System and method for modulus obfuscation

A non-transitory computer-readable medium storing instructions which, when executed by a computing device, cause the computing device to perform steps comprising:

• receiving input data on a server device;
• performing a modulus transformation on the input data to obtain a result;
• performing a plain operation on the result and an operation value to obtain server output data;
• and
• checking if the server output data matches corresponding client output data from a client device that (1) receives input data, (2) stores an operation value in a secure location, (3) performs a modulus obfuscation on the operation value, wherein the modulus obfuscation is based on an Euler phi function and coprime integers, (4) performs a modulus operation on the operation value and the input data, and (5) performs a modulus transformation on the operation value and the input data to obtain client output data.

A server computing device comprising:

• a processor;
• a memory storing instructions for controlling the processor to perform steps comprising:
• receiving server input data;
• performing a server modulus transformation on the server input data to obtain a result;
• performing a plain operation on the result based on a server operation value to yield server output data;
• and
• authenticating a client device if the server output data matches client output data from the client device, wherein the client device performs steps comprising:
• receiving client input data;
• storing an operation value in a secure location;
• performing a modulus obfuscation on the operation value, wherein the modulus obfuscation is based on an Euler phi function and coprime integers;
• performing a modulus operation on the operation value and the client input data;
• and
• performing a modulus transformation on the operation value and the client input data to obtain client output data.