One possible algorithm for shuffling cards without the use of a trusted third party is to use a commutative encryption scheme. A commutative scheme means that if some data is encrypted more than once, the order in which you decrypt this data will not matter.

Example: Alice has a plaintext message. She encrypts this, producing a garbled ciphertext which she gives this to Bob. Bob encrypts the ciphertext again, using the same scheme as Alice but with another key. When decrypting this double encrypted message, if the encryption scheme is commutative, it will not matter who decrypts first.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.