Computer program product, computer system and computer implement method for omputing digital signature authentication sign with encrypted key instruction

A single architected instruction to produce a signature for a message is executed. The executing includes determining an encrypted sign function of a plurality of encrypted sign functions supported by the instruction to be performed and obtaining input for the instruction. The input includes a message and an encrypted cryptographic key. Based on the encrypted sign function to be performed and the input, a signature to be used to verify the message is produced.