This paper introduces “hyper-and-elliptic-curve cryptography”, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (e.g., Diffie–Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (e.g., key generation) and multi-scalar m...

We prove that, for any fixed base x ≥ 2 and sufficiently large prime q, no perfect q-th powers can be written with 3 or 4 digits 1 in base x. This is a particular instance of rather more general results, whose proofs follow from a combination of refined lower bounds for linear forms in Archimedean and non-Archimedean logarithms.

In speech recognition, acoustic modeling mismatches for the shapes of distributions are unavoidable when we use fixed-shape base distributions, such as the Gaussian. This paper proposes a new base distribution called the "generalized Laplacian distribution (GLD)", which offers more flexibility in terms of the distribution shape. The effectiveness of the GLD-based modeling is proven through spee...

forces and moments which are generated at the base of the ma-nipulator. Hence, diiect application of the analysis and control schemes for the fixed base robots to space robots is not possible. Fig. 2. In the first category, the position and orientation of the + for the development of dynamic models of space ;bots.