Cryptography, Cybersecurity.
take a few examples to illustrate this. Example 1. For a=x²+x+1 (7–111b) and b=x+1 (3–011b) with a primitive of x⁴+x+1 (GF(2⁴)), for addition we get x² (4–100b), and for multiplication we get x3+1(9–1001b): Add=(x²+x+1)+(x+1)=x² Mult=(x²+x+1)×(x+1)=x³+x²+x²+x+x+1=x³+1 As we are using modulo 2