Manifest: Wednesday 26 September 2001

Assignments Due
Monday, 1 October	Projects Preliminary Proposal

Readings
MBC Chapter 10.1-10.3, 10.5 (Rest of chapter 10 is optional)
MBC Chapter 16.1 (16.2-16.6 are optional)

Optional reading for more information: (see web version for links)

• A Tale of Two Sieves, Carl Pomerance. Notices of the AMS, Dec 1996. Good description of historical and modern factoring algorithms.
• Derek Atkins, et. al., The Magic Words are Squeamish Ossifrage, AsiaCrypt 1994.
• Papers on factoring

Questions

• How can we find large probably prime numbers?
• How hard is it to factor large numbers? Why do we think so?
• How big should n be for RSA to be secure?
• Is it possible to prove breaking RSA is as hard as factoring?

The problem of distinguishing prime numbers from composites, and of resolving composite numbers into their prime factors, is one of the most important and useful in all of arithmetic. The dignity of science seems to demand that every aid to the solution of such an elegant and celebrated problem be zealously cultivated.

Johann Carl Friedrich Gauss, Disquisitiones Arithmeticae, 1801.

From http://world.std.com/~reinhold/math/sneakers.adleman.html:

The Story of my Involvement with the Movie Sneakers by Len Adleman

18 Jan 1998

Larry Lasker was one of the writers of the 1983 hit movie War Games. Based on that success, he started to produce his own movies. While looking for a new project, he called me at USC and we arranged to meet. He was considering making a movie based on cryptography. While we spoke he mentioned that he was also considering a movie based on a new treatment for Parkinson's disease. Patients who had been "frozen" for many years would wake-up under treatment - sort of a Rip Van Winkle thing. I said that that sure seemed a lot more interesting than crypto - and he disappeared. The next time I heard of him was in 1990 when his movie Awakenings, starring Robin Williams and Robert De Niro, appeared.

A short while later, Larry again made contact. This time he was well on his way to making Sneakers, starring Robert Redford, Sidney Poitier, Mary McDonnell, Dan Aykroyd and River Phoenix. He told me that there would be a scene wherein a researcher would lecture on his mathematical work regarding a breakthrough in factoring - and hence in cryptography. Larry asked if I would prepare the slides and words for that scene. I liked Larry and his desire for verisimilitude, so I agreed. Larry offered money, but I countered with Robert Redford - I would do the scene if my wife Lori could meet Redford.

I worked hard on the scene. The "number field sieve," (the fastest factoring algorithm currently known) is mentioned along with a fantasy about towers of number fields and Artin maps. I was tempted to name the new breakthrough the "function field sieve," -- since I was actually working on a paper at the time which would later appear with that title - but I decided against it, for reasons which escape me now.

I made beautiful slides on my Mac. This took a great deal of time (graphics programs were not as user friendly as they are now) but I wanted the stuff to look impressive. As it turns out, Larry had them redrawn by hand by some guy on his crew - he said that hand drawn slides looked more realistic. Of course he was right - but I could have saved a lot computer time had I known in the first place.

The lecture scene was actually shot at a small college in LA. Larry told me that some physics professor there saw the slides and said that they did not show math at all. He offered to redraw them for a small fee - Larry declined.

Lori and I were there when the scene was shot. I was most pleased with my phrase "a breakthrough of Gaussian proportions," -- the Prince of Mathematics could use a plug in a major motion picture. We were introduced to Redford and chatted with him for about five minutes - that is Bobb and I chatted - Lori said hello and then apparently was too star struck to add more.

I was given credit at the end of the movie as (in my recollection) "mathematical consultant." Anyway the Academy snubbed me - since apparently the mathematical consultant Oscar for that year went to someone else.

---

Leonard Adleman holds the Henry Salvatori Chair in Computer Science at the University of Southern California. His contributions to the theory of computation and cryptography include work developing the now widely-used RSA system for data encryption, The "A" in RSA stands for Adleman. Prof. Adleman is given credit as the first scientist to actually solve a mathematical problem using DNA. Another notable publication was a new probabilistic test to establish if a given number is prime. He also coined the term "computer virus" to describe the first example, which was programmed by a student in his class in 1983.

University of Virginia Department of Computer Science CS 588: Cryptology - Principles and Applications

David Evans evans@virginia.edu