Homomorphic signatures for polynomial functions
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Identity-Based (lossy) trapdoor functions and applications
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Functional encryption for threshold functions (or fuzzy IBE) from lattices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Inner-product lossy trapdoor functions and applications
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Security and Communication Networks
How to share a lattice trapdoor: threshold protocols for signatures and (H)IBE
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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We revisit the problem of generating a ‘hard’ random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptographic schemes that use such a procedure to generate public/secret key pairs. In these applications, a shorter basis corresponds to milder underlying complexity assumptions and smaller key sizes. The contributions of this work are twofold. First, we simplify and modularize an approach originally due to Ajtai (ICALP 1999). Second, we improve the construction and its analysis in several ways, most notably by making the output basis asymptotically as short as possible.