It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize common secret-key, which can be subsequently used keep their group messages confidential. As one its salient features, the involved in GSK extract randomness from subset channels, referred as source (CSR). Unlike two-user key generation, some must act facili...

A classical problem in algebraic geometry is to describe quantities that are invariants under birational equivalence as well as to determine some convenient birational model for each given variety, a minimal model. One such quantity is the ring of objects which transform like a tensor power of a differential of top degree, known as the canonical ring. The histories of the existence of minimal m...

We generalize the combinatorial algebraic approach first proposed by Dhurandhar et al. to construct various classes of modified second-generation time-delay interferometry (TDI) solutions. The main idea behind original algorithm is enumerate, in a given order, specific type commutator between two monomials defined products particular time-displacement operators. On one hand, enumeration process...

A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with nite diierences and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and eeciency. Diierent smoothers are tried to improve the convergence of iterations. The methods are ap...

Specific vectorial boolean functions, such as S-Boxes or APN functions have many applications, for instance in symmetric ciphers. In cryptography they must satisfy some criteria (balancedness, high nonlinearity, high algebraic degree, avalanche, or transparency [2, 7]) to provide best possible resistance against attacks. Functions satisfying most criteria are however difficult to find. Indeed, ...