Secure computation using a server module

A computing device comprising:

• one or more processing devices;
• and
• one or more computer-readable memories or storage devices storing instructions which, when executed by the one or more processing devices, configure the one or more processing devices to:
• generate a key and a modifier factor;
• encrypt a first input using the key to obtain a first ciphertext;
• send the first ciphertext and the modifier factor to a server module configured to perform a multi-party computation, the multi-party computation involving an evaluation of an arithmetic circuit on the first ciphertext and a second ciphertext provided by a second computing device, the server module using the modifier factor to perform the multi-party computation without the key being revealed to the server module;
• receive an encrypted output from the server module;
• and
• decrypt the encrypted output using the key to derive a polynomial function and use the polynomial function to obtain a result of the evaluation of the arithmetic circuit,
• the use of the modifier factor in the multi-party computation affecting a corresponding degree of the polynomial function used to obtain the result.

A method performed by a computing device, the method comprising:

• generating a key and a modifier factor;
• concealing a first input using the key to obtain a first ciphertext;
• sending the first ciphertext and the modifier factor to another computing device that performs a multi-party computation by evaluating an arithmetic circuit using the first ciphertext, a second ciphertext provided by a second computing device, and the modifier factor, the modifier factor not revealing the key to the another computing device;
• receiving a concealed output from the another computing device;
• and
• performing interpolation using the concealed output to derive a polynomial function;
• and
• evaluating the polynomial function to obtain a result of the evaluation of the arithmetic circuit,
• the use of the modifier factor in the multi-party computation influencing a number of samples involved in the interpolation used to derive the polynomial function.