Arithmetic circuit for finite field GF (2m)

An arithmetic processor capable of executing arithmetic operations of multiplication A*B, exponential BN and inverse multiplication operation B−1, where N is a positive integer, for loading elements A and B in a finite field GF(2m) and performing all arithmetic operations but an addition operation A+B in the finite field GF(2m), comprising:

• a calculating processor capable of performing arithmetic operations AB and AB2, for loading elements A and B in the finite field GF(2m) and outputting AB or AB2 according to a control signal;
• registers storing the outcome of the calculating processor;
• and
• control circuits selectively transmitting the elements A and B in the finite field GF(2m) from the input terminal of the arithmetic processor or the registers to the input terminals of the calculation processor according to the control signal so that the calculating processor can correctly output AB, AB2;
• wherein, a first and a second control signals are applied to the arithmetic processor:
• when the first and second control signals are logic low, the arithmetic processor performs a loading operation and an input D=[dm−1, dm−2, . . . , d0] is stored in a first register from the registers, when the first control signal is 0 and the second control signal is 1, the arithmetic processor performs multiplication, multiplying the input D=[dm−1, dm−2, . . . , d0] or a data C stored in a second register from the registers by the data stored in the first register and loading the outcome to the first register, when the first and second control signals are logic high, the arithmetic processor performs exponentiation by replacing exponential operation with the (m−1) times C*D2, where m is a positive integer, represents the degree of GF(2m), when the first control signal is 1 and the second control signal is 0, the arithmetic processor performs inverse multiplication D−1,where DεGF(2m) and D−1=D2m−2.