Composite finite field multiplier

A composite finite field multiplier, comprising:

• an input port, configured to input an operand a(x), an operand b(x), an operand c(x), an irreducible polynomial p(x) selected over the GF(2n) field, an irreducible polynomial q(x) selected over the GF((2n)m) field and a control signal k;
• a GF(2n) standard basis multiplier, configured to implement the multiplication (a(x)×b(x)×c(x))mod(p(x)) of the three operands a(x), b(x) and c(x) on the standard basis over GF(2n);
• a GF(2n) look-up table multiplier, configured to implement the multiplication (a(x)d×b(x)×c(x))mod(p(x)) of the three operands a(x), b(x) and c(x) based on the look-up table over GF(2n);
• a GF((2n)2) multiplier, comprising a first processor and a scheduler interconnected with each other;
• the first processor is configured to implement the multiplication (a(x)×b(x)×c(x))mod(q(x)) of the three operands a(x), b(x) and c(x) over GF((2n)2);
• when processing the addition operation over the GF(2n) field, using an XOR gate circuit included in the first processor to obtain an intermediate calculation result, while when processing the multiplication over the GF(2n) field, the scheduler calls the GF(2n) look-up table multiplier or GF(2n) standard basis multiplier to obtain an intermediate calculation result;
• a controller, configured to parse the control signal k and control the GF((2n)2) multiplier, the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier based on the parsing result;
• an output port, configured to output the results;
• wherein the controller is connected respectively to the input port, the output port, the GF((2n)2) multiplier, the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier;
• the GF((2n)2) multiplier is connected respectively to the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier.