A data processing system 2 includes a single instruction multiple data register file 12 and single instruction multiple processing circuitry 14. The single instruction multiple data processing circuitry 14 supports execution of cryptographic processing instructions for performing parts of a hash algorithm. The operands are stored within the single instruction multiple data register file 12. The cryptographic support instructions do not follow normal lane-based processing and generate output operands in which the different portions of the output operand depend upon multiple different elements within the input operand.