Bounded-Collusion IBE from Key Homomorphism

  • Shafi Goldwasser
  • Allison Lewko
  • David A. Wilson
Conference paper

DOI: 10.1007/978-3-642-28914-9_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7194)
Cite this paper as:
Goldwasser S., Lewko A., Wilson D.A. (2012) Bounded-Collusion IBE from Key Homomorphism. In: Cramer R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg

Abstract

In this work, we show how to construct IBE schemes that are secure against a bounded number of collusions, starting with underlying PKE schemes which possess linear homomorphisms over their keys. In particular, this enables us to exhibit a new (bounded-collusion) IBE construction based on the quadratic residuosity assumption, without any need to assume the existence of random oracles. The new IBE’s public parameters are of size O(logI) where I is the total number of identities which can be supported by the system, t is the number of collusions which the system is secure against, and λ is a security parameter. While the number of collusions is bounded, we note that an exponential number of total identities can be supported.

More generally, we give a transformation that takes any PKE satisfying Linear Key Homomorphism, Identity Map Compatibility, and the Linear Hash Proof Property and translates it into an IBE secure against bounded collusions. We demonstrate that these properties are more general than our quadratic residuosity-based scheme by showing how a simple PKE based on the DDH assumption also satisfies these properties.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shafi Goldwasser
    • 1
  • Allison Lewko
    • 2
  • David A. Wilson
    • 3
  1. 1.MIT CSAIL and Weizmann InstituteUSA
  2. 2.UT AustinUSA
  3. 3.MIT CSAILUSA

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