Computational Complexity and Computability Lecture 3 – Algorithms & Computable Functions Koushik Pal University of Toronto January 18, 2021 Example 1 – PAL Goal: Describe a TM on the alphabet {, } for the languauge PAL = {set of even length palindromes} = {yyreverse | y ∈ {,}∗}. Solution. , → R q ⊔→L […]
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Computational Complexity and Computability Lecture 10 – Some More Decidable & Undecidable Problems Koushik Pal University of Toronto February 10, 2021 Kolmogorov Complexity Definition Let x ∈ {,}∗. The minimal description of x, denoted d(x), is the lexicographically shortest string ⟨M,w⟩ such that M is a TM that on input w halts with only x
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Computational Complexity and Computability Lecture 2 – Turing Machines Koushik Pal University of Toronto January 13, 2021 Motivation Goal Define computation as abstractly and generally as possible Obtain a rigorous definition of algorithm Obtain a rigorous definition of efficiency Turing Machine start q q q qreject Control Unit qaccept Tape ⊔ a
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Graphics for Games CPI 411 2/18/2021 Term Project • Phase 1: March 16 – PresentationofProposal • Phase 2: April 20, 22 (Last week) – Demonstration • Paper Submission: April 27 @ noon. 2/18/2021 • 1. 2. 3. Description The term project is to develop a shader tool to visualize some algorithms used in the current
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CPI 411 Graphics for Games Assignment 2 (Environment Map) This assignment is to develop an environment map tool to demonstrate several reflection and refraction algorithms. You are asked to implement following items in MonoGame and Visual Studio. Several items in gray are from the previous assignment. If you could not complete them, check the solution
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Primitive root 𝑚𝑜𝑑 𝑝 A primitive root 𝑚𝑜𝑑 𝑛 is a value 1 ≤ 𝑎 ≤ 𝑛 − 1 such that the series 𝑎, 𝑎2, 𝑎3, … , 𝑎𝑛−1 is a permutation of all of the values between 1 and 𝑛 − 1. As the book demonstrates, 2 is a primitive root 𝑚𝑜𝑑 13 but
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Understanding Cryptography – A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 3 – The Data Encryption Standard (DES) ver. Nov 26, 2010 These slides were prepared by Markus Kasper, Christof Paar and Jan Pelzl 2/29 Chapter 3 of Understanding Cryptography by Christof Paar and Jan Pelzl Some legal stuff
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CSC 440, Notes from synchronous Zoom session, January 7th Introduction This presentation was meant to introduce some of the mathematics used to analyze and understand cryptosystems. This connection is a consistent theme throughout the course. We begin with integer groups, a concept from the field of abstract algebra. We tie these objects to each of
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Arithmetic in Galois Fields of the form 𝐺𝐹(2𝑛) Galois fields are finite fields, that is, they have a finite number of elements. (An example of an infinite field is the real numbers.) The number of elements must always be non- negative integer power of a prime number. In our examples, the prime will always be
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Federal Information Processing Standards Publication 197 November 26, 2001 Announcing the ADVANCED ENCRYPTION STANDARD (AES) Federal Information Processing Standards Publications (FIPS PUBS) are issued by the National Institute of Standards and Technology (NIST) after approval by the Secretary of Commerce pursuant to Section 5131 of the Information Technology Management Reform Act of 1996 (Public Law