Harry Yosh | Searcharxiv

arXiv2011

A solution of Dirichlet problem using second partial derivatives of boundary function

In Boundary Element Method, Green's function with no boundary conditions is used for solving Laplace's equation with Dirichlet boundary condition. To determine the gradient of solution on the boundary, we need to solve the boundary integral equation numerically in most practical cases. Here we discuss the alternative method to avert solving that boundary integral equation. It is based on the solution for Poisson's equation which has the singularity on the boundary specified by the boundary function and shown it is applicable to arbitrary shaped domain and reduces calculation cost considerably.

math.AP↗

arXiv2011

The key exchange cryptosystem used with higher order Diophantine equations

One-way functions are widely used for encrypting the secret in public key cryptography, although they are regarded as plausibly one-way but have not been proven so. Here we discuss the public key cryptosystem based on the system of higher order Diophantine equations. In this system those Diophantine equations are used as public keys for sender and recipient, and sender can recover the secret from the Diophantine equation returned from recipient with a trapdoor. In general the system of Diophantine equations is hard to solve when it is positive-dimensional and it implies the Diophantine equations in this cryptosystem works as a possible one-way function. We also discuss some problems on implementation, which are caused from additional complexity necessary for constructing Diophantine equations in order to prevent from attacking by tamperers.

cs.IT↗