How to Fool an Unbounded Adversary with a Short Key

  • Authors:
  • Alexander Russell;Hong Wang

  • Affiliations:
  • -;-

  • Venue:
  • EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
  • Year:
  • 2002

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Abstract

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 mes- sage space in f0;1gn with minimum entropy n¡ ' and for any Boolean function h : f0;1gn ! f0;1g, no adversary can predict h(m) from the ciphertext of m with more than 1=n!(1) advantage; this is achieved with keys of length '+!(logn). In general, keys of length '+s yield a bound of 2¡£(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented e-ciently.