Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth 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
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
SIAM Journal on Computing
Many-to-One Trapdoor Functions and Their Ralation to Public-Key Cryptosystems
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
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
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Discrete Applied Mathematics
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Revocation Systems with Very Small Private Keys
SP '10 Proceedings of the 2010 IEEE Symposium on Security and Privacy
Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Efficient lattice (H)IBE in the standard model
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Chameleon all-but-one TDFs and their application to chosen-ciphertext security
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
On the security of a bidirectional proxy re-encryption scheme from PKC 2010
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
General construction of chameleon all-but-one trapdoor functions
ProvSec'11 Proceedings of the 5th international conference on Provable security
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
All-But-Many lossy trapdoor functions
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Identity-Based (lossy) trapdoor functions and applications
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Selective opening chosen ciphertext security directly from the DDH assumption
NSS'12 Proceedings of the 6th international conference on Network and System Security
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To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.