The Mathematics of Communication:
keeping secrets
Three may keep a secret, if two of them are dead.
Benjamin Franklin

This is a annotated course diary of a course given twice during the academic year 1999-2000. This material is not principally intended for students, but is primarily directed at those who may want to teach such a course. The course covered some of the mathematics of communication and was directed at liberal arts students assuming only minimal math background. The top row of links below (History ... Outcomes) lead to more detailed information. Each meeting of the course is further described in the links below (Lecture #1 ... #28), along with material created to use in class and as homework. The support of the National Science Foundation (grant number DUE-9850071) for the preparation of much of this material is gratefully acknowledged. I would be happy if what is displayed here were used by others. Please let me know if this occurs. Thank you.

Stephen Greenfield, Math Department
Rutgers University, New Brunswick, New Jersey
e-mail address:
home page:

History: How this
course came about
Aims: Matching the
students and the subject
Methods: Planning
the course for the students
Outcomes: evaluation (final
exam, etc.) & suggestions
Lecture #1
Introduction & Caesar cipher
Lecture #2
More basic crypto & meeting Maple
Lecture #3
Secret sharing
Lecture #4
Medical record privacy
Lecture #5
Modular arithmetic
Lecture #6
More modular arithmetic
Lecture #7
The difficulty of arithmetic
Lecture #8
Algorithms and hardness
Lecture #9
Guest lecture by J. Reeds
Lecture #10
P vs. NP and experimentation
Lecture #11
Diffie-Hellman key exchange
Lecture #12
Fermat's little theorem
Lecture #13
Lecture #14
Working with RSA
Lecture #15
Attacking Diffie-Hellman;
digital signatures & trust
Lecture #16
Beginning binary
Lecture #17
Randomness & one-time pads
Lecture #18
The first crypto policy presentations
Lecture #19
Bitstreams and xor
Lecture #20
More policy presentations
Lecture #21
Beginning authentication
Lecture #22
Lecture #23
Intellectual property
Lecture #24
Protecting digital intellectual property
Lecture #25
A discussion about DES
Lecture #26
Enigma on videotape
Lecture #27
Enigma discussion & review for the final
Lecture #28
Conclusion and evaluation

How math is displayed here

The typesetting language TeX has been used to display mathematics. You can try this example [PDF|PS|TeX]. The source file is available for those who wish to examine or modify it under the TeX link, while Adobe PDF and Postscript versions are available under the PDF and PS links. The variant of TeX used is plain TeX in all but two cases (LaTeX was used for material in Lectures 13 and 25). The macro package epsf was used to include Postscript pictures in five TeX files. The names of these pictures are given in the first lines of the indicated files, and the pictures are available in the directory containing the TeX files. Answers to some homework problems can be found after the "/end" statements in the corresponding TeX file.

A steganographic example
discussed in Lecture #24
Secret sharing at  
Piscataway High School

The picture on this page was taken by D. Sontag on 10/21/1999.
Maintained by and last modified 5/27/2000.