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There are well-known techniques for message authentication using universal hash functions. This approach seems very promising, as it provides schemes that, are: both efficient and provably secure under reasonable assumptions. This paper contributes to this line of research in two ways. First, it analyzes the basic construction and some variants under more realistic and practical assumptions. Second, it shows how these schemes can be efficiently implemented, and it reports on the results of empirical performance tests that demonstrate that these schemes arc competitive with other commonly employed schemes whose security is less well-established.