Cryptographic operations are normally carried out by a single machine. Sometimes, however, this machine cannot be trusted completely. Threshold cryptography offers an alternative where the cryptographic operation is distributed to a group of machines in such a way that the key used in the cryptographic operation is not revealed to anyone. The tool used to achieve this is threshold secret sharing, by which a secret can be distributed among a group so that subsets (of the members of the group) that are larger than some threshold can cooperate to recover the secret, while subsets smaller than this threshold cannot.

This thesis concerns distributed stream ciphers which is a generalisation of threshold cryptography in the sence that the suggested scheme is not restricted to the use of threshold secret sharing schemes. We describe how to do distributed decryption of a ciphertext encrypted by an additive stream cipher. The system works for any secret sharing scheme that is linear under addition.

We present a modification of how secret sharing of sequences is done. Due to this modification we can generate shares locally using linear feedback shift registers instead of transmitting shares of each symbol in a sequence. A distributed decryption scheme where the keystream is distributed in this modified way is constructed.