Math 348:01 - Spring 2012
Final Project Description
The Mathematics 348 cryptography project is due at the last day of
class April 27, 2012. 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 8 to 12
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):
General qualities as a term paper:
Are accurate citations provided, is the paper legible and
correctly spelled and divided into paragraphs, and is the writing your own
with proper acknowledgment of sources?
- Quality of writing
Are the basic rules of English composition followed, is the paper
written in complete sentences adhering to standard practices of
English grammar, and are all new terms explained adequately?
- Quality of analysis
Is the paper organized into a coherent whole with a beginning,
an end and a clear explanation of the topic without unexplained gaps?
- Quality of the technical explanations
Does the paper convince the reader, is the mathematics well
explained and correct, and are sufficient details provided that the reader
can follow the technical points and arguments?
- Overall impression given by the term paper
Does the paper explain the topic and leave the reader with the impression
that the author understand the topic and conveyed it well, does the
paper tell the story in an interesting fashion, and is it correct?
Topics for the Mathematics 348 project
- 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 .
- 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.
- 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.
- 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 .
- 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.
- 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.
- 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!
- 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.
- Primality testing and proving - How can we efficiently test if
a number is prime, and prove it prime?