Recognition of Cheating in Secret Sharing Schemes by Tests on Consistency
Abstract
Secret Sharing Schemes are systems, in which a secret is distributed in such a way on a potentially large group of participants, that only determined, predefined user groups have access to this secret. Such groups of participants are called admissible. All other groups of participants do not receive any information about the central secret. For this purpose partial secrets are assigned to the participants. From the partial secrets of a admissible set of participants an access control instance can reconstruct the secret. A participant is called cheater, if he brings a partial secret into the reconstruction process, that differs from the one assigned to him.. Such a cheat is to be discovered with probability given in advance, since a cheat can provide under certain circumstances information about the actual secret or convince the other participants of a wrong secret. The available thesis presents tests, which can recognize such a cheat and under certain conditions also can expose the cheater. For the execution of the tests reconstructions for different subsets of the participant set are accomplished several times. From the consistency of the reconstruction results are derived statements about the reliability of the received secret. The tests are presented for the three most well-known Secret sharing Schemes. These are: As basis for the tests "minimum participant sets" are defined. Those are admissible participant sets, which become inadmissible by exclusion of any participant. For every of these minimum subsets of a participant configuration the reconstruction is accomplished. From the consistency of the results safety statements are derived. Realization of Secret sharing Schemes is frequently done in PG(d,q), the finite projective geometry of the dimension d and the order q. The probabilities, with which a cheater in the three examined systems in the geometrical realization is discovered, is determined here. Contrary to tests developed so far, the presented consistency tests get along without any additional information. An has to control instance only has to reconstruct repeated; an ability, which such an instance must have also without execution of consistency tests.
Threshold Schemes
multi-level Schemes
Compartment Schemes
