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: 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: The process for the preparation and isolation of the hypolipaemic active substance lovastatin in substantially pure form having a purity of at least 95% which comprises lactonizing the mevinolinic acid to lovastatin in a totally aqueous medium.