Approximate algebraic operations for homomorphic encryption

A computing device, comprising:

• a memory configured to store a public key of a fully homomorphic encryption scheme and a set of operations, wherein the set of operations includes a square root function, a rectified linear activation function (ReLU), or a multiplicative inverse function;
• and
• a processor, communicatively coupled to the memory, configured to:
• receive, from a client, the public key, and one or more encrypted numbers generated by encrypting one ormore corresponding unencrypted numbers usingthe public key;
• perform the set of operations on the one or more encrypted numbers togenerate an encrypted operational result, wherein the encrypted operational result generated by the set of operations is an approximation of performing an algebraic operation on the one or more encrypted number, wherein an algebraicoperation ReLU has an approximation obtained by a set of operations including a square root, a multiplicative inverse of 2, and an addition;
• and
• transmit, to the client, the encrypted operational result, whereby the encrypted operational result is decrypted using at least a private key associated with the public key of the fully homomorphic encryption scheme togenerate a decrypted operational result.

A non-transitory computer-readable medium having instructions stored thereon that, when executed by a computing device, cause the computing device to perform operations comprising:

• receiving, from a client, a public key of a fully homomorphic encryption scheme and one or more encrypted numbers generated by encrypting one or more corresponding unencrypted numbers using the public key;
• performing a set of operations comprising a square root function, a rectified linear activation function (ReLU), ora multiplicative inversefunction on the one or more encrypted numbers togenerate an encrypted operational result, wherein the encrypted operational result generated by the set of operations is an approximation of performing an algebraic operation on the one or more encrypted number, wherein an algebraicoperation ReLU has an approximation obtained by a set of operations including a square root, a multiplicative inverse of 2, and an addition;
• and
• transmitting to the client, the encrypted operational result, whereby the encrypted operational result is decrypted using at least a private key associated with the public key of the fully homomorphic encryption mechanism to generate a decrypted operational result.