Hi Dustin, A finite field crypto system based on exponentiation is El Gamal. The underlying problem is Discrete Log.
IIRC, Discrete Log is NP-Complete. However, it is not known where factoring (RSA) lies. It is believed to be a hard problem, but it is not proven. RSA generally cannot handle messages of arbitrary length. Small data (such as a symmetric key) can be handled. Jeff > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Dustin Frike > Sent: Tuesday, May 04, 2004 8:34 AM > To: [EMAIL PROTECTED] > Subject: RSA Encryption > > > Hello, > > I am trying to find a way of obtaining a RSA > encryption - decryption key from hashing a passphrase > and using it to encrypt-decrypt some very small amount > of sensible data. > > I don't know if I can do it, but I'm thinking of > generating a p - q pair and making n=p*q and I=LCM > (p-1, q-1) public. Then I would find the first good > exponent higher than a large enough number(200+ bits) > derived from the hash and I would be able to calculate > the other exponent. And then I could encrypt - decrypt > using the exponents and the modulus. And anyone trying > to break this "system" would have a hard time finding > the exponents, even by knowing n, I and possibly even > factoring n. But will this be secure enough? > > How does this sound? Is there a better way of actually > doing this? I'm sorry if it doesn't make too much > sense. I came to think of this when fearing that some > symmetric algorithms might be broken so why not use > RSA instead, for small data? > > Thanks for reading this and for any help, > Dustin. > > > > > __________________________________ > Do you Yahoo!? > Win a $20,000 Career Makeover at Yahoo! HotJobs > http://hotjobs.sweepstakes.yahoo.com/careermakeover >
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