Truly Stealthy PGP (algorithm)
Hal
hfinney at shell.portal.com
Sun Mar 6 11:21:28 PST 1994
(I'm having a bit of trouble with my mail UA; all of my saved messages on
this thread keep disappearing, so I apologize for a slight lack of
continuity here. I'm having to work solely from memory of the earlier
discussion.)
If I understand Eric's general idea, we would keep trying session keys
under a set of rules which would lead to the desired statistical
distribution of the encrypted key. Here is an algorithm which would work.
(I hope I am remembering the notation Eric used correctly.)
Let L be the next power of 256 above the modulus n. Let t be the integer
part of L/n, so that L = n*t + s with s in [0,n). Call the PGP IDEA session
key SK, and the encrypted version of that m = SK^e. Now do these steps:
1) Pick a random SK in [0,n).
2) RSA-encrypt it to form m = SK^e mod n.
3) Choose a random k in [0,t].
4) Calculate the "stegged" encrypted key as M = m + k*n. This will be
uniform in [0,(t+1)*n) if m is uniform in [0,n), which I think it is.
5) if M is not in [0,L) (i.e. if M >= L) then go back to step 1.
6) Otherwise store M as a raw binary number taking log base 256 of L bytes.
The idea is that once we get M uniform in [0,(t+1)*n) we can make it
uniform in [0,L) simply by rejecting those candidates which were too high.
This will only happen if k=t and m>=s.
Now, it seems to me that the worst case for rejection is when n=L-1, in
which case t=1, s=1, and almost one-half of all initial SK choices will
be rejected. Following Eric's reasoning, this would be an effective loss
of one bit of key length, from say 1024 to 1023, which is tolerable.
(Eric actually suggested that as many as two bits could be lost, but I
don't see that happening with this algorithm. It doesn't really matter
anyway because both 1 and 2 are so small.)
Using this algorithm with the current Stealth PGP would produce a
"truly stealthy" version which I think would be indistinguishable from
random bytes without access to the receiver's private key.
Hal
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