Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Public-key cryptosystems provably secure against chosen ciphertext attacks
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Communications of the ACM
Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
SIAM Journal on Computing
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
Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Practical Chosen Ciphertext Secure Encryption from Factoring
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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
Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
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
CCA proxy re-encryption without bilinear maps in the standard model
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key 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
Adaptive trapdoor functions and chosen-ciphertext security
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Lossy functions do not amplify well
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Dual projective hashing and its applications -- lossy trapdoor functions and more
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
On homomorphic encryption and chosen-ciphertext security
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
NTRUCCA: how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Lossy trapdoor functions from homomorphic reproducible encryption
Information Processing Letters
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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Lossy Trapdoor Functions (LTDFs), introduced by Peikert and Waters (STOC 2008) have been useful for building many cryptographic primitives. In particular, by using an LTDF that loses a (1−1/ω(logn)) fraction of all its input bits, it is possible to achieve CCA security using the LTDF as a black-box. Unfortunately, not all candidate LTDFs achieve such a high level of lossiness. In this paper we drastically lower the lossiness required to achieve CCA security, showing that an LTDF that loses only a noticeable fraction of a single bit can be used in a black-box way to build CCA-secure PKE. To show our result, we build on the recent result of Rosen and Segev (TCC 2009) that showed how to achieve CCA security from functions whose products are one-way on particular types of correlated inputs. Lastly, we give an example construction of a slightly lossy TDF based on the assumption that it is hard to distinguish the product of two primes from the product of three primes.