AbstractIn the traditional scenario in cryptography there is one sender, one receiver and an active or passive eavesdropper who is an opponent. Large bank transactions require two people to sign, implying two senders. So the power to generate a valid transaction is shared. Threshold cryptography allows one to share the power of a cryptosystem. Threshold cryptosystems are distinct from threshold schemes in which the power to regenerate a secret key is shared. A normal threshold scheme is not directly suited for threshold signatures. Using a threshold scheme directly would require the shareholders to send their shares to a trusted person who would apply the cryptosystem for them. But the use of such a trusted person violates the main point of threshold cryptography. We motivate the need for treshold cryptosystems, overview the research in the field, and give some simple examples. We will conclude by giving a list of open problems.