A processor of an aspect includes a decode unit to decode an elliptic curve cryptography (ECC) point-multiplication with obfuscated input information instruction. The ECC point-multiplication with obfuscated input information instruction is to indicate a plurality of source operands that are to store input information for an ECC point-multiplication 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 ECC point-multiplication with obfuscated input information instruction, is to store an ECC point-multiplication result in a destination storage location that is to be indicated by the ECC point-multiplication with obfuscated input information instruction. Other processors, methods, systems, and instructions are disclosed.