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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 &#x201C;collective known-plaintext attack&#x201D; 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.

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