PPT-ELLIPTIC CURVE CRYPTOGRAPHY

By Abhijith Chandrashekar and Dushyant Maheshwary Introduction What are Elliptic Curves Curve with standard form y 2 x 3 ax b a b ϵ ℝ Characteristics of Elliptic Curve. 897 Special Topics in Cryptography Instructors Ran Canetti and Ron Rivest Lecture 25 PairingBased Cryptography May 5 2004 Scribe Ben Adida 1 Introduction The 64257eld of PairingBased Cryptography has exploded By . Abhijith. . Chandrashekar. . and . Dushyant. . Maheshwary. Introduction. What are Elliptic Curves?. Curve with standard form y. 2. = x. 3 . + ax + b a, b . ϵ ℝ. Characteristics of Elliptic Curve. Itay. . Khazon. Eyal. . Tolchinsky. Instructor: . Barukh. . Ziv. Introduction. Public key cryptography is based on the hardness of several mathematical problems such as factoring and DLP.. The public key protocols in use today are based on the discrete logarithm problem over . This problem can be solved in sub-exponential time.. ATM Conference, Telford. Jonny Griffiths, April 2011. 10. 3. +9. 3. =12. 3. +1. 3. = 1729. x. 3. +y. 3. = 1729. Symmetrical about y = x. x. 3. +y. 3. =(. x+y. )(x. 2. -xy+y. 2. ). (1,12). (9,10). (10,9). Elliptic Curve Cryptography. CSCI 5857: Encoding and Encryption. Outline. Encryption as points on ellip. tic curves in space. Elliptic curves and modular arithmetic. Mathematical operations on elliptic curves. w. ith reference to . Lyness. cycles. Jonny Griffiths, UEA, November 2010. a. x. + by + c = 0. Straight line. a. x. 2. + . bxy. + cy. 2. + . dx. + . ey. + f = 0. Conics. Circle, ellipse, parabola, hyperbola, . Curves, Pairings, Cryptography. Elliptic Curves. Basic elliptic . cuves. :. Weierstrass. equation:. , with .  . The values . come from some set, usually a field.  . Part 1. Sets, Groups, Rings, Fields. Cycles, Elliptic Curves,. and . Hikorski. Triples. Jonny Griffiths, Maths Dept. Paston. Sixth Form College. Open University, June 2012. MSc by Research, UEA, 2009-12. (Two years part-time). Supervisors:. Presented by Hans Georg Ritter. Sergei’s 60. th. Birthday. 16 Nov 13. Sergei at Work. 2. r. ecent at Wayne State. Happy . S. ergei. 3. 2008 at . J. aipur. 2002 at MSU. Sergei Exploring the Unknown. Legendrian Knots. Y. . Eliashberg. , M. Fraser. arXiv:0801.2553v2 [math.GT]. Presented. . by . Ana Nora Evans. University of Virginia. April 28, . 2011. I don’t even know what a knot is!. TexPoint fonts used in EMF. . Daniel Dreibelbis. University of North Florida. Outline. Define the Key Exchange Problem. Define elliptic curves and their group structure. Define elliptic curves mod . p. Define the Elliptic Curve Discrete Log Problem. Algorithms. draft-mcgrew-fundamental-ecc-02. mcgrew@cisco.. com. kmigoe@nsa.gov. Elliptic Curve Cryptography. Alternative to integer-based Key Exchange and Signature algorithms. Smaller keys and signatures. The . art and science of concealing the messages to introduce secrecy in . information security . is recognized as cryptography. .. The word ‘cryptography’ was coined by combining two Greek words, ‘Krypto’ . Session 6 . – . Contents. Cryptography Basics. Elliptic Curve (EC) Concepts. Finite Fields. Selecting an Elliptic Curve. Cryptography Using EC. Digital Signature. Cryptography Basics. Security Services Security Mechanisms.