Abstract
An almost k-wise independent sample space is a small subset of m bit sequences in which any k bits are “almost independent”. We show that this idea has close relationships with useful cryptologic notions such as multiple authentication codes (multiple A-codes), almost strongly universal hash families and almost k-resilient functions.
We use almost k-wise independent sample spaces to construct new efficient multiple A-codes such that the number of key bits grows linearly as a function of k (here k is the number of messages to be authenticated with a single key). This improves on the construction of Atici and Stinson [2], in which the number of key bits is Ω (k 2).
We also introduce the concept of ∈-almost k-resilient functions and give a construction that has parameters superior to k-resilient functions.
Finally, new bounds (necessary conditions) are derived for almost k-wise independent sample spaces, multiple A-codes and balanced ε-almost k-resilient functions.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kurosawa, K., Johansson, T., Stinson, D. (1997). Almost k-wise Independent Sample Spaces and Their Cryptologic Applications. In: Fumy, W. (eds) Advances in Cryptology — EUROCRYPT ’97. EUROCRYPT 1997. Lecture Notes in Computer Science, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69053-0_28
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DOI: https://doi.org/10.1007/3-540-69053-0_28
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