All-But-Many Lossy Trapdoor Functions

We put forward a generalization of lossy trapdoor functions (LTFs). Namely, all-but-many lossy trapdoor functions (ABM-LTFs) are LTFs that are parametrized with tags. Each tag can either be injective or lossy, which leads to an invertible or a lossy function. The interesting property of ABM-LTFs is that it is possible to generate an arbitrary number of lossy tags by means of a special trapdoor, while it is not feasible to produce lossy tags without this trapdoor. Our definition and construction can be seen as generalizations of all-but-one LTFs (due to Peikert and Waters) and all-but-N LTFs (due to Hemenway et al.). However, to achieve ABM-LTFs (and thus a number of lossy tags which is not bounded by any polynomial), we have to employ some new tricks. Concretely, we give two constructions that employ “disguised” variants of the Waters, resp. Boneh-Boyen signature schemes to make the generation of lossy tags hard without trapdoor. In a nutshell, lossy tags simply correspond to val...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Dennis Hofheinz
• Keywords: Group Elements, IACR 2011, Polynomial Number, Valid Signatures