Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
Generating Hard Instances of the Short Basis Problem
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Worst-Case to Average-Case Reductions Based on Gaussian Measures
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On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
Trapdoors for hard lattices and new cryptographic constructions
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Short and Stateless Signatures from the RSA Assumption
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Asymptotically efficient lattice-based digital signatures
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Efficient identity-based encryption without random oracles
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Efficient lattice (H)IBE in the standard model
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The geometry of lattice cryptography
Foundations of security analysis and design VI
Ring signature schemes from lattice basis delegation
ICICS'11 Proceedings of the 13th international conference on Information and communications security
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
Random oracles in a quantum world
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Short signatures from weaker assumptions
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Trapdoors for lattices: simpler, tighter, faster, smaller
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Lattice signatures without trapdoors
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ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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International Journal of Electronic Security and Digital Forensics
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International Journal of High Performance Systems Architecture
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We propose a framework for adaptive security from hard random lattices in the standard model. Our approach borrows from the recent Agrawal-Boneh-Boyen families of lattices, which can admit reliable and punctured trapdoors, respectively used in reality and in simulation. We extend this idea to make the simulation trapdoors cancel not for a specific forgery but on a non-negligible subset of the possible challenges. Conceptually, we build a compactly representable, large family of input-dependent “mixture” lattices, set up with trapdoors that “vanish” for a secret subset which we hope the forger will target. Technically, we tweak the lattice structure to achieve “naturally nice” distributions for arbitrary choices of subset size. The framework is very general. Here we obtain fully secure signatures, and also IBE, that are compact, simple, and elegant.