How to Fool an Unbounded Adversary with a Short Key

  • Alexander Russell
  • Hong Wang
Conference paper

DOI: 10.1007/3-540-46035-7_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2332)
Cite this paper as:
Russell A., Wang H. (2002) How to Fool an Unbounded Adversary with a Short Key. In: Knudsen L.R. (eds) Advances in Cryptology — EUROCRYPT 2002. EUROCRYPT 2002. Lecture Notes in Computer Science, vol 2332. Springer, Berlin, Heidelberg


We consider the symmetric encryption problem which manifests when two parties must securely transmit a message m with a short shared secret key. As we permit arbitrarily powerful adversaries, any encryption scheme must leak information about m - the mutual information between m and its ciphertext cannot be zero. Despite this, we present a family of encryption schemes which guarantee that for any message space in {0,1|n with minimum entropy n - l and for any Boolean function h: {0,1|n → {0,1|, no adversary can predict h(m) from the ciphertext of m with more than 1/nω(1) advantage; this is achieved with keys of length l+ω)(logn). In general, keys of length l+s yield a bound of 2−θ(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alexander Russell
    • 1
  • Hong Wang
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of ConnecticutStorrsUSA

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