Annual International Cryptology Conference

CRYPTO 1998: Advances in Cryptology — CRYPTO '98 pp 283-298

Many-to-one trapdoor functions and their relation to public-key cryptosystems

  • Mihir Bellare
  • Shai Halevi
  • Amit Sahai
  • Salil Vadhan
Conference paper

DOI: 10.1007/BFb0055735

Volume 1462 of the book series Lecture Notes in Computer Science (LNCS)

Abstract

The heart of the task of building public key cryptosystems is viewed as that of“making trapdoors;” in fact, public key cryptosystems and trapdoor functions are often discussed as synonymous. How accurate is this view? In this paper we endeavor to get a better understanding of the nature of“trapdoorness” and its relation to public key cryptosystems, by broadening the scope of the investigation: we look at general trapdoor functions; that is, functions that are not necessarily injective (ie., one-to-one). Our first result is somewhat surprising: we show that non-injective trapdoor functions (with super-polynomial pre-image size) can be constructed from any one-way function (and hence it is unlikely that they suffice for public key encryption). On the other hand, we show that trapdoor functions with polynomial pre-image size are sufficient for public key encryption. Together, these two results indicate that the pre-image size is a fundamental parameter of trapdoor functions. We then turn our attention to the converse, asking what kinds of trapdoor functions can be constructed from public key cryptosystems. We take a first step by showing that in the random-oracle model one can construct injective trapdoor functions from any public key cryptosystem.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Mihir Bellare
    • 1
  • Shai Halevi
    • 2
  • Amit Sahai
    • 3
  • Salil Vadhan
    • 3
  1. 1.Dept. of Computer Science & EngineeringUniversity of California at San DiegoLa JollaUSA
  2. 2.T. J. Watson Research CenterIBMYorktown HeightsUSA
  3. 3.MIT Laboratory for Computer ScienceCambridgeUSA