Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > LATTICE-BASED CRYPTOGRAPHY:
Reports tagged with Lattice-based cryptography:
TR07-133 | 20th November 2007
Craig Gentry, Chris Peikert, Vinod Vaikuntanathan

#### Trapdoors for Hard Lattices and New Cryptographic Constructions

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 >>>

TR08-100 | 14th November 2008
Chris Peikert

#### Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem

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 >>>

TR10-066 | 14th April 2010
Sanjeev Arora, Rong Ge

#### Learning Parities with Structured Noise

Revisions: 1

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 >>>

TR21-050 | 2nd April 2021
Marshall Ball, Alper Cakan, Tal Malkin

#### Linear Threshold Secret-Sharing with Binary Reconstruction

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 >>>

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