From: Karl Lui Barrus <klbarrus@owlnet.rice.edu>
Date: Tue, 5 Oct 93 20:39:11 PDT
To: cypherpunks@toad.com
Subject: Re: Crypto Idea; Multi-Part Sigs
In-Reply-To: <9310050349.AA04200@alumni.cco.caltech.edu>
Message-ID: <9310060336.AA11903@flammulated.owlnet.rice.edu>
MIME-Version: 1.0
Content-Type: text/plain


nobody@alumni.cco.caltech.edu wrote:

>Is it possible to produce a set of keys (for example, 3 private 1 public)
>such that       -all three private keys are needed to sign a message from that
>                I.D.  and
>                -any of the private keys can decrypt anything encrypted with
>                the single pubkey.
>

An excellent paper (author and title have slipped my mind - the paper
describes key-and, key-or, and other operations) describes how to do
something related to part 2 of the above.

In that scheme, you would have the three key pairs for the
individuals, Pa, Sa, Pb, Sb, Pc, Sc, and the "joint" keypair Pj, Sj.  

A message encrypted with Pj can only be unlocked with Sj, which in
turn is encrypted with Pa, Pb, Pc.  Thus, the final message looks like

E(M, Pj); E(Sj, Pa); E(Sj, Pb); E(Sj, Pc)

where the four parts are passed around as one, and E(a,b) means a
encrypted with b.  Thus, each of the individuals, knowing their own
private keys, can extract Sj, and then the message M.

Offhand, I'm not sure if the paper describes joint signings in this
manner.

-- 
Karl L. Barrus: klbarrus@owlnet.rice.edu         
keyID: 5AD633 hash: D1 59 9D 48 72 E9 19 D5  3D F3 93 7E 81 B5 CC 32 

"One man's mnemonic is another man's cryptography" 
  - my compilers prof discussing file naming in public directories