Chosen-Ciphertext Security via Correlated Products

We initiate the study of one-wayness under correlated products. We are interested in identifying necessary and sufficient conditions for a function f and a distribution on inputs (x1, . . . , xk), so that the function (f(x1), . . . , f(xk)) is one-way. The main motivation of this study is the construction of public-key encryption schemes that are secure against chosen-ciphertext attacks (CCA). We show that any collection of injective trapdoor functions that is secure under very natural correlated products can be used to construct a CCA-secure public-key encryption scheme. The construction is simple, black-box, and admits a direct proof of security. We provide evidence that security under correlated products is achievable by demonstrating that any collection of lossy trapdoor functions, a powerful primitive introduced by Peikert and Waters (STOC '08), yields a collection of injective trapdoor functions that is secure under the above mentioned natural correlated products. Although ...

• Type: Conference
• Year: 2009
• Where: TCC
• Authors: Alon Rosen, Gil Segev
• Keywords: Correlated Products, Cryptography, Injective Trapdoor Functions, Lossy Trapdoor Functions, TCC 2009