Math

Finding a Close Point in a Lattice

Reference [Bab85] On Lovász’ lattice reduction and the nearest lattice point problem [Kle00] Finding the closest lattice vector when it’s unusually close [GPV08] Trapdoors for Hard Lattices and New Cryptographic Constructions [DP16] Fast Fourier Orthogonalization [GMRR22] Power analysis attacks on falcon.

Jul 10, 2023 6 min read Note

Principal Component Analysis (PCA)

Principal Component Analysis (PCA) can be viewed as a linear transform which maps a $n$-dimensional random vector to a smaller dimensional vector, but preserving most of its information.

Nov 15, 2022 3 min read Note

Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD) is a way to decompose any real matrix $A \in \mathbb{R}^{m\times n}$ into a simple form. $$ A = U\Sigma V^T $$ where $U \in \mathbb{R}^{m \times m}$ and $V \in \mathbb{R}^{n \times n}$ and $\Sigma \in \mathbb{R}^{m \times n}$ is a matrix with only diagonal values.

Nov 15, 2022 3 min read Note