1. A computer program product for executing a machine instruction in a central processing unit, the computer program product comprising: a non-transitory computer readable storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: obtaining, by a processor, a machine instruction for execution, the machine instruction being defined for computer execution according to a computer architecture, the machine instruction comprising: at least one opcode field to provide an opcode, the opcode identifying a Vector Galois Field Multiply Sum and Accumulate operation; a first register field to be used to designate a first register, the first register comprising a first operand; a second register field to be used to designate a second register, the second register comprising a second operand; a third register field to be used to designate a third register, the third register comprising a third operand; a fourth register field to be used to designate a fourth register, the fourth register comprising a fourth operand; and a mask field to specify a size of elements of one or more of the first operand, the second operand, the third operand or the fourth operand, wherein the mask field specifies the size of the elements of the second operand and the third operand; and executing the machine instruction, the executing comprising: multiplying one or more elements of the second operand with one or more elements of the third operand using carryless multiplication to obtain a plurality of products; performing a first mathematical operation on the plurality of products to obtain a first result; performing a second mathematical operation on the first result and one or more selected elements of the fourth operand to obtain a second result; and placing the second result in the first operand.