PPT-Measuring The Elliptic Genus

Gregory Moore Rutgers AndyFest Harvard July 31 2015 Nicolaus Ginsparnicus of Ithaka This talk has its origins in the D1D5system where Andy has done such great work H olographically. 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. Sixth Edition. by William Stallings . Chapter 10. Other Public-Key Cryptosystems. “Amongst the tribes of Central Australia every man, woman, and child has a secret or sacred name which is bestowed by the older men upon him or her soon after birth, and which is known to none but the fully initiated members of the group. This secret name is never mentioned except upon the most solemn occasions; to utter it in the hearing of men of another group would be a most serious breach of tribal custom. When mentioned at all, the name is spoken only in a whisper, and not until the most elaborate precautions have been taken that it shall be heard by no one but members of the group. The native thinks that a stranger knowing his secret name would have special power to work him ill by means of magic.”. 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. 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. . Kyungpook National University. Heavy Ion Meeting 2011-02, . Muju. Resort. Feb. 27-Mar. 1, 2011. Hadronic. . rescattering. in elliptic flow & Heavy quarks at RHIC. Contents . Introduction. Hadronic. 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. 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. & . 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…. 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. . = 1.  . Elliptic . Cone: . +. .  . Hyperboloid . of one . sheet:. +. . . = 1.  . Hyperboloid of two . sheets: .  . Elliptic . paraboloid: .  . Hyperbolic . paraboloid: .  . LI THOERLE12AVIER a new species from the Amazonas region in Ecuadoris described illustrated compared with similar species and its generic placement discussed is distinguished from all other species in 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.