01Jan 2017


  • Asst professor of Mathematics G. Narayanamma Institute of Technology and Science(Women). Shaikpet. Hyderabad.
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This paper studies the mathematics of elliptic curves, starting with their derivation and the proof of how points upon them form an additive abelian group. I then worked on the mathematics necessary to use these groups for cryptographic purposes, specifically results for the group formed by an elliptic curve over a finite field, E(Fq). I examine the mathematics behind the group of torsion points, to which every point in E(Fq) belongs, and prove Hasse’s theorem along with a number of other useful results. I finish by describing how to define a discrete logarithmic problem using E(Fq) and showing how this can form public key cryptographic systems for use in both encryption and decryption key exchange.

  1. Certicom, \"standards for Efficient Cryptography,SEC 1:Elliptic curve Cole, Eric, Jason Fossen, Stephen Northcutt, Hal Pomeranz. SANS Security Essentials with CISSP CBK, Version 2.1.USA: SANS Press, 2003.
  2. Edge,an introduction to elliptic curve ,cryptography, http://Iwn.net/Articles/174127/.2006.
  3. Koblitz,A course in Number theory and cryptography,2nd ed.,brookes/Cole,1997.
  4. H.Silverman,The Arithmetic of Elliptic curves, Springer –Verlag,1986.
  5. RSA” Wikipedia.wikipedia,n.d.web.09 feb 2011.Stalings,William. Cryptography and network security.fourth,pearson,2009.print.
  6. Alfredj Menezes, paul c,vanoorschot and scott A.vanstone,guide to Elliptic curve Cryptography ,1996.
  7. Koblitz.CM-curves with good cryptographic properties. In Advances in Cryptology: Crypto 91’ volume 576 of in computer science, pages 279-287,springer-verlag,1992. Notes
  8. The Thesis of on 2-Spreads in PG(5,3) by K. Hanumanthu  under the super vision of      K.Satyanarayana.
  9. Thesis of Dr. K .V. Durga Prasad : “Construction ofTranslation planes and Determinition of their translation complements”,Ph.D Thesis,Osmania University
  10. Diffie, W., and M. E. Hellman. “New directions in cryptography.” IEEE Transactions on Information Theory,, 1976: 644- 654.
  11. A Scalar Multiplication in Elliptic Curve Cryptography with Binary Polynomial Operations in Galois Field Hero Modares(thesis of master science.

[S. Vasundhara. (2017); AN APPROACH TO ELLIPTIC CURVES AND DISCRETE LOGARITHMIC PROBLEM. Int. J. of Adv. Res. 5 (1). 450-457] (ISSN 2320-5407). www.journalijar.com


Article DOI: 10.21474/IJAR01/2766       DOI URL: http://dx.doi.org/10.21474/IJAR01/2766

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