A-B-a-b encryption

[David Wagner]

martin f krafft  wrote:
>it came up lately in a discussion, and I couldn't put a name to it:
>a means to use symmetric crypto without exchanging keys:
>
>  - Alice encrypts M with key A and sends it to Bob
>  - Bob encrypts A(M) with key B and sends it to Alice
>  - Alice decrypts B(A(M)) with key A, leaving B(M), sends it to Bob
>  - Bob decrypts B(M) with key B leaving him with M.
>
>Are there algorithms for this already? What's the scheme called?

It's called Pollig-Hellman.  It only works if your encryption scheme
is commutative.  Most symmetric-key encryption schemes aren't commutative,
but one scheme that does work is A(M) = M^A mod p.  One scheme that doesn't
work is A(M) = M xor A; XOR is indeed commutative, but it becomes insecure
when used in the above protocol.

Anyway, the Pollig-Hellman protocol is no better (and probably no worse)
than a straight Diffie-Hellman, so there seems to be little reason to adopt
it.  Just stick to standard Diffie-Hellman.

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