Perform polynomial addition, subtraction and multiplication of 2x2 + 4 | Information Security 2082

Information Security20825 marksNumerical: Polynomial arithmetic over GF(7)Finite fields and polynomial operations

Perform polynomial addition, subtraction and multiplication of $2x^2 + 4x + 2$ and $5x + 6$ over $GF(7)$ . [5]

Perform polynomial addition, subtraction and multiplication of $2x^2 + 4x + 2$ and $5x + 6$ over $GF(7)$. [5]

$A(x) = 2x^2 + 4x + 2$ $B(x) = 5x + 6$ Field: $GF(7)$ , so all coefficients reduced $\bmod 7$ . Coefficient vectors: - $A: [x^2, x^1, x^0] = [2, 4, 2]$ - $B: [x^2, x^1, x^0] = [0, 5, 6]$ Degree A B Sum mod 7 -------------------------- $x^2$ 2 0 2 2 $x^1$ 4 5 9 2 $x^0$ 2 6 8 1 $$\boxed{A(x) + B(...

$$A(x) = 2x^2 + 4x + 2$$ $$B(x) = 5x + 6$$ Field: $GF(7)$, so all coefficients reduced $\bmod 7$. Coefficient vectors: - $A: [x^2, x^1, x^0] = [2, 4, 2]$ - $B: [x^2, x^1, x^0] = [0, 5, 6]$ Degree A B Sum mod 7 -------------------------- $x^2$ 2 0 2 2 $x^1$ 4 5 9 2 $x^0$ 2 6 8 1 $$\boxed{A(x) + B(...

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Perform polynomial addition, subtraction and multiplication of 2x2 + 4x + 2 and 5x + 6 over GF(7).