The present invention provides permutation instructions which can be used in software executed in a programmable processor (14) for solving permutation problems in cryptography, multimedia and other applications. The permute instructions are based on an omega-flip network comprising at least two stages in which each stage can perform the function of either an omega network stage or a flip network stage. Intermediate sequences of bits are defined that an initial sequence of bits from a source register are transformed into. Each intermediate sequence of bits is used as input to a subsequent permutation instruction. Permutation instructions are determined for permuting the initial source sequence of bits into one or more intermediate sequence of bits until a desired sequence is obtained. The intermediate sequences of bits are determined by configuration bits.