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XOR, often written ⊕, is one of the basic operations on bits and bit-sequences. It is a building block of many cryptographic primitives (and some higher-level algorithms, like modes of operations).
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Proof of the standard pseudorandom generator + XOR encryption scheme in Goldreich
The inequality is obtained by a distance argument.
Consider two points $X,Y$ on the real line. Taking another point $Z$, you have $|X-Z| + |Y-Z| \geq |X-Z+Z-Y| = |X-Y|$.
Applying this "triangle" ine …