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Almost k-wise independent sample spaces and their cryptologic applications

Publiceringsår: 1997
Språk: Engelska
Sidor: 409-421
Publikation/Tidskrift/Serie: Advances in Cryptology / Lecture Notes in Computer Science
Volym: 1233
Dokumenttyp: Konferensbidrag
Förlag: Springer


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.


  • Electrical Engineering, Electronic Engineering, Information Engineering


International Conference on the Theory and Application of Cryptographic Techniques - EUROCRYPT'97
  • ISSN: 0302-9743
  • ISSN: 1611-3349
  • ISBN: 978-3-540-62975-7

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