PPT-Elliptic Curve Crypto

amp ECC DiffieHellman Presenter Le Thanh Binh Outline What is Elliptic Curve Addition on an elliptic curve Elliptic Curve Crypto ECC ECC DiffieHellman Lets start with a puzzle. 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. Number Theory and Cryptography. A Pile of Cannonballs A Square of Cannonballs. 1. 4. 9. .. .. .. 1 + 4 + 9 + . . . + x. 2. . = x (x + 1) (2x + 1)/6. x=3:. 1 + 4 + 9 = 3(4)(7)/6 = 14. 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). Keeping the Smart Grid Secure. A . smart grid. delivers electricity from suppliers to consumers using digital technology to monitor (and optionally control) appliances at consumers' . homes.. Utilize . 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, . 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:. A Pile of Cannonballs A Square of Cannonballs. 1. 4. 9. .. .. .. 1 4 9 . . . x. 2. . = x (x 1) (2x 1)/6. x=3:. 1 4 9 = 3(4)(7)/6 = 14. The number of cannonballs in x layers is. 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. 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. 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. 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.