This is an upper level MATH course. It is directed at students in mathematics, electrical engineering, or computer science who have strong interest in mathematics and want to learn about the exciting applications of algebra and number theory to cryptography. Topics to be covered include:

Cryptography: Simple Ciphers and Cryptograms. Vigenere Cipher, Hill Cipher, Data Encryption Standard.
Public-Key ciphers: Rivest-Shamir-Adleman (RSA), Diffie-Hellman and trapdoors. Public Key Protocols.
Number Theory: Congruences. Finite fields. Finding large primes, pseudoprimes and primality testing.

Possible Topics for Term paper due May 2:

• The DVD CSS algorithm and its weaknesses
• Strong encryption: pros and cons
• US cryptography export policy
• The NSA (National Security Agency)
• Contemporary concept of "digital signature"
• Recent cryptanalysis of DES (or How to crack DES in 1 day)
• Zero-knowledge proofs
• quantum computing
• quantum cryptography
• insecurity of wireless computing
• clever algorithms for large integer arithmetic
• the new European Union privacy laws: effects on web pages, etc.
• Signatures, authentication and non-repudiation protocols
• Implementation of large-integer "fast" algorithms
• Enigma (cipher machine used by Third Reich in WWII)
• Candidates for AES (Advanced Encryption Standard) (pros and cons)
• "Fast" factorization methods: rho method, p-1 method, continued fraction sieve, quadratic sieve, etc.
• Public keys based on the knapsack-problem: failures and revisions
• McEliece Public-Key cipher (based on coding theory issues)
• Pseudo-random number generators
• DNA encryption (and microdots)
• FBI's "Carnivore" email surveillance system.
• The "Echelon" intercept system
• Security/insecurity of the "Bluetooth" wireless protocol

Miscellaneous Links:
Handbook of Applied Cryptography
Britain's GCHQ challenge potentially leading to employment
MIT Lecture Notes

Return to Top of page or to Weibel's Home Page