August 4th, 2002, 10:00 PM
All modern encryption obsoleted?!?
The subject was more an attention grabber than an actuality. It comes from an article i read in the science section of the local paper this morning about a "Million dollar math problem." The thing that caught my eye was a line about its application to cryptography.
Im nowhere near an expert, or even knowlegeable of encryption methods etc, but after a quick search of the web, i found a news site that had a similar story on it.
It is about Rieman's 143 year old hypothesis that uses Rieman's own "zeta function" to estimate primes. Apparently, understanding the logic behind this approach, and why it works has been under speculation for quite some time now, and if it is ever found, could impact our ability to bypass encryption standards.
If anyone happens to be a math genius, this site explains the problem in an "elementary way" (lol)
Considering that most encryption schemes rely on the difficulty of determining if a number is a prime, if this hypothesis is proven,we may need to head back to the security blackboard.
The first site is a pretty quick read, and easy to understand and kind of interesting. Check it out.
August 6th, 2002, 04:37 AM
Interesting question - prime numbers & the number theory that goes with it have been of interest to mathematicians for a long time now. It was a hot topic when I was taking my maths degree, but I've not really seen anything new in the public domain to suggest that significant progress has been made since.
Some encryption algorithms do rely on the fact that your public key (z) is made up of x*y, where x & y are prime numbers. z is freely available, so if you can somehow deduce what x or y are, then you can break the encryption.
In this sort of situation, the maths can be used to narrow down the values to look for (x or y in this case), and raw brute force computing power is then used to check likely candidates.
I can't see how you could keep a major development in this area secret for long - and there are all sorts of other algorithms that can be used if this was to be compromised.
August 7th, 2002, 04:54 PM
Like Darkes said, there are many other algorithms one could use for which this process would be ineffective. Symmetric ciphers like AES and Blowfish are immune to this type of cryptanalysis: for them, you have virtually no other option than to try every possible key. As algorithms like this can be created with extremely large keys, it is extremely difficult to do so.
Anyone could get 1024-bit symmetric encryption for free if he or she knew where to look. In this case, it would be far more secure than asymmetric encryption.