Circuit for operating finite fields

DETAILED DESCRIPTION The present invention relates to a circuit for operating finite fields which performs a multiplication or a division in relation to arbitrary elements .
alpha.
.
sup.
i and .
alpha.
over a finite field (where, .
alpha.
is a root of a primitive polynomial of the finite field), wherein this circuit includes: an accumulator to store the arbitrary element .
alpha.
.
sup.
i ; an adder to perform a module 2 addition of the contents of the accumulator and represented by a vector the primitive polynomial; and a control section to control the bit-shift of the accumulator and the operation of the adder in accordance with a program.
The present invention also relates to a circuit for operating finite field which performs a multiplication or a division in relation to two elements .
alpha.
.
sup.
i and .
alpha.
.
sup.
j over a finite field (where, .
alpha.
is a root of a primitive polynomial of the finite field), wherein this circuit includes: a first table to generate the exponents from the elements over the finite field; a second table to generate the elements over the finite field from the exponents; a binary arithmetic operating unit to perform an addition or a subtraction in relation to the exponents; and a control section to control the data conversions which are performed by the first and second tables and the operation of the binary arithmetic operating unit in accordance with a program.