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Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller

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…
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Worst-case to average-case reductions based on Gaussian measures

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.
IEEE (opens in a new tab)

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.
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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.
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Multicast security: a taxonomy and some efficient constructions

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.
IEEE (opens in a new tab)

Complexity of lattice problems - a cryptographic perspective

This chapter discusses low-Degree Hypergraphs, Cryptographic Functions, and Interactive Proof Systems, and some of the algorithms used in these systems.

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.
ACM (opens in a new tab)

A deterministic single exponential time algorithm for most lattice problems based on voronoi cell computations

A new method to solve the closest vector problem with preprocessing (CVPP) that uses the Voronoi cell of the lattice (described as intersection of half-spaces) as the result of the preprocessing function is given.
ACM (opens in a new tab)

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.
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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′.
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