Sankhanil Dey and Ranjan Ghosh Positional Arithmetic: Subtraction, Multiplication and Division over Extended Galois Field GF(p^q). (200K, PDF) ABSTRACT. The method to Subtract, Multiply and Divide two Field Numbers over the Extended Galois Field GF(p^q) is a well needed solution to the field of Discrete Mathematics as well as in Cryptology. In this paper the addition of two Galois Field Numbers over Extended Galois Field GF(p^q) has been reviewed and Subtraction, Multiplication and Division of two Galois Field Number over Extended Galois Field GF(p^q) has been defined.