## Lossy Trapdoor Functions and Their Applications (2007)

Venue: | ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 80 (2007) |

Citations: | 78 - 16 self |

### BibTeX

@MISC{Peikert07lossytrapdoor,

author = {Chris Peikert and Brent Waters},

title = { Lossy Trapdoor Functions and Their Applications},

year = {2007}

}

### OpenURL

### 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 standard lattice problems. Using lossy TDFs, we develop a new approach for constructing many important cryptographic primitives, including standard trapdoor functions, CCA-secure cryptosystems, collisionresistant hash functions, and more. All of our constructions are simple, efficient, and black-box. Taken all together, 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 worst-case lattice assumptions.