Quantum Distinguisher Between the 3-Round Feistel Cipher and the Random Permutation

No polynomial classical algorithms can distinguish between the 3-round Feistel cipher with internal permutations and a random permutation. It means that the 3-round Feistel cipher with internal permutations is secure against any chosen plaintext attack on the classical computer. This paper shows that there exists a polynomial quantum algorithm for distinguishing them. Hence, the 3-round Feistel cipher with internal permutations may be insecure against a chosen plaintext attack on a quantum computer. This distinguishing problem is an instance that can be efficiently solved by exploiting the quantum parallelism. The proposed algorithm is the first application of Simon's algorithm to cryptographic analysis.