I hate to say this, but I think I have reason to believe that PGP might actually be an easy crack. Before now, it probably was only easy to those with access to specially designed analog computers, which means that it really wasn't a problem. But there is now in the public domain an algorithm solution method that will generate a fast numerical solution for most systems of differential equations, given an initial value.
That means that a digital solution is out there, and I think that people within the security community need to check this out before someone outside the security community does. Specifically, I think that if you have the public key, and the encrypted data, and know (or can guess) what the unencrypted data is, then you can quickly deduce the private key. That's bad... unless steps are taken to eliminate this hole. --- before I go on, for responses please cc: me at [EMAIL PROTECTED] --- Specifically, imagine a function that has a periodic nature at every nth integer being 0, but being 1 at all other integers, and is in the form of a broken triangular function. __ ___ ___ ___ ___ \/ \/ \/ \/ Now, at one location, add in an upside down triangular function to make the value 1 at that location. __ ___ ________ ___ ___ \/ \/ \/ \/ Also, define that the width of the triangle -- no matter what the spacing -- is always, say +/- 0.25. Now, define this function to be F, and define P to be the product of a whole bunch of functions F. Now, define that a function F is to be centered at any integer location where the value of the function is 1. If you can do all that, then you can generate a function that will drop out all the primes and only primes. That is, the value of the function will be 1 whereever there is a prime, and zero everywhere else. Now go research the Parker-Souchacki solution to the Picard iteration. It's actually a very simple, fast algorithm that will generate bits in linear time for any or most systems of equations or differential equations. (Developed by Ed Parker and Jim Souchacki of James Madison University in Harrisonburg, VA USA... some info available on the web, enough to learn their method.) I am pretty sure that their method can be used in this way to generate primes. More than that, if you link the primes algorithm to the known input data and the known output data and the public key, then concievably you could have an algorithm that simply drops the digits of the private key out one by one in almost no time. --> Proposed solution: It may be necessary to shift to white-noise encryption for truly secure documents such as financial transactions. There are combinations of white-noise + PGP that may offer moderate security for "mostly secure" documents. More than that, our attitudes about the security of RSA and PGP may need to change. - Mike -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
