Probabilistic Encryption

[hughes@ah.com (Eric Hughes)]

   I hope we're not about
   to get the usual kiddy PRNG exor encryption lecture. 

A PRNG XOR-ed with a data stream is a perfectly good stream cipher,
provided the PRNG is sufficiently strong.  It's that sufficiently
strong part that usually goes wrong.  LFSR doesn't cut it (Linear
Feedback Shift Register).  Neither does LC (Linear Congruential).  I
should point out that these are both iterates of 

	x_{i+1} = x_i * A + B (mod C)

where the domain is Z_2[x] (polynomials with coefficients mod 2) for
LFSR and Z (integers) for LC.

Blum-Blum-Shub makes a very good stream cipher, even with just XOR.

For those of you may have interpreted GT's comments as to disparage
all PNRG-XOR combinations, I hope the above may help.

Graham, you can read up on probabilistic encryption on page 406 of
Schneier.  In fact, it discusses the BBS generator in this context.

Eric