Why does Bluetooth security use XOR as an operation of symmetric encryption and decryption? The formula of symmetric as follows.

C = Enc (P, K)

P = Dec (C, K)

Where

C is cypher text.

P is plain text.

Enc is a symmetric encryption algorithm.

Dec is a symmetric decryption algorithm

K is a key of the encryption and decryption.

The true table of XOR is as follows.

A B X

-----

0 0 0

0 1 1

1 0 1

1 1 0

A XOR B = C

C XOR B = (A XOR B) XOR B = A XOR (B XOR B) = A XOR 0 = A

Therefore we got the formula.

A XOR B = C

C XOR B = A

Lets rename A to P (plain text), and B to K (key), and keep C (cipher).

P XOR K = C

C XOR K = P

Transform it.

C = XOR (P, K)

P = XOR (C, K)

We proof that XOR can be a symmetric encryption and decryption.

-Count

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