Lossy trapdoor functions and their applications

  • Authors:
  • Chris Peikert;Brent Waters

  • Affiliations:
  • SRI International, Menlo Park, CA, USA;SRI International, Menlo Park, CA, USA

  • Venue:
  • STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
  • Year:
  • 2008

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Abstract

We propose a new general primitive called lossy trapdoor functions (lossy TDFs), and realize it under a variety of different number theoretic assumptions, including hardness of the decisional Diffie-Hellman (DDH) problem and the worst-case hardness of lattice problems. Using lossy TDFs, we develop a new approach for constructing several important cryptographic primitives, including (injective) trapdoor functions, collision-resistant hash functions, oblivious transfer, and chosen ciphertext-secure cryptosystems. All of the constructions are simple, efficient, and black-box. These results resolve some long-standing open problems in cryptography. They give the first known injective trapdoor functions based on problems not directly related to integer factorization, and provide the first known CCA-secure cryptosystem based solely on the worst-case complexity of lattice problems.