What are some practical applications of XOR in algorithms [closed]

Question

To be honest I am rusty in bit operations.
What I am interested in is the XOR operation. Well, I know what it does bitwise, and that it is used in encryption and that we can do swapping without any temporary variable, but I was interested if there are specific approaches in algorithms that XOR's properties fit.
I mean I am interested in practical applications of XOR in algorithms (e.g. we could use it to finding unique element among duplicates). Is there a pattern of problems (or a formulation of a problem) that one could see that the use of XOR is the way to go? (Same way as there is a pattern when to use binary search?)
Is there some list of practical applications of XOR on algorithms that is related to the core algorithm, not simply use it e.g. to do math operations faster like we can use >> instead of divide by 2.

Any input is welcome

Answer 1

A few examples that came up in my mind:

Toggling bits:

int i = 123;
i ^= (1 << 4); // toggle bit 5

Some kind of randomness:

int i = 123;
for (int k = 0; k < 100; k++)
{
   i = i ^ (i << 1) + i;
   System.out.println(i);
}

"Weak Encryption":

int b = 235321;
int key = 24552;
int encrypted = b ^ key;
int decrypted = encrypted ^ key; // equals 235321