1. Introduction. COS 126* Princeton University Fall Overview. Kevin Wayne. Grades. The Usual Suspects

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1 Overview 1. Introduction What is COS 126? Broad, but technical, intro to CS in the context of scientific, engineering, and commercial applications. No prerequisites, intended for novices. COS 126* Princeton University Fall 2004 Kevin Wayne * Some lectures overlap with CHM/COS/MOL/PHY 232 Goals. Empower you to exploit available technology. Demystify computer systems. Build awareness of substantial intellectual underpinnings. Topics. Programming in Java. Machine architecture. Theory of computation. Applications. Introduction to Computer Science Robert Sedgewick and Kevin Wayne 2 The Usual Suspects Grades Lectures: Kevin Wayne. Tuesdays and Thursdays, 10:00-10:50, Frist 302. Course grades. No preset curve or quota. Precepts: Chris Bienia, Eden Chlamtac, Chris De Coro, Donna Gabai, Elena Nabieva, Kevin Wayne. COS 126: Fridays and Mondays. CHM/COS/MOL/PHY 232: Thursday. Tips on assignments, worked examples, clarify lecture material. Programming assignments: 40% (can drop lowest one) 2 exams: 50% Final project: 10% Staff discretion. Adjust borderline cases. Friend 016/017 lab: Undergrad lab assistants. Weekday evenings, weekend afternoons. Full schedule to be posted on Web. you are here 3 4

2 Course Materials Programming Assignments Course website. Programming assignments. Lecture notes. Exam archive. Required readings. Sedgewick and Wayne. Intro to Computer Science. draft of some sections: Pequod copy booksite: Recommended readings. (U-Store) King. Java Programming From the Beginning. Harel. What computers can't do. Desiderata. Address an important scientific or commercial problem. Illustrate the importance of a fundamental CS concept. Examples. YOU build tools and solve REAL N-body simulation. scientific and commercial problems. DNA sequence alignment. Digital signal processing of MP3 files. Traveling salesperson problem. Markov model of natural language. Due: Wednesdays 11:59pm via Web submission. Computing equipment. Your machine. (Linux, OS X, Unix, Windows, Java cell phone,... ) OIT machines. (Friend 016 and 017 labs). 5 6 What's Ahead? Thursday. CHM/COS/MOL/PHY 232 meets in Icahn atrium at 1:30. A Simple Machine Friday. COS 126 precept meets in Friend 11x. If not in precept (e.g., all first-years), request one today. Check course web page at midnight for precept assignments. Weekend. Read sections of Intro to CS. Monday. Optional COS 126 precept meets in Friend 11x. Tuesday. Lecture 2: Introduction to Java. Due Wednesday. Assignment 0. Setup Java programming environment. Lots of help available, don't be bashful. END OF ADMINISTRATIVE STUFF 7 Introduction to Computer Science Robert Sedgewick and Kevin Wayne

3 Secure Chat A Cryptographic Example Alice wants to send a secret to Bob? Can you read the secret gx76w3v7k? But Bob can. How? How to make a simple machine that produces "random" bits. Linear feedback shift register. Linear congruential generator. What we can do with it. Encrypt and rypt secret s. Encrypt DVDs with CSS. Decrypt DVDs with DeCSS! Use as subroutine in military cryptosystems. Science behind it Encryption Machine Digital Data Goal: design a machine to encrypt and rypt data. encrypt Computers store all data as a sequence of bits. Text. Images (JPEG), audio (MP3), video (DivX). Programs. Bit = 0 or 1 rypt Base64 encoding: use 6 bits to represent each alphanumeric symbol

4 1. Convert text to N bits. One-Time Pad Encryption Bit = 0 or 1 Y One-Time Pad Encryption 1. Convert text to N bits. 2. Generate N (one-time pad) Are these 2000 numbers random? Random Numbers If not, what is the pattern? One-Time Pad Encryption 1. Convert text to N bits. 2. Generate N (one-time pad). 3. Take bitwise XOR of two strings. Sum pair of bits (1 if sum is odd, 0 if even). XOR Truth Table x y x ^ y XOR 18 19

5 One-Time Pad Encryption One-Time Pad Decryption 1. Convert text to N bits. 2. Generate N (one-time pad). 3. Take bitwise XOR of two strings. 4. Convert back into text. X Convert encrypted to. X encrypted XOR encrypted One-Time Pad Decryption Why Does It Work? 1. Convert encrypted to. 2. Use same N (one-time pad). 3. Take bitwise XOR of two strings. 4. Convert back into text. Y Notation a b ^ Meaning original one-time pad XOR operator a ^ b encrypted encrypted (a ^ b) ^ b rypted Crucial property: (a ^ b) ^ b = a. Decrypted = original. XOR Why is crucial property true? Use properties of XOR. (a ^ b) ^ b = a ^ (b ^ b) = a ^ 0 = a always

6 A Cryptographic Example Shift Register How to make a simple machine that produces "random" bits. Linear feedback shift register. Linear congruential generator. What we can do with it. Encrypt and rypt secret s. Encrypt DVDs with CSS. Decrypt DVDs with DeCSS! Use as subroutine in military cryptosystems. Science behind it. Shift register terminology. Bit: 0 or 1. Cell: storage element that holds one bit. Register: sequence of cells. Seed: initial sequence of bits. Shift register: when clock ticks, bits propagate one position to left time t ? time t + 1 register Linear Feedback Shift Register Linear feedback shift register. 11 bit shift register. New output bit 0 is XOR of previous bits 8 and 10. LFSR demo Output bit = bit 0. ^ b 10 b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 time t b 9 b 8 b 7 b 6 b 2 b 1 b 8^b 10 time t + 1 b 5 b 4 b 3 b 0 Are these 2000 numbers random? Random Numbers No. This is output of an bit LFSR!

7 The Science Behind It LFSR and "General Purpose Computer" Are the bits really random? No! Real machines are deterministic. fill in answer How did the computer scientist die in the shower? The instructions on the shampoo read "lather, rinse, repeat." Important properties. Built from simple components. Scales to handle huge problems. Requires a deep understanding to use effectively. Will bit pattern repeat itself? Yes, after = 2047 steps. What if I need more bits? Scalable: 20 cells for 1 million bits, 30 for 1 billion. Basic Component Control Clock Memory Input LFSR Start, stop, load Regular pulse 11 bits Seed Computer same 2.8 GHz pulse 1 GB Sequence of bits Will the machine work equally well if we XOR bits 4 and 10? No, need to understand theory of abstract rings. Computation Output Shift, XOR Pseudo- Logic, arithmetic,... Sequence of bits How many cells do I need to guarantee a certain level of security? Subject of active research. Critical difference. General purpose machine can be programmed to simulate ANY abstract machine Simulating The Abstract Machine in Java Java program prints same bits as LFBSR. You'll understand this program by next week. public class LFBSR { public static void main(string[] args) { int N = Integer.parseInt(args[0]); boolean b10 = false, b9 = true, b8 = true, b7 = false; boolean b6 = true, b5 = false, b4 = false, b3 = false; boolean b2 = false, b1 = true, b0 = false; for (int i = 0; i < N; i++) { boolean bit = b8 ^ b10; b10 = b9; b9 = b8; b8 = b7; b7 = b6; b6 = b5; b5 = b4; b4 = b3; b3 = b2; b2 = b1; b1 = b0; b0 = bit; update } } if (bit) System.out.print(1); else System.out.print(0); } System.out.println(); print % java LFBSR