At the moment the plan is to continue reading from a variety of sources and basically assimilating as much information as possible. Some of the ideas will be laid out on this page along with updates of previous ideas. The expectation is that there will be many possible avenues which to investigate, but time will not allow each to be followed up on. By constructing a large base early on, I will have more of an idea on which areas to focus on after Christmas.
This website serves the purpose of advertising my intentions in the hope dialog will improve the content (of this site and the final report). At some point I hope to publish some encrypted messages and various sizes of public key, to try to display what can be cracked, and with what algorithms.
As part of his first year maths course, my supervisor Micheal Mac An Airchnaigh publishes, via the web, a selection of encrypted messages and public private key pairs, which his students use to decrypt their messages as part of their e-test. As a demonstration I will crack their keys (which are NOT large enough to be secure) to reveal their messages.
One of the strengths of the keys of RSA is that factorisation of large numbers is difficult. We will show some factorization times for various sizes of keys in order to show that large enough primes are invulnerable (at least with today's algorithms and technology).
It has been a long time coming but I am now starting to update the site regularly.
I found a paper, "Are 'Strong' Primes Needed for RSA?" written by Rivest which discusses the conception that using strong primes is necessary for complete security in RSA. Due to new advances in the factoring problem the need for strong primes (which were good at stopping p+-1 attacks) are now obsolete. Using sufficiently large primes that aren't strong does not significantly weaken the system. The other attack the "cycling" attack which was also supposed to be hindered by using strong primes, can just as easily be hindered by using large enough primes. Therefore the need for strong primes is no longer there. I wish to investigate both these atacks (using smaller primes and strong primes to see if there is a noticeable difference).
I have become interested in elliptic curves and their varying uses. One use is for factorization. Another is used in primality proving. A newer area is the one of cryptosystems based on elliptic curves. Please see the links in the bibliography (although I hope to have a section for elliptic curves by themselves soon).
Over the Christmas period I have been working on a set of notebooks that I can use to try to attack the RSA system. I began generating keys, the creating functions for encoding, decoding, encrypting and decrypting. I have finished the first attack notebook, which uses the cycle attack of Simmons and Norris. All these are available from the front page.
I have written the outline for the report using LaTeX. I havn't gone into much detail and have just laid out the bare chapter headings. I will update the above link as I write the document. Micheal has told me to use double line spacing, but since I'm new to LaTeX it's taking me a while to get used to.
I recently completed progreamming the Faulty Encryption attack. This is now available as a notebook from the front page or from this link. This attack also demonstrates the weakness of the common modulus protocol of RSA.
I have started the Other Cryptosystems part of the project. This contains a link to a servlet that I wrote to demonstrate AES and ElGamal.
The other changes are simply just adding more to the front page. There is now a link to the most recent update entry on this page.
Some sections added. Made website W3C xhtml 1.0 compliant, but cannot display certificate as Tripod corrupts the data stream to add the ads and its html code does not conform to the standard.
I have been slack about maintaining this web site. A heavy load of course work is to blame. But from now until May I will finish writing up the report. With this update I have replaced the old Mathematica notebooks and the report and filled in a few gaps in the web site. I demonstrated my project in front of my supervisor and 2nd readers yesterday. The slides are available here.
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