Almost k-wise independent sample spaces and their cryptologic applications

  • Authors:

  • Kaoru Kurosawa;Thomas Johansson;Douglas Stinson

  • Affiliations:

  • Dept. of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan;Dept. of Information Technology, Lund University, Lund, Sweden;Dept. of Computer Science and Engineering, University of Nebraska, Lincoln, NE

  • Venue:
  • EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
  • Year:
  • 1997

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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(k2). We also introduce the concept of Ɛ-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 Ɛ-almost k- resilient functions.