A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Efficient oblivious transfer protocols
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Circular-Secure Encryption from Decision Diffie-Hellman
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
A Framework for Efficient and Composable Oblivious Transfer
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
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Deterministic and efficiently searchable encryption
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Circular and leakage resilient public-key encryption under subgroup indistinguishability
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Smooth projective hashing and two-message oblivious transfer
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications 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
On homomorphic encryption and chosen-ciphertext security
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Leakage-resilient lossy trapdoor functions and public-key encryption
Proceedings of the first ACM workshop on Asia public-key cryptography
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Lossy Trapdoor Functions (LTFs) were introduced by Peikert and Waters in STOC '08 and since then have found many applications and have proven to be an extremely useful and versatile cryptographic primitive. Lossy trapdoor functions were used to build the first injective trapdoor functions based on DDH, the first IND-CCA cryptosystems based on lattice assumptions, and they are known to imply deterministic encryption, collision resistant hash-functions, oblivious transfer and a host of other important primitives. While LTFs can be instantiated under most known cryptographic hardness assumptions, no constructions until today existed based on generic cryptographic primitives. In this work, we show that any Homomorphic Smooth Hash Proof System, introduced by Cramer and Shoup in EUROCRYPT '02, can be used to construct LTFs. In addition to providing a connection between two important cryptographic primitives --- our construction implies the first construction of LTFs based on the QR assumption. Smooth Hash Proof Systems (SHPs) can be seen as a generalization of the DDH assumption, yet can be built on other cryptographic assumptions, such as the DCR or QR assumptions. Yet, until today, a "translation" of results proven secure under DDH to results under DCR or QR has always been fraught with difficulties. Thus, as our second goal of this paper, we ask the following question: is it possible to streamline such translations from DDH to QR and other primitives? Our second result formally provides this connection. More specifically, we define an Extended Decisional Diffie Hellman (EDDH) assumption, which is a simple and natural generalization of DDH. We show that EDDH can be instantiated under both the DCR and QR assumptions. This gives a much simpler connection between the DDH and the DCR and QR assumptions and provides an easy way to translate proofs from DDH to DCR or QR. That is, the advantage of the EDDH assumption is that most schemes (including LTFs) proven secure under the DDH assumption can easily be instantiated under the DCR and QR assumptions with almost no change to their proofs of security.