I'm just wondering is there any possible way for differant keys to be passed between processes and still be symmetrical? I am currently going through an old exam paper and have come across this and it's racking my brains!

To quote :
Using GF(2) on a polynomial basis, show mathematically that it would be possible to exchange data securely by means of the symmetric cryptographic techqnique when the sender and recipient of the data had different keys.

Thanks in advance. Everything else I think I am ok with, but this one has been a real teaser.