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.
- 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.
- Edge,an introduction to elliptic curve ,cryptography, http://Iwn.net/Articles/174127/.2006.
- Koblitz,A course in Number theory and cryptography,2nd ed.,brookes/Cole,1997.
- H.Silverman,The Arithmetic of Elliptic curves, Springer –Verlag,1986.
- RSA” Wikipedia.wikipedia,n.d.web.09 feb 2011.Stalings,William. Cryptography and network security.fourth,pearson,2009.print.
- Alfredj Menezes, paul c,vanoorschot and scott A.vanstone,guide to Elliptic curve Cryptography ,1996.
- 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
- The Thesis of on 2-Spreads in PG(5,3) by K. Hanumanthu under the super vision of K.Satyanarayana.
- Thesis of Dr. K .V. Durga Prasad : “Construction ofTranslation planes and Determinition of their translation complements”,Ph.D Thesis,Osmania University
- Diffie, W., and M. E. Hellman. “New directions in cryptography.” IEEE Transactions on Information Theory,, 1976: 644- 654.
- 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 (Jan). 450-457] (ISSN 2320-5407). www.journalijar.com
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