01Jan 2017

AN APPROACH TO ELLIPTIC CURVES AND DISCRETE LOGARITHMIC PROBLEM.

  • 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.


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[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


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


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