bit-operations – Is it possible to find the encryption key using xor?

Question:

There is a system of equations:

x = a xor b;
y = b xor c;

if only x and y are known, is it possible to know b?

Answer:

No. Due to the commutative property, we will always have two pairs. It's easy to check.

For x = 1, y = 0:

1 = 1 xor 0
0 = 0 xor 0

or

1 = 0 xor 1
0 = 1 xor 1

For x = 1, y = 1:

1 = 1 xor 0
1 = 0 xor 1

or

1 = 0 xor 1
1 = 1 xor 0

etc.

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