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Category Archives: Cryptography
Lwe Reductions
The discrete Gaussian distribution $D_{\mathcal{L}, r}(x)$ is defined over a lattice $\mathcal{L}$ with parameter $r$ such that the probability of sampling a lattice vector $x \in \mathcal{L}$ is proportional to its weight $$ w(x) = e^{-\pi \|x\|^2 / r^2} $$ where $r$ is the Gaussian parameter, ensures that vectors closer… Continue reading
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A Decade of Lattice Cryptography
Why do we need worse-case to average-case reductions in lattice-based cryptography? Lattice hard problems are believed to be difficult to solve in the worst case. But not every instance of these problems is hard, and some instances may be easy to solve, for example when we use orthogonal basis vectors.… Continue reading
Complexity of Lattice Problems
In complexity theory, we say a problem is hard if it it hard for the worst-case instance; while in cryptography, a problem is deemed hard only if it is hard for the average-case instance (i.e., for all but a negligible fraction of instances). Basics Lattice Definition of a Lattice Continue reading
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Index
This section will collect learning notes on cryptographic primitives, protocols, and the mathematics behind their security. Planned topics Complexity of Lattice Problems Continue reading
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Index
Complexity of Lattice Problems Planned topics (notes not yet published): Continue reading