How to Fool an Unbounded Adversary with a Short Key

  • Alexander Russell
  • Hong Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2332)


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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