Elliptic curves are some specific type of curves known as hyper elliptic curves. Compared to the integer factorization problem(IFP) based systems, using elliptic curve based cryptography will significantly decrease key size of the encryption. Therefore, application of this type of cryptography in systems that need high security and smaller key size has found great attention. Hyperelliptic curve...

In this work, we propose an algorithm to produce the double-base chain that optimizes the time used for computing an elliptic curve scalar multiplication, i.e. the bottleneck operation of the elliptic curve cryptosystem. The double-base number system and its subclass, double-base chain, are the representation that combines the binary and ternary representations. The time is measured as the weig...

We present our recent results on the mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the potential flow equation. The shock diffraction problem can be formulated as an initial-boundary value problem, which is invariant under the selfsimilar scaling. Then, by employing its self-similar invariance, the problem is reduced ...

We consider two simple conservative systems of parabolic-elliptic and parabolic-degenerate type arising in modeling chemotaxis and angiogenesis. Both systems share the same property that when the L d 2 norm of initial data is small enough, where d ≥ 2 is the space dimension, then there is a global (in time) weak solution that stays in all the L spaces with max{1; d 2 − 1} ≤ p < ∞. This result i...