Links
I will be looking for relevant links that appear in the news (current events)
and will post them here. If you hear an interesting story, pass it on and I will
probably post it.
(January 4, 2013) This article was from two years ago, but it will be relavant
for the material at the end of our course.
A 232 digit
number was factored into the product of two primes.
This number was part of a challenge offered by RSA (the company) and there was a cash prize but
the prize expired in 2007. The security of RSA (the code) is based on the factoring problem
and we will learn more about this towards the last third of the course.
(February 26, 2013) The 48th Mersenne prime
was recently discovered (it was first announced on January 25th but the announcement made
its way through the press in the subsequent weeks).
It has over 17.4 million digits. Prime numbers are a mysterious
family of integers because we really don't understand how they are distributed throughout
the number line. We use them in cryptography because algorithms for factoring integers
into primes are "slow" but algorithms for multiplying integers together are "fast".
Mersenne primes are a special family of primes of the form 2^p -1 where p is prime.
(March 17, 2013) The Turing Prize was recently
awarded to Silvio Micali and Shafi Goldwasser for introducing the idea of zero-knowledge proofs
back in 1983.
This is an important concept in cryptography that I would cover in a more advanced course
or if I had a few extra weeks in this course. The ideas lead, for example, to how chip cards can
identify a user without revealing information that can be copied onto a duplicate card.
(March 23, 2013) In a recent news release
(strangely it is dated March 24 but I am reading it on March 23), the company Lockheed-Martin
is announcing that it is commercially deploying the use of
quantum computers. Many people
doubt that real quantum computing
currently exists since it seems that there are
many mathematical challenges that are needed to be overcome in order to
make it practical. I have a hard time evaluating the information which is publicly
available to decide if this invention is true or if it is just a marketing gimmick.
One known application of quantum computing is a polynomial time algorithm for factoring
integers. This would make many of the codes that we are beginning to study vulnerable to
computational attack.
The web comic xkcd.com has a cult following of
people who get a laugh from nerdy cultural references. It
often has comics related to cryptography and mathematics from this course.
