I multiply 2 numbers using their polynomial representation and addition via XOR. Do I need to find the remainder of the division by $x ^ 8 + x ^ 4 + x ^ 3 + x + 1$, using the operator "%" or by division, using the rules of finite fields?
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3Welcome to Cryptography. Keep a while we find you a good duplicate. In short $x ^ 8 = x ^ 4 + x ^ 3 + x + 1$ use this identity. That is very common in Finite Field applications that eliminates the polynomial division/remainder. – kelalaka May 06 '20 at 16:59
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2How to perform the modular reduce of Rijndael's finite field How is multiplication in field GF(28) done? – kelalaka May 06 '20 at 17:06
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6Does this answer your question? How is multiplication in field $GF(2^{8})$ done? – hardyrama May 06 '20 at 18:14