Question

This question concerns the field GF(256). The modulus is P(x)=x⁸+x⁴+x³+x+1.
For computing inverses in this field, you should use the table in the textbook.

Please answer the following questions about arithmetic in this field.

a) If p(x)=x⁶+x⁴, and q(x)=x⁵+x⁴+x³+x, what is p(x)/q(x)?

b) If p(x)=x⁷+x⁶+x⁵+x, and q(x)=x⁷+x⁵+x⁴+x², what is p(x)/q(x)?

Answer 1

Solution:-

The algorithm we will use here will be polynomial Long division algo.

1, We will divide the numberator first ter with the denominator's first term.("after dividing the result we will obtain a ")

2. Then we will multiply the a with the denominator and will the result below numerator.

3. then we subtract the numerator with the polynomial below it and the result obtained will be new numerator.

4. then we will repeat the above setps until the degree of numerator is greater than degree of denominator.

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