We show how to construct a variety of ``trapdoor'' cryptographic tools
assuming the worst-case hardness of standard lattice problems (such as
approximating the shortest nonzero vector to within small factors).
The applications include trapdoor functions with \emph{preimage
sampling}, simple and efficient ``hash-and-sign'' digital signature
schemes, universally composable oblivious transfer, ... more >>>

We construct public-key cryptosystems that are secure assuming the
\emph{worst-case} hardness of approximating the length of a shortest
nonzero vector in an $n$-dimensional lattice to within a small
$\poly(n)$ factor. Prior cryptosystems with worst-case connections
were based either on the shortest vector problem for a \emph{special
class} of lattices ... more >>>

In the {\em learning parities with noise} problem ---well-studied in learning theory and cryptography--- we
have access to an oracle that, each time we press a button,
returns a random vector $ a \in \GF(2)^n$ together with a bit $b \in \GF(2)$ that was computed as
$a\cdot u +\eta$, where ... more >>>

Motivated in part by applications in lattice-based cryptography, we initiate the study of the size of linear threshold (`$t$-out-of-$n$') secret-sharing where the linear reconstruction function is restricted to coefficients in $\{0,1\}$. We prove upper and lower bounds on the share size of such schemes. One ramification of our results is ... more >>>

Computational problems on point lattices play a central role in many areas of computer science including integer programming, coding theory, cryptanalysis, and especially the design of secure cryptosystems. In this survey, we present known results and open questions related to the complexity of the most important of these problems, the ... more >>>

A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. Avoid) and the remote point problem (abbrev. RPP). The upper and lower bounds for these meta problems provide a unified ... more >>>