T., Winterhof A.: Interpolation of the discrete logarithm in $F_q$ by Boolean functions and by polynomials in several variables modulo a divisor of $q-1$. Discrete Appl. Math. 128 (2003), 193–206. | MR
[9] Meidl W., Winterhof A.: Lower bounds on the linear complexity of the discrete logarithm in finite fields. IEEE Trans. Inform. Theory 47 (2001), 2807–2811. | MR | Zbl
[10] Meletiou G. C.: Explicit form for the discrete logarithm over the field ${\text GF}(p,k)$. Arch. Math. (Brno) 29 (1993), 25–28. | MR | Zbl
[11] Meletiou G. C.: Explicit form for the discrete logarithm over the field ${\text GF}(p,k)$. Bul. Inst. Politeh. Iaşi. Secţ. I. Mat. Mec. Teor. Fiz. 41(45) (1995), 1–4. | MR
[12] Meletiou G. C., Mullen G. L.: A note on discrete logarithms in finite fields. Appl. Algebra Engrg. Comm. Comput. 3 (1992), 75–78. | MR | Zbl
[13] Menezes A. J., van Oorschot P. C., Vanstone S. A. : Handbook of applied cryptography. CRC Press, Boca Raton, FL 1997. | MR | Zbl
[14] Mullen G. L., White D.: A polynomial representation for logarithms in ${\text GF}(q)$. Acta Arith. 47 (1986), 255–261. | MR
[15] Niederreiter H.: A short proof for explicit formulas for discrete logarithms in finite fields. Appl. Algebra Engrg. Comm. Comput. 1 (1990), 55–57. | MR | Zbl
[16] Niederreiter H., Winterhof A.: Incomplete character sums and polynomial interpolation of the discrete logarithm. Finite Fields Appl. 8 (2002), 184–192. | MR
[17] Risler J.-J.: Khovansky’s theorem and complexity theory. Rocky Mountain J. Math. 14 (1984), 851–853. | MR
[18] Risler J.-J.: Additive complexity of real polynomials. SIAM J. Comp. 14 (1985), 178–183. | MR
[19] Rojas J. M.: Additive complexity and p-adic roots of polynomials. Lecture Notes in Comput. Sci. 2369 (2002), 506–516. | MR
[20] Rojas J. M.: Arithmetic multivariate Descartes’ rule. Amer. J. Math. 126 (2004), 1–30. | MR | Zbl
[21] Shparlinski I.: Number theoretic methods in cryptography. Complexity lower bounds. Birkhäuser, Basel 1999. | MR | Zbl
[22] Shparlinski I.: Cryptographic applications of analytic number theory. Complexity lower bounds and pseudorandomness. Birkhäuser, Basel 2003. | MR
[23] Winterhof A.: Some estimates for character sums and applications. Des. Codes Cryptogr. 22 (2001), 123–131. | MR | Zbl
[24] Winterhof A.: Incomplete additive character sums and applications. In: Jungnickel, D. and Niederreiter, H. (eds.): Finite fields and applications, 462–474, Springer, Heidelberg 2001. | MR | Zbl
[25] Winterhof A.: Polynomial interpolation of the discrete logarithm. Des. Codes Cryptogr. 25 (2002), 63–72. | MR | Zbl
[26] Winterhof A.: A note on the linear complexity profile of the discrete logarithm in finite fields. Progress Comp. Sci. Appl. Logic 23 (2004), 359–367. | MR | Zbl