From: Gary Howland <gary@systemics.com>
Date: Sat, 1 Jun 1996 09:11:37 +0800
To: cypherpunks@toad.com
Subject: Re: Backdoor in RSA Discovered
Message-ID: <199605311811.UAA10519@internal-mail.systemics.com>
MIME-Version: 1.0
Content-Type: text/plain



>  In this paper we present a mechanism that can quite easily be
>  added to PGP that allows the person who modifies PGP to learn
>  the private keys of those who use it to generate keys. Furthermore
>  the keys are leaked securely and subliminally, i.e. even if you
>  analyze the source code you cannot determine previously generated
>  keys or future keys, only the attacker can. The only way to detect the
>  presence of the mechanism itself is by looking over the source code, or
>  the compiled code. The attack has the effect of turning a database of
>  public keys into a database of public/private key pairs with respect to
>  the attacker *exclusively*.

Sounds like they are doing something like this:

        Generate a prime P of 500 bits (say)
        Encrypt with Mallets public key
        Generate start_q using (E(P) << 524)/P
        Keep incrementing start_q until prime, and call this Q
        Generate N by multiplying P and Q to get a 1024 bit key
        Top 500 bits of N will be E(P)

It could also be done like this:

        Generate a random H of, say, 290 bits
        Keep incrementing H until (H << 300) + 1 is prime
        and call this Q
        Encrypt H for Mallet
        H <<= 10
        Keep incrementing H until prime
        Generate N by multiplying P by Q, to get a 900 bit key
        Bottom 300 (but 10) bits of N will E(P)

I'm sure there are few mistakes, and there need to be
a few other trivial tests in there somewhere, but I think this
should work.

The first method should produce "better" keys than the first
(as if Mallet cares)

I'll try and knock some code up to demonstrate this over the next
few days.


Gary
--
pub  1024/C001D00D 1996/01/22  Gary Howland <gary@systemics.com>
Key fingerprint =  0C FB 60 61 4D 3B 24 7D  1C 89 1D BE 1F EE 09 06