A processor of an aspect includes a decode unit to decode a modular exponentiation with obfuscated input information instruction. The modular exponentiation with obfuscated input information instruction is to indicate a plurality of source operands that are to store input information for a modular exponentiation operation. At least some of the input information that is to be stored in the plurality of source operands is to be obfuscated. An execution unit is coupled with the decode unit. The execution unit, in response to the modular exponentiation with obfuscated input information instruction, is to store a modular exponentiation result in a destination storage location that is to be indicated by the modular exponentiation with obfuscated input information instruction. Other processors, methods, systems, and instructions are disclosed.