ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE. School of Mathematical Sciences

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1 ! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-367 Codes and Ciphers 1.0 Course designations and approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee College Curriculum Committee Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.0 Course information: Course Title: Codes and Ciphers Credit Hours: 3 Prerequisite(s): COS-MATH-190 or -200 Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 3 35 Lab Workshop Other (specify) 2.1 Course conversion designation: (Please check which applies to this course) Semester Equivalent (SE) to: Semester Replacement (SR) to: New 2.2 Semester(s) offered: Fall Spring Summer Offered every other year only Other Page 1 of 6

2 2.3 Student requirements: Students required to take this course: (by program and year, as appropriate) None Students who might elect to take the course: Students majoring in Applied Mathematics, Computational Mathematics, or Applied Statistics, Mathematics minors, and students seeking to strengthen their technical background in mathematics 3.0 Goals of the course: (including rationale for the course, when appropriate) 3.1 To become familiar with enciphering. 3.2 To encode and decode using classical enciphering and deciphering techniques. 3.3 To learn and practice the use of current enciphering techniques. 3.4 To learn the basic principles of cryptograhy and how it is used in modern computer and communication systems. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-367 Codes and Ciphers This course will introduce, explain and employ the basic techniques of cryptography, both classical and modern. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, one-time pad encryption, Enigma, cryptosystems such as DES (Data Encryption Standard) and AES (Advanced Encryption Standard), public key encryption schemes (RSA), and hash functions. The course will include an introduction to number theoretic tools used in cryptography. (COS-MATH-190 or -200) Class 3, Credit 3 (S) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 W. Trappe and L. Washington, Introduction to Cryptography with Coding Theory, Pearson-Prentice Hall, Upper Saddle River, NJ. 5.2 J. Buchmann, Introduction to Cryptography, Springer, New York, NY. 5.3 P. Garrett, Making, Breaking Codes, Prentice Hall, Upper Saddle River, NJ. 5.4 R. Lewand, Cryptological Mathematics, MAA, Washington, DC. 5.5 T. Barr, Invitation to Cryptology, Prentice Hall, Upper Saddle RIver, NJ. 5.6 A. Young, Mathematical Ciphers: From Caesar to RSA, AMS, Providence, RI. 5.7 D. Kahn, The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet, Scribner, New York, NY. 5.8 Fiction: Stephenson, Cryptonmicon, Avon, New York, NY. 5.9 Movies: Tora, Tora, Tora; U 571; Windtalkers; Firewall. 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Simple Ciphers The shift cipher Page 2 of 6

3 6.1.2 One-time pad Symmetric and asymmetric cryptosystems Affine ciphers and their cryptanalysis Permutations Substitution ciphers 6.2 Serious Ciphers Introduction to matrices The Vignére cipher Kasiski and Friedman tests Cryptanalysis of Vignére cipher Block ciphers Hill ciphers Attacks on Hill ciphers Stream ciphers and linear feedback shift registers 6.3 Basic Number Theory Divisibility Solving linear diophantine equations Introduction to modular arithmetic and congruences Euler totient function and its properties Modular exponentiation Fermat s and Euler s theorems (without proofs) Square roots modn 6.4 Data Encryption Standard (DES) Feistel ciphers DES algorithm Security of DES Algorithm Advanced Encryption Standard (AES) 6.5 Public Key Cryptography (PKC) Idea of PKC and trapdoors RSA cryptosystem Attacks on RSA Miller-Rabin cryptosystem Idea of discrete log problem Diffie-Hellman key exchange El-Gamal cryptosystem Merkle-Hellman knapsack cipher 6.6 Cryptographic Hash Functions Hash functions and compression functions Hash functions from compression functions Page 3 of 6

4 6.6.3 Birthday attack Efficient hash functions Message authentication codes 6.7 Games and Secret Sharing Flipping coins over the telephone Poker over the telephone Shamir s and other threshold schemes 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Assessment Methods Learning Outcomes 7.1 Recognize computationally hard mathematical problems 7.2 Describe the fundamentals of cryptographic protocol design 7.3 Evaluate the correctness of cryptosystems 7.4 Compare and contrast the security of various cryptosystems 7.5 Encode and decode messages using historically interesting techniques 7.6 Identify the different approaches to quantifying secrecy Homework Quiz/Exam/Final Project Computer Work Class Presentation 8.0 Program goals supported by this course: 8.1 To develop an understanding of the mathematical framework that supports engineering, science, and mathematics. 8.2 To develop critical and analytical thinking. 8.3 To develop an appropriate level of mathematical literacy and competency. 8.4 To provide an acquaintance with mathematical notation used to express physical and natural laws. Page 4 of 6

5 9.0 General education learning outcomes and/or goals supported by this course: Assessment Methods General Education Learning Outcomes 9.1 Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion 9.2 Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information 9.3 Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions 9.4 Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes Homework Quiz/Exam/Final Project Computer Work Class Presentation Page 5 of 6

6 Assessment Methods General Education Learning Outcomes 9.5 Creativity, Innovation and Artistic Literacy Demonstrate creative/innovative approaches to coursebased assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created Homework Quiz/Exam/Final Project Computer Work Class Presentation 10.0 Other relevant information: (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) None Page 6 of 6