Abstract: A proactive threshold secret sharing cryptosystem using a set of servers. The cryptosystem is a threshold cryptosystem, in the sense that service is maintained if at least (k+1) out of n servers are active and honest. The secret signature key is compromised only if the adversary breaks into at least (k+1) servers. It is robust in the sense that the honest servers detect faulty ones and the service is not disrupted. It is recoverable, because if the adversary erases all the local information on the server it compromised, the information can be restored as soon as the server comes back to performing the correct protocol. The method and system has proactiveness, which means that in order to learn the secret, the adversary has to break into (k+1) servers during the same round of the algorithm because the shares of the secret are periodically redistributed and rerandomized. The present invention uses a verifiable secret sharing mechanism to get the security requirements during the update between two rounds.

Abstract: A method and apparatus for determining when a original document has been altered. With this invention the original information in the document is hashed using a one-way hash function. The hashed information is then encoded into a number of fingerprint pieces which are then transmitted to a number of locations. To verify the originality of the document a minimum number of fingerprint pieces are decoded and the purported genuine document is hashed using the one-way hash function. If the results of the latter hash equal the results of decoding the minimum number of fingerprint pieces, then the purported document is accepted as the genuine document.

Abstract: A method of verifying the authenticity of a message transmitted from a sender to a receiver in a communication system is partitioned into three stages. In the first stage, a key is secretly exchanged between the sender and receiver. This key is a binary irreducible polynomial p(x) of degree n. In addition, the sender and receiver share an encryption key composed of a stream of secret random, or pseudo-random bits. In the second stage, the sender appends a leading non-zero string of bits, which, in the simplest case, may be a single "1" bit, and n tail bits "0" to M to generate an augmented message, this augmented message considered as a polynomial having coefficients corresponding to the message bits. If the length of the message is known and cryptographically verified, then there is no need for a leading "1". The sender then computes a polynomial residue resulting from the division of the augmented message polynomial generated by the key polynomial p(x) exchanged by the sender and receiver.