Abstract: Pseudo-random numbers (PRNs) have great importance in data processing and encryption. The standard technique for generating PRNs on computers at the present time involves software implementation of recursively computing PRN.sub.n+1 =(PRN.sub.n)(b) mod M, in real number field which means that a relatively slow and involved multiplication must occur for each PRN, and each PRN calculation is strictly subsequent to previous PRM calculations. This disclosure shows a systolic multiplier implemented by a series of exclusive OR operations which generates simultaneously a new set of the PRN's from the current set of PRN's in parallel. The operation of multiplication mod M is performed over a finite field instead of a real number field. To facilitate the multiplication, the input operands are first transformed into a different representation that consists of more bits than that of the original ones. The operation of multiplication is then carried out in this transformed representation.

Abstract: A multiplier for use with polynomials in an error correction system wherein the multiplier and multiplicand are first encoded from m bits to N bits, where N is greater than m, and wherein the multiplication is accomplished on a bit basis by arrays of AND gates and where the resultant product is decoded from R bits to S bits where S is less than R.