Coercion-proof remailers (solved?)

[Mike Ingle <inglem@adnetsol.com>]

For a while I've been talking about the importance of a robust
infrastructure for anonymity, including coercion-resistant remailers.
Here is an approach that appears to eliminate the problem of
after-the-fact coercion.

Existing remailers chain messages by using a fixed public/secret key
pair in each remailer. This leaves them open to after-the-fact
compromise from the sender end. If you capture a message as the sender
sends it, you can later get the key of the first remailer, and decrypt
the first layer. You can then proceed on down the line to the
recipient. This creates a motive for an attacker to coerce remailers,
and it means the value of the remailers' keys continually increase as
more messages are sent.

Instead of using a fixed key, the sender can perform a Diffie-Hellman
exchange with the recipient at each point in a message's passage. This
eliminates the coercion problem, since there is no permanent key to
steal, but allows a corrupt remailer to see where the message is going.
If the first remailer is corrupt, the whole path is compromised.

The next step is to make sure there is no first remailer.

The sender S generates a message and header requesting mailing     S
to the recipient R. The sender splits it into two pieces using    / \
a method that requires both pieces to recover any data. Then he  1   2
adds a header to each piece requesting remailing to remailer 3.   \ /
He sends one piece to remailer 1 and one piece to remailer 2.      3
The transmissions are protected by DH exchange and encryption.     |
Remailers 1 and 2 each send their pieces to remailer 3. These      R
transmissions are also protected by DH exchanges. Remailer 3
combines the two pieces, recovers the header requesting remailing
to R, and sends the recovered message to R.

This approach is secure against after-the-fact coercion or key theft,
because there is no persistent key to recover. It is also secure
against any one of the three remailers being corrupt. If 3 is corrupt,
it sees both pieces as it combines them, and knows they came from 1 and
2, but does not know where 1 and 2 got them from. If 1 is corrupt, it
knows that a message from S went to 3, but it has only half of the
split message, so it can't find out where 3 sent it to. If any two of
the three are corrupt, the path is exposed.

It is possible to add more levels. This one uses seven remailers,  /S\
and can survive any two being corrupt. Some questions I don't    / | | \
know the answers to: What is the best possible arrangement of   1  2 3  4
remailers, so that the highest percentage of them have to be     \ / \ /
corrupt before the path is revealed? If any continuous line       5   6
from S to R is corrupt, the path is revealed. And if any two       \ /
remailers in a 'triangle' are corrupt, the whole triangle is        7
corrupt. For example, 1 and 2, 1 and 5, or 2 and 5.                 |
Is there a better arrangement, reusing some remailers, that         R
allows the message to remain secure with a higher number of corrupt
remailers in the path?

							Mike