Batch verification can provide large computational savings when several signatures, or other constructs, are verified together. Several batch verification algorithms have been published in recent years, in particular for both DSA-type and RSA signatures. We describe new attacks on several of these published schemes. A general weakness is explained which applies to almost all known batch verifiers for discrete logarithm based signature schemes. It is shown how this weakness can be eliminated given extra properties about the underlying group structure. A new general batch verifier for exponentiation in any cyclic group is also described as well as a batch verifier for modified RSA signatures.

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While the functional requirements of a system can be effectively modeled through the use case driven approach, there is no standard or de facto method for modeling non-functional requirements (NFR) of the system architecture. Often such requirements are dealt with in a reactive manner, rather than proactively. Yet increasingly a contributing factor in project difficulty and failure are the NFR imposed on the solution architecture. This paper outlines a control case approach to record and model NFR. This technique enables the control case to represent the NFR from different perspectives, most typically the various operating conditions. We also propose an extension to the ''4 + 1'' view model for depicting software architecture by adding the control case view. In addition, a detailed control case modeling example is illustrated to demonstrate how these techniques may be applied during development. Taken together, we suggest that the combination of both the use case and control case views thus reflects the complete requirements across the collective system life cycle views: design, process, implementation and deployment.

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