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REMARK OF Pi,k ON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING

  • Kim, Dae-Yeoul (National Institute for Mathematical Sciences) ;
  • Kim, Min-Soo (Department of Mathematics, KAIST)
  • Received : 2011.03.02
  • Accepted : 2011.04.05
  • Published : 2011.06.25

Abstract

Greg([Greg]) considered that $$N_k= \sum\limits_{i=1}^k(-1)^{i+1}P_{i,k}(p)N_1^i$$ where the $P_{i,k}$'s were polynomials with positive integer coefficients. In this paper, we will give the equations for $\sum\limits{P_{i,k}$ modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.

Keywords

Congruences;Elliptic curve

References

  1. Inam, I., Soydan, G., Demirci, M. Bizim, O., Cangul, I. N.,Corrigendum On The Number of Points on Elliptic Curves E : $y^2\,=\,x^3\,+\,cx\;over\,F_p$ mod 8, Commun. Korean Math. Soc. 22 (2007), no. 2, 207-208. https://doi.org/10.4134/CKMS.2007.22.2.207
  2. D. Kim, W. Jeon, Remarks of the number of points on elliptic curves mod 24, submitted.
  3. M. Gregg, Combinatorial aspects of elliptic curves, Sem. Lothar. Combin. 56 (2006/07), Art. B56f, 31 pp.
  4. H. Park, D. Kim, E. Lee The number of points on elliptic curves E : $y^2\,=\,x^3\,+\,cx\;over\,F_p$ mod 8, Commun. Korean Math. Soc. 18(2003), 31-37. https://doi.org/10.4134/CKMS.2003.18.1.031
  5. S. You, H. Park and H. Kim The number of points on elliptic curves $E^0_A\,:\,y^2\,=\,x^3\,+\,a^3\;over\,F_p$ mod 24, Honam Mathematical J. 31 (2009), No. 3, pp. 437-449. https://doi.org/10.5831/HMJ.2009.31.3.437
  6. J. H. Silverman, The arithmetic of elliptic curves, Springer-Verlag, New York, 1986.
  7. A. Weil, Sur Courbes Algebriques Varietes qui s'en Deduisent, Hermann, Paris, 1948.
  8. Stalling, William, Data and Computer Communications, Printice Hall. 2004