Apparatus for dividing the elements of a Galois field

摘要

Data representing one element αⁱ of a Galois field GF(2^m) are stored in a first linear shift register (52), and data representing another element α^j of the Galois field GF(2^m) are stored in a second linear shift register (53). 2^m elements of Galois field GF(2^m) are divided into n groups. A table of the reciprocals of n elements located at specific positions respectively in n groups is stored in a converter (51) which includes a decoder (511) and an encoder (512).;The data representing element αj are supplied from the second linear shift register (53) to the decoder (511). If the data representing the reciprocal of element αj are stored in the converter (51), they are read from the encoder (512). If they are not stored in the converter (51), the first linear shift register (52) and the second linear shift register (63) are shifted N times by control pulses generated by a NOR gate (NOR,) and an AND gate (AND,o) until any one of the reciprocal data are read from the encoder (512), whereby the register (52) supplies data representing αi+N and the register (53) supplies data representing α-(j+N). A multiplier (54) multiplies element αi by reciprocal αj or multiplies element α1+N by reciprocal α-(j+N), thereby performing the division: ai ÷ αj(= αi-j).