PPT-Pseudorandom Generators for Polynomial Threshold Functions

1 Raghu Meka UT Austin joint work with David Zuckerman Polynomial Threshold Functions 2 Applications Complexity theory learning theory voting theory quantum computing Halfspaces 3. uoagr Abstract Pseudorandom sequences have many applications in cryp tography and spread spectrum communications In this dissertation on one hand we develop tools for assessing the randomness of a sequence and on the other hand we propose new constru Motors and Generators. Electromagnets. Magnet Poles. Parts of a Basic DC Motor. Electric Generators. From the Power Plant to Your Home. Motors and Generators . Small DC Motor. Generator in a Hydro Plant. 3b. . Pseudorandomness. .. B. ased on: Jonathan . Katz and Yehuda . Lindell. . Introduction . to . Modern Cryptography. 2. Pseudorandomness. An introduction. A distribution . D. is pseudorandom if no PPT . Objectives: Identify Polynomial functions. Determine end behavior recognize characteristics of polynomial functions. Use factoring to find zeros of polynomial functions.. Polynomials of degree 2 or higher have graphs that are smooth and continuous. By smooth we mean the graphs have rounded curves with no sharp corners. By continuous we mean the graphs have no breaks and can be drawn without lifting your pencil from the rectangular coordinate system..  . An order . differential equation has a . parameter family of solutions … or will it?.  . 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 1. 1. 2. 3. 4. 0. 2. 2. 3. 4. 0. 1. 3. 3. 4. 0. 1. 2. 4. 4. 0. 1. 2. Algebra 2. Chapter 5. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . Quadratic Function. A . quadratic function . is defined by a quadratic or second-degree polynomial.. Standard Form. , . where . a. . ≠ 0. .. Vertex Form. , where a. . ≠ 0..  . Vertex and Axis of Symmetry. Now, we have learned about several properties for polynomial functions. Finding y-intercepts. Finding x-intercepts (zeros). End behavior (leading coefficient, degree). Testing values for zeros/factors (synthetic division) . Section 4.1. Polynomial Functions. Determine roots of polynomial equations. Apply the Fundamental Theorem of Algebra. Polynomial in one variable. A polynomial in one variable x, is an expression of the form a. Objectives:. To approximate . x. -intercepts of a polynomial function with a graphing utility. To locate and use relative . extrema. of polynomial functions. To sketch the graphs of polynomial functions. Cryptography Lecture 6 Pseudorandom generators (PRGs) Let G be an efficient, deterministic algorithm that expands a short seed into a longer output Specifically, let |G(x)| = p(|x|) G is a PRG if: when the distribution of x is uniform, the distribution of G(x) is “indistinguishable from uniform” Objective: . Recognize the shape of basic polynomial functions. Describe the graph of a polynomial function. Identify properties of general polynomial functions: Continuity, End Behaviour, Intercepts, Local . Which of the following encryption schemes is CPA-secure (G is a PRG, F is a PRF)?. Enc. k. (m) chooses uniform r; outputs <r, G(r) .  . m>. Enc. k. (m) chooses uniform r; outputs <r, . F.