How to construct random functions
Journal of the ACM (JACM)
Journal of Cryptology
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Synthesizers and their application to the parallel construction of pseudo-random functions
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Chosen-Ciphertext Security via Correlated Products
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Deterministic and efficiently searchable encryption
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Correlated-input secure hash functions
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Better security for deterministic public-key encryption: the auxiliary-input setting
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Two is a crowd? a black-box separation of one-wayness and security under correlated inputs
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
More constructions of lossy and correlation-secure trapdoor functions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Cryptographic agility and its relation to circular encryption
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
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It is well-known that the k -wise product of one-way functions remains one-way, but may no longer be when the k inputs are correlated. At TCC 2009, Rosen and Segev introduced a new notion known as Correlated Product secure functions. These functions have the property that a k -wise product of them remains one-way even under correlated inputs. Rosen and Segev gave a construction of injective trapdoor functions which were correlated product secure from the existence of Lossy Trapdoor Functions (introduced by Peikert and Waters in STOC 2008). In this work we continue the study of correlated product security, and find many differences depending on whether the functions have trapdoors. The first main result of this work shows that a family of correlated product secure functions (without trapdoors) can be constructed from any one-way function. Because correlated product secure functions are trivially one-way, this shows an equivalence between the existence of these two cryptographic primitives. In the second main result of this work, we consider a natural decisional variant of correlated product security. Roughly, a family of functions is Decisional Correlated Product (DCP) secure if f 1 (x 1 ),…,f k (x 1 ) is indistinguishable from f 1 (x 1 ),…,f k (x k ) when x 1 ,…,x k are chosen uniformly at random. When considering DCP secure functions with trapdoors, we give a construction based on Lossy Trapdoor Functions, and show that any DCP secure function family with trapdoor satisfies the security requirements for Deterministic Encryption as defined by Bellare, Boldyreva and O'Neill in CRYPTO 2007. In fact, we also show that definitionally, DCP secure functions with trapdoors are a strict subset of Deterministic Encryption functions by showing an example of a Deterministic Encryption function which according to the definition is not a DCP secure function.