Cryptography Course

## Home page for Math 267A, Winter 1997 Mathematical Foundations of Crytography Instructor: Sam Buss

### Complete scribe notes (student-written) for whole course: in PDF or postscript format.

Instructor: Sam Buss

Date/Time: Winter Quarter, Monday-Wednesday-Friday. 1:00-2:00.
Place: HSS 2152. University of California, San Diego.

Course announcement

This one-quarter course will cover the mathematical foundations of cryptography. The tentative course outline includes: introduction to one-way functions and applications to secure communications, descriptions of the usual candidates for secure encryption, pseudo-random number generators, the conversion of weak one-way functions into strong one-way functions, obtaining one-way functions from psuedo-random number generators and obtaining pseudo-random number generators from one-way functions, and other topics as time permits, such as stream and block cryptosystems, DES, trapdoor functions, cryptographic protocols.

### Course outline

The day-by-day course content listed below. The links are to postscript files for a single day's worth of notes --- these are included in the scribe notes for the whole course, and it is better to just download the whole course's notes above.

Day 1: Jeremy Martin. Introduction. One-time pad and pseudorandom number generators. P and NP.

Day 2: Rob Ellis. Feasibility, Randomization, BPP, RP, PP.

Day 3: Jason Ribando. P/poly. Function Ensembles. Definition of pseudorandom number generators.

Day 4: Chris Pollett. One-way functions. Examples. Public input.

Day 5: Dell Kronewitter. Pseudo-random number generators are one-way functions. Definition of weak one-qay functions. input.

Day 6: Mike Mastropietro. From weak one-way functions to one way functions.

Day 7: Tyler McIntosh. Reverse Expansion. Conclusion of proof of one-way functions from weak one-way functions.

Day 8: Jennifer Wagner. Weak one-way permutations. One-way permutations from weak one-way permutations. Square-roots and finding non-trivial factors.

Day 9: Preeti Mehta. Finding square roots versus finding non-trivial factors. Next-bit unpredictability.

Day 10: Imre Tuba. Stretching the output of pseudorandom number generators.

Day 11: Bill Wood. Private key stream cryptosystems. Passive attacks. Plaintext attacks.

Day 12: David Meyer. More on plaintext attacks. Block-cryptosystems. Definition of pseudorandom function generators.

Day 13: Roland Meyer. Block cryptosystems based on pseudorandom function generators. Construcing a pseudorandom function generator from a pseudorandom number generator.

Day 14: Christian Gromoll. Trapdoor functions and RSA.

Day 15: Tin Yen Lee. Square root extraction. Existence of pseudorandom number generators.

Day 16: Anand Desai. Simple probability. Markov inequality, Chebychev inequality, Chernoff bounds. Pairwise independent sampling theorem. Hidden inner product bits.

Day 17: David Little. Hidden Bit Theorem. Hidden Bit Technical Lemma.

Day 18: Howard Skogman. Many Hidden Bits.

Day 19: Jeremy Martin. Statistical distinguishability. Computation indistinguishability. Hidden Bit Theorems revisited. Entropy and Information.

Day 20: Anand Desai. Information and Entropy. Kullback-Liebler inequality.

Day 21: Jennifer Wagner. Prefix-free codes. Kraft inequality. Huffman codes.

Day 22: Robert Ellis. Pseudorandom number generators from one-way functions. Hash functions and one-way hash functions. The Birthday Attack.

Day 23: Tin Yen Lee. Applications of hash functions. The Birthday Attack again.

Day 24: Sam Buss. Thwarting the birthday attack. Blinded signatures.