PPT-Elliptic Curves

Number Theory and Cryptography A Pile of Cannonballs A Square of Cannonballs 1 4 9 1 4 9 x 2 x x 1 2x 16 x3 1 4 9 3476 14. :. An . Empirical Study. Gary M. Weiss. Alexander . Battistin. Fordham University. Motivation. Classification performance related to amount of training data. Relationship visually represented by learning 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.. 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. Nick Sinev, Maximilian . Swiatlowski. The most of the code (. fitint.c. ) was written by . M.Swiatlowski. . . I have optimized its speed by minimizing number of multiplications in the innermost loop of the fitter code, using only 32 bits integers there, replacing divisions and multiplications whenever possible by bit shifts.. 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. 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. . 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:. Yan and Jean. -Yves . Ollitrault. CNRS, . Institut . de . Physique Théorique . de . Saclay. and Art Poskanzer. LBNL. Azimuthal Anisotropy Distributions:. The Elliptic Power Distribution. Main Point. 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. . & . ECC Diffie-Hellman. Presenter. : Le . Thanh. . Binh. Outline. What is . Elliptic Curve ?. Addition on an elliptic curve. Elliptic Curve Crypto (ECC). ECC Diffie–Hellman . Lets start with a puzzle…. Warm-up Question. What do dating and marriage have to do with economics? . Scarcity. Choice. Utility maximization . Economics and Marriage. A market is any mechanism or institution that brings buyers together with sellers. Bob the Builder Example. Cost Curves: Bob the Builder Example. Total Cost. To employ Bob to work the firm needs to pay $420. Every additional worker is $420. Bricklayer. Total Cost. 1. $420. 2. $840. 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.