Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Resettable zero-knowledge (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
The relationship between public key encryption and oblivious transfer
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
Chosen-Ciphertext Security from Identity-Based Encryption
SIAM Journal on Computing
Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
On the Impossibility of Basing Identity Based Encryption on Trapdoor Permutations
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Chosen-Ciphertext Security via Correlated Products
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Towards a separation of semantic and CCA security for public key encryption
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Deterministic and efficiently searchable encryption
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Efficient chosen-ciphertext security via extractable hash proofs
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Chosen-Ciphertext Security via Correlated Products
SIAM Journal on Computing
On black-box separations among injective one-way functions
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Adaptive trapdoor functions and chosen-ciphertext security
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Correlated product security from any one-way function
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
On the power of nonuniformity in proofs of security
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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A family of trapdoor functions is one-way under correlated inputs if no efficient adversary can invert it even when given the value of the function on multiple correlated inputs. This powerful primitive was introduced at TCC 2009 by Rosen and Segev, who use it in an elegant black box construction of a chosen ciphertext secure public key encryption. In this work we continue the study of security under correlated inputs, and prove that there is no black box construction of correlation secure injective trapdoor functions from classic trapdoor permutations, even if the latter is assumed to be one-way for inputs from high entropy, rather than uniform distributions. Our negative result holds for all input distributions where each xi is determined by the remaining n−1 coordinates. The techniques we employ for proving lower bounds about trapdoor permutations are new and quite general, and we believe that they will find other applications in the area of black-box separations.