Security Evaluation of Y00 Protocol Based on Time-Translational Symmetry Under Quantum Collective Known-Plaintext Attacks

In this paper, we concretely formulate to derive the attacker's success probability of obtaining the shared secret keys for the Y00 protocol under a combination of a quantum collective attack with infinitely-long known-plaintext, naming it "collective known-plaintext attack" in this work. In contrast, our previous work showed only the necessary condition to design Y00 transmitters to be information-theoretic secure. The keystone of the security evaluations in this work is the time-translational symmetry of the Y00 signals modulated by pseudo-random number generators, such as linear-feedback shift registers or Mersenne twisters. With the assist of a true-random deliberate-signal-randomization, information-theoretic security would be realized. By numerical simulations, we can determine whether the designed Y00 transmitters are information-theoretic secure. However, this work's security evaluation may not apply to the transmitters with cryptographically-secure pseudo-random number generators because they might not have time-translational symmetry, even though such Y00 transmitters may be securer. We also describe future challenges for theorists to accelerate designing securer Y00 transmitters.