arXiv subjects

Shen Lu

Publications and source records attributed to Shen Lu.

3 recordsLinked to original sources

arXiv2021

The Design of the User Interfaces for Privacy Enhancements for Android

We present the design and design rationale for the user interfaces for Privacy Enhancements for Android (PE for Android). These UIs are built around two core ideas, namely that developers should explicitly declare the purpose of why sensitive data is being used, and these permission-purpose pairs should be split by first party and third party uses. We also present a taxonomy of purposes and ways of how these ideas can be deployed in the existing Android ecosystem.

cs.CR↗

arXiv2021

Constructing equivalence bimodules between noncommutative solenoids: a two-pronged approach

We revisit and generalize the application of a method introduced by Latrémolière and Packer for constructing finitely generated projective modules over the noncommutative solenoid C*-algebras. By realizing them as direct limits of rotation algebras, the method constructs directed systems of equivalence bimodules between rotation algebras that satisfy the necessary compatibility conditions to build Morita equivalence bimodules between the direct limit C*-algebras. In the irrational case, we use a fixed projection in a matrix algebra over the rotation algebra satisfying a key condition to build an equivalence bimodule at each stage following a construction of Rieffel. From this, our main result shows that two irrational noncommutative solenoids are Morita equivalent if and only if such a projection exists. We also make additional observations about the Heisenberg bimodules construction studied by the aforementioned two authors and connect the two constructions.

math.OA↗

arXiv2015

New algorithms for modular inversion and representation by binary quadratic forms arising from structure in the Euclidean algorithm

We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by the binary quadratic form $x^2 + 3xy + y^2$. The Euclidean algorithm is commenced with inputs from one of the families, and the first remainder less than a predetermined size produces the modular inverse or representation.

math.NT↗