The k-BDH Assumption Family: Bilinear Map Cryptography from Progressively Weaker Assumptions

  • Karyn Benson
  • Hovav Shacham
  • Brent Waters
Conference paper

DOI: 10.1007/978-3-642-36095-4_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7779)
Cite this paper as:
Benson K., Shacham H., Waters B. (2013) The k-BDH Assumption Family: Bilinear Map Cryptography from Progressively Weaker Assumptions. In: Dawson E. (eds) Topics in Cryptology – CT-RSA 2013. CT-RSA 2013. Lecture Notes in Computer Science, vol 7779. Springer, Berlin, Heidelberg

Abstract

Over the past decade bilinear maps have been used to build a large variety of cryptosystems. In addition to new functionality, we have concurrently seen the emergence of many strong assumptions. In this work, we explore how to build bilinear map cryptosystems under progressively weaker assumptions.

We propose k-BDH, a new family of progressively weaker assumptions that generalizes the decisional bilinear Diffie-Hellman (DBDH) assumption. We give evidence in the generic group model that each assumption in our family is strictly weaker than the assumptions before it. DBDH has been used for proving many schemes secure, notably identity-based and functional encryption schemes; we expect that our k-BDH will lead to generalizations of many such schemes.

To illustrate the usefulness of our k-BDH family, we construct a family of selectively secure Identity-Based Encryption (IBE) systems based on it. Our system can be viewed as a generalization of the Boneh-Boyen IBE, however, the construction and proof require new ideas to fit the family. Our methods can be extended to produce hierarchical IBEs and CCA security; and give a fully secure variant. In addition, we discuss the opportunities and challenges of building new systems under our weaker assumption family.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Karyn Benson
    • 1
  • Hovav Shacham
    • 1
  • Brent Waters
    • 2
  1. 1.University of CaliforniaSan DiegoUSA
  2. 2.University of Texas at AustinUSA

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