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(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.

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