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DA-Encrypt: Homomorphic Encryption via Non-Archimedean Diophantine Approximation --- Preliminary Report
homomorphic encryption lattice-based cryptography
2015/12/23
We give a theoretical description of a new homomorphic encryption
scheme DA-Encrypt that is based on (non-archimedean) Diophantine
Approximation.
PERIODIC BOXCAR DECONVOLUTION AND DIOPHANTINE APPROXIMATION
BOXCAR DECONVOLUTION DIOPHANTINE APPROXIMATION
2015/8/20
We consider the nonparametric estimation of a periodic function that is
observed in additive Gaussian white noise after convolution with a “boxcar,”
the indicator function of an interval. This is an...
Diophantine approximation with restricted numerators and denominators on semisimple groups
Diophantine approximation restricted numerators and denominators semisimple groups Dynamical Systems
2012/5/25
We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numera- tors and denominators and establish a quantitative approximation result f...
Inhomogeneous theory of dual Diophantine approximation on manifolds
Metric Diophantine approximation extremal manifolds
2010/12/14
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is e...
Polynomial estimates, exponential curves and Diophantine approximation
Polynomial estimates exponential curves Diophantine approximation
2010/12/10
Let ∈ (0, 1) \ Q and K = {(ez, e z) : |z| ≤ 1} ⊂ C2. If P is a polynomial of degree n in C2, normalized by kPkK = 1, we obtain sharp estimates for kPk2 in terms of n, where 2 is the closed u...