Lossy Trapdoor Functions and Their Applications

We propose a general cryptographic primitive called lossy trapdoor functions (lossy TDFs), and use it to develop new approaches for constructing several important cryptographic tools, including (injective) trapdoor functions, collision-resistant hash functions, oblivious transfer, and chosen ciphertext-secure cryptosystems (in the standard model). All of these constructions are simple, efficient, and black-box. We realize lossy TDFs 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 for quantum algorithms (alternately, under an average-case hardness assumption for classical algorithms). Taken together, our 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 chosen ciphertext-secure cryptosyst...

• Type: Journal
• Year: 2007
• Where: ECCC
• Authors: Chris Peikert, Brent Waters
• Keywords: ECCC 2007, Lossy Tdfs, Lossy Trapdoor Functions, Trapdoor Functions