Multiply elements of Galois field
c = gfmul(a,b,p)
c = gfmul(a,b,field)
Note: This function performs computations in GF(pm) where p is prime. To work in GF(2m), apply the .* operator to Galois arrays. For details, see Example: Multiplication.
The gfmul function multiplies elements of a Galois field. (To multiply polynomials over a Galois field, use gfconv instead.)
c = gfmul(a,b,p) multiplies a and b in GF(p). Each entry of a and b is between 0 and p-1. p is a prime number. If a and b are matrices of the same size, the function treats each element independently.
c = gfmul(a,b,field) multiplies a and b in GF(pm), where p is a prime number and m is a positive integer. a and b represent elements of GF(pm) in exponential format relative to some primitive element of GF(pm). field is the matrix listing all elements of GF(pm), arranged relative to the same primitive element. c is the exponential format of the product, relative to the same primitive element. See Representing Elements of Galois Fields for an explanation of these formats. If a and b are matrices of the same size, the function treats each element independently.
Arithmetic in Galois Fields contains examples. Also, the code below shows that
where A is a root of the primitive polynomial 2 + 2x + x2 for GF(9).
p = 3; m = 2; prim_poly = [2 2 1]; field = gftuple([-1:p^m-2]',prim_poly,p); a = gfmul(2,4,field)
The output is
a = 6