What does a circled plus mean?

math cryptography matrix
Léo Léopold Hertz 준영 picture Léo Léopold Hertz 준영 · May 8, 2009 · Viewed 96.4k times · Source

I cannot understand the calculation "66 ⊕ fa = 9c". The sum is clearly over "ff", so I am confused. The topic is simple encryption algorithm.

What does a circled plus mean?

Answer

Steve Jessop picture Steve Jessop · May 8, 2009

People are saying that the symbol doesn't mean addition. This is true, but doesn't explain why a plus-like symbol is used for something that isn't addition.

The answer is that for modulo addition of 1-bit values, 0+0 == 1+1 == 0, and 0+1 == 1+0 == 1. Those are the same values as XOR.

So, plus in a circle in this context means "bitwise addition modulo-2". Which is, as everyone says, XOR for integers. It's common in mathematics to use plus in a circle for an operation which is a sort of addition, but isn't regular integer addition.

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