Secure and efficient schemes to entrust the use of private keys

This paper presents a practical method which enables an owner of a private key to entrust the use of the key to an entrustee without exposing the actual key. The following are features of the method: it covers a wide variety of existing public-key cryptographic algorithms; it provides the owner of the private key with a means of preventing the entrustee from abusing the entrusted key beyond the limits which the key owner arbitrarily specifies; it only adds a very small, usually negligible, amount of overhead to calculations required in the base public-key cryptographic algorithm. An outline of our method is as follows. An owner of a private key issues to an entrustee data called a ticket through the cooperation of a trusted third party. With the ticket, the entrustee can execute calculations, which yield the same results as those using the actual private key do