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MATH3024 Elementary Cryptography and Protocols
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MATH3024 Elementary Cryptography and Protocols
Cryptography is the branch of mathematics which provides the techniques for enabling confidential information to be transmitted over public networks. This unit is an introduction to cryptography, with an emphasis on the cryptographic primitives that are in most common use today. The first portion of the unit reviews classical cryptosystems and the attacks which render them insecure. The unit then covers modern symmetric cryptosystems, from the block ciphers such as DES and AES to stream ciphers. Finally asymmetric, or public key, cryptosystems such as RSA and ElGamal are treated. These cryptographic primitives will be used to construct protocols for realising digital signatures, data integrity, identification, authentication and key distribution. An important feature of the course will be weekly exercises in practical cryptography using the Computer Algebra System Magma.

The unit of study information sheet covers the specifics of the course contents and assessment criteria.

Tutorial exercises and solutions
Week Tutorials Solutions Week Tutorials Solutions
2 Exercises & Solutions 8 Exercises & Solutions
3 Exercises & Solutions 9 Exercises & Solutions
4 Exercises & Solutions 10 Exercises & Solutions
5 Exercises & Solutions 11 Exercises & Solutions
6 Exercises & Solutions 12 Exercises & Solutions
7 Exercises & Solutions 13 Exercises & Solutions
Lecture Materials
Overviews of the main lecture topics an be downloaded:
01: Elementary Cryptography. 05: Modes of Operation 09: RSA.
02: Elementary Cryptanalysis. 06: Stream Ciphers 10: ElGamal.
03: Information Theory. 07: Modular Arithmetic. 11: Secret Sharing.
04: Block Ciphers 08: Protocols. 12: Hashing, Digital Signatures, and Cash.
Ciphertext Samples
The sample plaintext Black Cat, by Edgar A. Poe, can be used for generating standard English frequencies.
Black cat (ascii) Cipher 01 (ascii) Cipher 02 (ascii) Cipher 03 (ascii) Cipher 04 (ascii) Cipher 05 (ascii)
Cipher 06 (ascii) Cipher 07 (ascii) Cipher 08 (ascii) Cipher 09 (ascii) Cipher 10 (ascii) Cipher 11 (ascii)
  Vigenère ciphertext analyzer. This javascript program, based on a program of Fred Richman, can be used to analyze and decipher ciphertext from simple substitution and Vigenère ciphers.
The first assignment is available. Check here for your individual data and assignment sheet. Data for digraph frequencies can be used for cryptanalysis of substitution ciphers. The due date for this assignment was Friday 30 April. Submission was through the online submission form and only your recovered keys and data were required. Assignment results can be obtained with your submission receipt; solution strategies and code are available here.
The second assignment is available. Follow the link in README for your individual data. The assignment FAQ sheet answers many of the frequently asked questions, and gives general hints. The Magma FAQ may be of general assistance. The due date for the assignment was Tuesday 15 June.
The University of Sydney Library maintains a database of previous years' exams.
Magma computational algebra system
Tutorial exercises will emphasize both hand computations and computer exercises in Magma. The Introduction to Magma for Cryptography provides a brief overview to the syntax and concepts in Magma. The student version of magma can be downloaded for home use. You will also need to download the magma cryptography package for this course.



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