Math 348:01 - Spring 2005

Final Project Description

The Mathematics 348 cryptography project is due at the Final Exam (May 5, 2005). It will consist of a legibly written clear discussion of some aspect of cryptography that you have researched. Possible projects are discussed below. The paper should be 7 to 10 typewritten pages, should be well organized and written in complete English sentences, and should cite correctly any writings by others that you consulted. Include a bibliography citing your sources. The mathematics should be explained clearly, and any calculations you make should be described in enough detail that others may reproduce them. The paper should give a thorough exposition of its subject. Once you have selected your project, begin researching it in the library or the vast extension of the library, the internet. The projects involve differing amounts of technical background - for example you you should not choose a project involving quantum mechanics without some understanding of the physics involved.

The project should consist of your own work. Plagiarized writing will not be accepted. Consult a source such as the Indiana University Writing Tutorial Services to make sure you understand proper assignment of credit for ideas of others in your writing.

The grading of the project will be based on the degree to which the paper satisfies the following criteria (equal weight is assigned to the five areas):

Topics for the Mathematics 348 project

  1. The Playfair cipher - Discuss the history, mathematical description and analysis of the Playfair cipher and its relatives. Describe the characteristics of this cipher and compare it to others discussed in the course. Describe some historical uses of this cipher and discuss the security of the Playfair cipher. Use your analysis to decrypt this Playfair cipher .

  2. Quantum cryptography - Research how the physics of quantum mechanics can be used to encrypt information. Discuss the security of quantum encryption and the current status of implementations.

  3. Quantum decryption - It has been proved that a quantum computer could give an efficient attack on the RSA cipher, as well as other ciphers based on the difficulty of reversing certain mathematical operations. Discuss the method used to do this and consequences for the current implementation of RSA ciphers.

  4. The Beaufort cipher - Report on this and other variants in the long history of the Vigenere cipher, such as the autokey Vigenere and the Variant Beaufort. Describe the methods of enciphering, the analysis of such ciphers, and the security of such a cipher. Illustrate your analysis by decrypting this Beaufort cipher .

  5. Cryptography in Literature - Compare and contrast the appearance of cryptography in literature such as Edgar Allan Poe's The Goldbug, The Adventure Of The Dancing Men by Sir Arthur Conan Doyle, Dorothy L. Sayers Have His Carcase or Neal Stephen's Cryptonomicon. Read at least two such works and discuss the author's analysis of the ciphers in the story, justifying the author's cryptanalysis or pointing out errors.

  6. Cryptography and the internet - Discuss the encryption methods used in such protocols as SSH, secure web pages. or the wireless WEP standard. Discuss the strengths and weaknesses of the methods, and the details of the standards.

  7. Discuss the Kryptos sculpture at the headquarters of the CIA and other cryptographic sculptures by the same artist. Your discussion should include an analysis of the decryption of certain aspects of the sculpture . If you decrypt portions that are still unsolved you will receive extra credit!

  8. Research the history of mechanical aids to encryption, ranging from Babbage up to the Enigma machine and relatives used in the first half of the twentieth century. Describe the history of such devices, and some technical details about encryption and decryption and the effect on world events.