TY - GEN

T1 - Chosen-ciphertext security via correlated products

AU - Rosen, Alon

AU - Segev, Gil

PY - 2009

Y1 - 2009

N2 - 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 (x 1, ⋯, x k ), so that the function (f(x 1), ⋯, f(x k )) 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 a very natural correlated product can be used to construct a CCA-secure 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 lossy trapdoor functions (Peikert and Waters, STOC '08) yield injective trapdoor functions that are secure under the above mentioned correlated product. Although we currently base security under correlated products on existing constructions of lossy trapdoor functions, we argue that the former notion is potentially weaker as a general assumption. Specifically, there is no fully-black-box construction of lossy trapdoor functions from trapdoor functions that are secure under correlated products.

AB - 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 (x 1, ⋯, x k ), so that the function (f(x 1), ⋯, f(x k )) 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 a very natural correlated product can be used to construct a CCA-secure 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 lossy trapdoor functions (Peikert and Waters, STOC '08) yield injective trapdoor functions that are secure under the above mentioned correlated product. Although we currently base security under correlated products on existing constructions of lossy trapdoor functions, we argue that the former notion is potentially weaker as a general assumption. Specifically, there is no fully-black-box construction of lossy trapdoor functions from trapdoor functions that are secure under correlated products.

UR - http://www.scopus.com/inward/record.url?scp=67650674979&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-00457-5_25

DO - 10.1007/978-3-642-00457-5_25

M3 - Conference contribution

AN - SCOPUS:67650674979

SN - 3642004563

SN - 9783642004568

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 419

EP - 436

BT - Theory of Cryptography - 6th Theory of Cryptography Conference, TCC 2009, Proceedings

T2 - 6th Theory of Cryptography Conference, TCC 2009

Y2 - 15 March 2009 through 17 March 2009

ER -