Results 1 
3 of
3
ChosenCiphertext Security via Correlated Products
"... We initiate the study of onewayness 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 oneway. The main motivation of this study is the construction o ..."
Abstract

Cited by 43 (4 self)
 Add to MetaCart
(Show Context)
We initiate the study of onewayness 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 oneway. The main motivation of this study is the construction of publickey encryption schemes that are secure against chosenciphertext 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 CCAsecure publickey encryption scheme. The construction is simple, blackbox, 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 we eventually base security under correlated products on lossy trapdoor functions, we argue that the former notion is potentially weaker as a general assumption. Specifically, there is no fullyblackbox construction of lossy trapdoor functions from trapdoor functions that are secure under correlated products.
A unified approach to deterministic encryption: New constructions and a connection to computational entropy
 TCC 2012, volume 7194 of LNCS
, 2012
"... We propose a general construction of deterministic encryption schemes that unifies prior work and gives novel schemes. Specifically, its instantiations provide: • A construction from any trapdoor function that has sufficiently many hardcore bits. • A construction that provides “bounded ” multimessa ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
(Show Context)
We propose a general construction of deterministic encryption schemes that unifies prior work and gives novel schemes. Specifically, its instantiations provide: • A construction from any trapdoor function that has sufficiently many hardcore bits. • A construction that provides “bounded ” multimessage security from lossy trapdoor functions. The security proofs for these schemes are enabled by three tools that are of broader interest: • A weaker and more precise sufficient condition for semantic security on a highentropy message distribution. Namely, we show that to establish semantic security on a distribution M of messages, it suffices to establish indistinguishability for all conditional distribution ME, where E is an event of probability at least 1/4. (Prior work required indistinguishability on all distributions of a given entropy.) • A result about computational entropy of conditional distributions. Namely, we show that conditioning on an event E of probability p reduces the quality of computational entropy by a factor of p and its quantity by log 2 1/p. • A generalization of leftover hash lemma to correlated distributions. We also extend our result about computational entropy to the average case, which is useful in reasoning about leakageresilient cryptography: leaking λ bits of information reduces the quality of computational entropy by a factor of 2 λ and its quantity by λ.
CorrelatedInput Secure Hash Functions
"... Abstract. We undertake a general study of hash functions secure under correlated inputs, meaning that security should be maintained when the adversary sees hash values of many related highentropy inputs. Such a property is satisfied by a random oracle, and its importance is illustrated by study of ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We undertake a general study of hash functions secure under correlated inputs, meaning that security should be maintained when the adversary sees hash values of many related highentropy inputs. Such a property is satisfied by a random oracle, and its importance is illustrated by study of the “avalanche effect, ” a wellknown heuristic in cryptographic hash function design. One can interpret “security ” in different ways: e.g., asking for onewayness or that the hash values look uniformly and independently random; the latter case can be seen as a generalization of correlationrobustness introduced by Ishai et al. (CRYPTO 2003). We give specific applications of these notions to passwordbased login and efficient search on encrypted data. Our main construction achieves them (without random oracles) for inputs related by polynomials over the input space (namely Zp), based on corresponding variants of the qDiffie Hellman Inversion assumption. Additionally, we show relations between correlatedinput secure hash functions and cryptographic primitives secure under relatedkey attacks. Using our techniques, we are also able to obtain a host of new results for such relatedkey attack secure cryptographic primitives. 1