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Mathematics BSc (Hons)


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Module CG0013 - Algebraic Codes and Mathematical Cryptology

(20.00 Credits)

SYNOPSIS OF MODULE This module provides the students with a comprehensive introduction to both classical and contemporary cryptology. It will provide the skills necessary to allow students to identify the type of encryption method used and to attempt to decipher the message. Assessment is by a combination of a class test and one formal examination.


INDICATIVE READING LIST OR OTHER LEARNING RESOURCES Hill, R (1986): A First Course in Coding Theory, Oxford. Jones, G A & Jones, JM (2000). Information and Coding Theory, Springer. Sanwing & Chaoping Xing (2004), Coding Theory - A First Course, Cambridge. Beutelspacher, A (1994) Cryptology, MAA. Simmons, G. J. (2003), Cryptology (pp913-924), Enc. Brit (Vol 16). Sinkov, A (1998). Elementary Cryptanalysis, (2nd Ed), MAA Barr, TM. (2002), Invitation to Cryptology, Prentice Hall.

Trappe, W & Washington, LC.(2002) , Introduction to Cryptography, Prentice Hall.


OUTLINE SYLLABUS Classical Crytpology: Encryption and decryption using direct standard alphabets, alphabets based on decimations, monoalphabets, mixed alphabets, affine ciphers, Vigenere cipher, Kasiski test, polyalphabetic ciphers, polyalphabetic ciphers with mixed cipher sequence, polygraphic ciphers, transposition ciphers. (50%) Contemporary Cryptology: Boolean and numerical functions, computational complexity, stream ciphers, block ciphers, feedback shift registers, hash functions, prime number factorisation attack, Merkle-Hellman knapsack, Fermat’s Little Theorem, RSA public key crypto system, key agreement, digital signatures, zero knowledge identification protocols (50%).


AIMS OF MODULE 1. To provide an introduction to algebraic codes and to mathematical cryptology. 2. To develop an awareness of a range of encryption methods used in classical cryptology and to develop an approach to deciphering such messages. 3 To develop an awareness of the main features of cipher design and cipher breaking and the utilisation of the relevant algebra, statistics, probability and number theory. 4. To develop an awareness of how cryptological methods are used in the modern world and an appreciation of the mathematical theory that ensures secrecy.


LEARNING OUTCOMES By the end of the module the student should be able to: 1. Using appropriate methods, identify the encryption method used to encipher a message. 2. Where practically possible, decipher a message using appropriate tools and techniques. 3. Identify large prime numbers efficiently 4. Critically appraise the use of cryptology in commerce as used today.


PREREQUISITES None


COREQUISITE(S) None.


DISTANCE LEARNING DELIVERY None


LEARNING, TEACHING AND ASSESSMENT STRATEGY The module will be delivered using a combination of lectures and seminars, which will enable students to obtain help with associated problems. In-course test assesses Learning Outcomes 1 and 2. Examination assesses Learning Outcomes 1 to 4.


IMPLICATIONS FOR CHOICE None


Notional Student Workload (Hours) Module and Location Full Time at City Campus (the duration is 30 weeks) Lectures 39 Seminars 13 Tutorials 0 Lab Work 0 Directed Learning 39 Independent Learning 104 Formal Assessment 5 Other 0 Total 200



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