More Constructions of Lossy and Correlation-Secure Trapdoor Functions

We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC ’08), and correlation-secure trapdoor functions (Rosen and Segev, TCC ’09). Our constructions widen the set of number-theoretic assumptions upon which these primitives can be based, and are summarized as follows: • Lossy trapdoor functions based on the quadratic residuosity assumption. Our construction relies on modular squaring, and whereas previous such constructions were based on seemingly stronger assumptions, we present the first construction that is based solely on the quadratic residuosity assumption. We also present a generalization to higher order power residues. • Lossy trapdoor functions based on the composite residuosity assumption. Our construction guarantees essentially any required amount of lossiness, where at the same time the functions are more efficient than the matrix-based approach of Peikert and Waters. • Lossy trapdoor functions based on the d-Linear assum...

• Type: Conference
• Year: 2010
• Where: PKC
• Authors: David Mandell Freeman, Oded Goldreich, Eike Kiltz, Alon Rosen, Gil Segev
• Keywords: Correlation-secure Trapdoor Functions, Cryptology, Lossy Trapdoor Functions, PKC 2010, Residuosity Assumption