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Foster Student Living Center . If am 1 then the congruence ax mod phas exactly one solution modulo Constructive Solve the linear system sa tm 1 Then sba tbm b So sba mod gives the solution sb If and are solutions then au mod and au mod au au mod mod since a for Programming Contests. Basics. Number . Represenation. in . varius. bases. Basic operations. Divisibility. Reading long . long. . long. numbers. Basic math functions like factorial. http://www.spoj.pl/problems/FCTRL/. Raymond Flood. Gresham Professor of Geometry. Overview. Key terms and guidelines. Caesar ciphers. Substitution cipher. Polyalphabetic cipher. Enigma. Modern . ciphers. Stream ciphers. Block ciphers. Diffie. name: Dr. Kerry . A. McKay. Date of most recent change: . 4/23/13. Understanding Cryptology:. Cryptanalysis . All materials is licensed under a Creative Commons . “. Share Alike. ”. license.. http://creativecommons.org/licenses/by-sa/3.0/. Dec 29. This Lecture. In this last lecture for number theory, we will see probably the. most important application of number theory in computer science –. the design of cryptosystem.. Introduction to cryptograph. Selected Exercises. Goal:. Introduce fundamental . number . theory concepts: . T. he . division . algorithm. Congruences. Rules of modular arithmetic. Copyright © Peter . Cappello. 2. Exercise 10. Merkle offered $100 award for breaking singly - iterated knapsack. Singly-iterated Merkle - Hellman KC was broken by Adi Shamir in 1982   . At the CRYPTO ’83 conference, Adleman used an Apple II computer to demonstrate Shamir’s method . (Ben . Adida. ). Jimin. Park. Carleton University. COMP 4109 Seminar. 15 February 2011. “ If you think. cryptography. is the solution. to your problem….. … then you. don’t understand. cryptography…. Lecture 9: Cryptography. 2. Topics. Introduction. Definitions and Terminology. Steganography. Transposition Ciphers. Substitution Ciphers. 3. Introduction. Throughout history, people have had the need to send messages to other people . Module C . Legal Liability. “When men are pure, laws are useless; when men are corrupt, . laws are broken.”. Benjamin Disreali, Former British Prime Minister. Mod C-. 2. Module Objectives. Identify and describe auditors’ exposure to lawsuits and loss judgments.. ICS 6D. Sandy . Irani. Cryptography Intro. Alice wants to send a message to Bob so that even if Eve can see the transmitted information, she does not learn the true message.. message. message. message. ICS 6D. Sandy . Irani. Number representation. Our number system represents numbers in base 10 (also called decimal notation). Each place represents a power of 10:. 3045 = . 3. ·. 10. 3. + . 0. ·. & . 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…. Announcements. Essay due. Next homework – crypto (on paper). This week: more on encryption and authentication, then on to access control. Last time: symmetric key cryptography. Based on shared knowledge of a private key.