Fast simulation of large-scale growth models

We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process. Starting from an approximation for the odometer, we successively correct under- and overestimates and provably arrive at the correct final state. Internal diffusion-limited aggregation (IDLA) is one of the models amenable to our technique. The boundary fluctuations in IDLA were recently proved to be at most logarithmic in the size of the growth cluster, but the constant in front of the logarithm is still not known. As an application of our method, we calculate the size of fluctuations over two orders of magnitude beyond previous simulations, and use the results to estimate this constant.Comment: 27 pages, 9 figures. To appear in Random Structures & Algorithm

Random number generation with multiple streams for sequential and parallel computing

International audienceWe provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing

Testing the Randomness of Cryptographic Function Mappings

A cryptographic function with a fixed-length output, such as a block cipher, hash function, or message authentication code (MAC), should behave as a random mapping. The mapping\u27s randomness can be evaluated with statistical tests. Statistical test suites typically used to evaluate cryptographic functions, such as the NIST test suite, are not well-suited for testing fixed-output-length cryptographic functions. Also, these test suites employ a frequentist approach, making it difficult to obtain an overall evaluation of the mapping\u27s randomness. This paper describes CryptoStat, a test suite that overcomes the aforementioned deficiencies. CryptoStat is specifically designed to test the mappings of fixed-output-length cryptographic functions, and CryptoStat employs a Bayesian approach that quite naturally yields an overall evaluation of the mappings\u27 randomness. Results of applying CryptoStat to reduced-round and full-round versions of the AES block ciphers and the SHA-1 and SHA-2 hash functions are reported; the results are analyzed to determine the algorithms\u27 randomness margins

Sampling Algorithms for Evolving Datasets

Perhaps the most flexible synopsis of a database is a uniform random sample of the data; such samples are widely used to speed up the processing of analytic queries and data-mining tasks, to enhance query optimization, and to facilitate information integration. Most of the existing work on database sampling focuses on how to create or exploit a random sample of a static database, that is, a database that does not change over time. The assumption of a static database, however, severely limits the applicability of these techniques in practice, where data is often not static but continuously evolving. In order to maintain the statistical validity of the sample, any changes to the database have to be appropriately reflected in the sample. In this thesis, we study efficient methods for incrementally maintaining a uniform random sample of the items in a dataset in the presence of an arbitrary sequence of insertions, updates, and deletions. We consider instances of the maintenance problem that arise when sampling from an evolving set, from an evolving multiset, from the distinct items in an evolving multiset, or from a sliding window over a data stream. Our algorithms completely avoid any accesses to the base data and can be several orders of magnitude faster than algorithms that do rely on such expensive accesses. The improved efficiency of our algorithms comes at virtually no cost: the resulting samples are provably uniform and only a small amount of auxiliary information is associated with the sample. We show that the auxiliary information not only facilitates efficient maintenance, but it can also be exploited to derive unbiased, low-variance estimators for counts, sums, averages, and the number of distinct items in the underlying dataset. In addition to sample maintenance, we discuss methods that greatly improve the flexibility of random sampling from a system's point of view. More specifically, we initiate the study of algorithms that resize a random sample upwards or downwards. Our resizing algorithms can be exploited to dynamically control the size of the sample when the dataset grows or shrinks; they facilitate resource management and help to avoid under- or oversized samples. Furthermore, in large-scale databases with data being distributed across several remote locations, it is usually infeasible to reconstruct the entire dataset for the purpose of sampling. To address this problem, we provide efficient algorithms that directly combine the local samples maintained at each location into a sample of the global dataset. We also consider a more general problem, where the global dataset is defined as an arbitrary set or multiset expression involving the local datasets, and provide efficient solutions based on hashing

Architectural support for enhancing security in clusters

Cluster computing has emerged as a common approach for providing more comput- ing and data resources in industry as well as in academia. However, since cluster computer developers have paid more attention to performance and cost e±ciency than to security, numerous security loopholes in cluster servers come to the forefront. Clusters usually rely on ¯rewalls for their security, but the ¯rewalls cannot prevent all security attacks; therefore, cluster systems should be designed to be robust to security attacks intrinsically. In this research, we propose architectural supports for enhancing security of clus- ter systems with marginal performance overhead. This research proceeds in a bottom- up fashion starting from enforcing each cluster component's security to building an integrated secure cluster. First, we propose secure cluster interconnects providing con- ¯dentiality, authentication, and availability. Second, a security accelerating network interface card architecture is proposed to enable low performance overhead encryption and authentication. Third, to enhance security in an individual cluster node, we pro- pose a secure design for shared-memory multiprocessors (SMP) architecture, which is deployed in many clusters. The secure SMP architecture will provide con¯dential communication between processors. This will remove the vulnerability of eavesdrop- ping attacks in a cluster node. Finally, to put all proposed schemes together, we propose a security/performance trade-o® model which can precisely predict performance of an integrated secure cluster