Abstract: A multi-step digital signature system and method is provided having a distributed root certifying authority 20. Messages received at the root certifying authority 20 are distributed to root certifying authority members 22-30 who attach partial signatures to the message using root key fragments. In the system and method provided, the system adapts to system events such as the addition or removal of key fragment holders, the need to modify key fragments, etc., by changing key fragments.

Abstract: An off-line electronic cash system having an electronic coin, a bank B, a payee S, and a user U with an account at the bank B as well as a user password z.sub.u,i, has a method for performing an electronic cash transfer. An electronic coin is withdrawn from the bank B by the user U and an electronic record of the electronic coin is stored by the bank B. The coin is paid to the payee S by the user U. The payee S deposits the coin with the bank B. A determination is made that the coin is spent and the record of the coin is deleted by the bank B. A further deposit of the same coin after the record is deleted is determined. Additionally, a determination is made which user U originally withdrew the coin after deleting the record. To perform these operations a key pair is generated by the user, including public and secret signature keys. The public signature key along with a user password z.sub.u,i and a withdrawal amount are sent to the bank B by the user U.

Abstract: An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computiThe United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.

Abstract: A secure audio teleconferencing system is disclosed. The secure teleconferencing system comprises a centralized facility or bridge to which a plurality of participants is connected. The role of the bridge is to receive encrypted message signals from the participants and to add the encrypted message signals, modulo some known number. The result is then transmitted to the participants. Each participant is able to decrypt the modular sum of encrypted message signals, to obtain the desired ordinary sum of clear text message signals. In accordance with the invention, the message signals remain encrypted throughtout processing by the bridge. There are no non-encrypted messages.