Abstract: Disclosed herein are system, method, and computer program product embodiments for performing a set of operations on one or more encrypted numbers to be an approximation of performing an algebraic operation on the one or more encrypted number. A server can receive from a client, a public key of a fully homomorphic encryption scheme and one or more encrypted numbers, and perform a set of operations comprising a square root function, a rectified linear activation function (ReLU), or a multiplicative inverse function on the one or more encrypted numbers to generate an encrypted operational result. The encrypted operational result generated by the set of operations can be an approximation of performing an algebraic operation on the one or more encrypted number. The server can further transmit to the client the encrypted operational result.

Abstract: A system is provided for coordinating inter-satellite handoff in a telecommunications system that includes first and second communication satellites and a communications apparatus. The communications apparatus is configured to generate commands for transmission to the first communication satellite and the second communication satellite to steer respectively first and second spot beams to track and communicate with a user terminal during respective time intervals. The communication interface is also configured to determine a trajectory of the user terminal and a predicted handoff point on the trajectory for handoff between the satellites in which the second spot beam is automatically steered to the handoff point or a point proximate thereto no sooner than the user terminal is within the second spot beam when steered to the predicted handoff point.

Abstract: A system is provided for coordinating inter-satellite handoff in a telecommunications system that includes first and second communication satellites and a communications apparatus. The communications apparatus is configured to generate commands for transmission to the first communication satellite and the second communication satellite to steer respectively first and second spot beams to track and communicate with a user terminal during respective time intervals. The communication interface is also configured to determine a trajectory of the user terminal and a predicted handoff point on the trajectory for handoff between the satellites in which the second spot beam is automatically steered to the handoff point or a point proximate thereto no sooner than the user terminal is within the second spot beam when steered to the predicted handoff point.