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Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller
- Daniele Micciancio, Chris Peikert
- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 15 April 2012
We give new methods for generating and using "strong trapdoors" in cryptographic lattices, which are simultaneously simple, efficient, easy to implement (even in parallel), and asymptotically optimal…
Foundations of Group Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions
Strong, formal definitions for the core requirements of anonymity and traceability are introduced and it is shown that these imply the large set of sometimes ambiguous existing informal requirements in the literature, thereby unifying and simplifying the requirements for this primitive.
FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second
A new method to homomorphically compute simple bit operations, and refresh (bootstrap) the resulting output, which runs on a personal computer in just about half a second, and is presented on the performance of the prototype implementation.
Worst-case to average-case reductions based on Gaussian measures
- Daniele Micciancio, O. Regev
- Computer Science, Mathematics45th Annual IEEE Symposium on Foundations of…
- 17 October 2004
It is shown that solving modular linear equation on the average is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the rank of the lattice, and it is proved that the distribution that one obtains after adding Gaussian noise to the lattices has the following interesting property.
Multicast security: a taxonomy and some efficient constructions
- R. Canetti, J. Garay, G. Itkis, Daniele Micciancio, M. Naor, Benny Pinkas
- Computer ScienceIEEE INFOCOM '99. Conference on Computer…
- 21 March 1999
A taxonomy of multicast scenarios on the Internet and an improved solution to the key revocation problem are presented, which can be regarded as a 'midpoint' between traditional message authentication codes and digital signatures.
Generalized Compact Knapsacks Are Collision Resistant
This work shows that, while the function proposed by Micciancio is not collision resistant, it can be easily modified to achieve collision resistance under essentially the same complexity assumptions on cyclic lattices.
Faster exponential time algorithms for the shortest vector problem
The main result shows that the shortest vector in any <i>n</i>-dimensional lattice can be found in time 2.199, which improves the best previously known algorithm by Ajtai, Kumar and Sivakumar and provably uses an amount of space proportional to τ-n, the "kissing" constant in dimension <i*n.
A New Paradigm for Collision-Free Hashing: Incrementality at Reduced Cost
A simple, new paradigm for the design of collision-free hash functions, where any function emanating from this paradigm is incremental, which means that rather than having to re-compute the hash of x′ from scratch, I can quickly "update" the old hash value to the new one, in time proportional to the amount of modification made in x to get x′.
- Daniele Micciancio
- Computer Science, MathematicsEncyclopedia of Cryptography and Security
This chapter describes some of the recent progress in lattice-based cryptography, which holds a great promise for post-quantum cryptography, as they enjoy very strong security proofs based on worst-case hardness, relatively efficient implementations, as well as great simplicity.