A processor comprising: a decode unit to decode an elliptic curve cryptography point-multiplication with obfuscated input information instruction, the ECC point-multiplication with obfuscated input information instruction to indicate a plurality of source operands that are to store input information for an ECC point-multiplication operation, wherein at least a portion of the input information that is to be stored in the plurality of source operands is to be obfuscated; and an execution unit coupled with the decode unit, the execution unit, in response to the ECC point-multiplication with obfuscated input information instruction, 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, wherein the execution unit, in response to a second instance of the ECC point-multiplication with obfuscated input information instruction, is to: stop performing the second instance of the ECC point-multiplication with obfuscated input information instruction after an interruption; encrypt an intermediate state associated with interrupted performance of the second instance of the ECC point-multiplication with obfuscated input information instruction with a secret key of the processor that is not readable by software; and store the encrypted intermediate state in a storage location. a decode unit to decode an elliptic curve cryptography point-multiplication with obfuscated input information instruction, the ECC point-multiplication with obfuscated input information instruction to indicate a plurality of source operands that are to store input information for an ECC point-multiplication operation, wherein at least a portion of the input information that is to be stored in the plurality of source operands is to be obfuscated; and an execution unit coupled with the decode unit, the execution unit, in response to the ECC point-multiplication with obfuscated input information instruction, 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, wherein the execution unit, in response to a second instance of the ECC point-multiplication with obfuscated input information instruction, is to: stop performing the second instance of the ECC point-multiplication with obfuscated input information instruction after an interruption; encrypt an intermediate state associated with interrupted performance of the second instance of the ECC point-multiplication with obfuscated input information instruction with a secret key of the processor that is not readable by software; and store the encrypted intermediate state in a storage location. stop performing the second instance of the ECC point-multiplication with obfuscated input information instruction after an interruption; encrypt an intermediate state associated with interrupted performance of the second instance of the ECC point-multiplication with obfuscated input information instruction with a secret key of the processor that is not readable by software; and store the encrypted intermediate state in a storage location.