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If we have say,key=‘0110‘ and 𝑚=‘1100‘, how will 𝑚⊕key mod 2 be calculated and what will be the answer equal to?

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The operation $\oplus$ is the same as bitwise XOR. The same symbol is used for direct sum, but there is otherwise absolutely no relation.

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  • $\begingroup$ Can this be also used when m has larger number of bits than key like m="101010" while key="101"? If so, how? $\endgroup$ – Deepika Bhargava May 5 '20 at 7:58
  • $\begingroup$ Yes. You pad the smaller one with zeroes. $\endgroup$ – Yuval Filmus May 5 '20 at 7:58
  • $\begingroup$ I warmly recommend experimenting with the XOR operation in any programming language that supports it. This will answer all your questions. $\endgroup$ – Yuval Filmus May 5 '20 at 8:00

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