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arXiv:2001.11150 · IEEE Access

Analysis of Y00 Protocol Under Quantum Generalization of a Fast Correlation Attack: Toward Information-Theoretic Security

Takehisa Iwakoshi

Published Jan 1, 2020• 9 citations
arXivHTMLPDF

Abstract

In our previous work, it was demonstrated that the attacker could not pin-down the correct keys to start the Y00 protocol with a probability of one under the assistance of unlimitedly long known-plaintext attacks and optimal quantum measurements on the attacker's quantum memory. However, there were several assumptions that the Y00 system utilized linear-feedback shift registers as pseudo-random-number generators, and a fast correlation attack was disabled by irregular mapping on the Y00 systems. This study generalizes such an attack to remove the assumptions of the previous work. The framework of the security analyses of this study reiterates two well-known results from the past: (1) Y00 systems would be cryptanalyzed when the system is not designed well; (2) the system is possibly information-theoretically secure when the system is designed well, although the attacker's confidence in the correct key increases over time but the success probability of key recovery does not reach unity in finite time; (3) the breach probability of the shared keys increases with time. Hence, a key-refreshment procedure for the Y00 protocol is provided herein. Such security analyses are important not only in key refreshment but also in initial key agreement.

DOI
10.1109/access.2020.2969455

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In our previous work, it was demonstrated that the attacker could not pin-down the correct keys to start the Y00 protocol with a probability of one under the assistance of unlimitedly long known-plaintext attacks and optimal quantum measurements on the attacker's quantum memory. However, there were several assumptions that the Y00 system utilized linear-feedback shift registers as pseudo-random-number generators, and a fast correlation attack was disabled by irregular mapping on the Y00 systems. This study generalizes such an attack to remove the assumptions of the previous work. The framework of the security analyses of this study reiterates two well-known results from the past: (1) Y00 systems would be cryptanalyzed when the system is not designed well; (2) the system is possibly information-theoretically secure when the system is designed well, although the attacker's confidence in the correct key increases over time but the success probability of key recovery does not reach unity in finite time; (3) the breach probability of the shared keys increases with time. Hence, a key-refreshment procedure for the Y00 protocol is provided herein. Such security analyses are important not only in key refreshment but also in initial key agreement.
The previous work showed that the Y00 protocol could stay secure with the eavesdropper's guessing probability on the secret keys being strictly less than one under an unlimitedly long known-plaintext attack with quantum memory. However, an assumption that at least a fast correlation attack is completely disabled by irregular mapping. The present study shows that the Y00 protocol can be information-theoretic secure under any quantum-computational crypto-analyses if the Y00 system is well designed. The Y00 protocol directly encrypts messages with short secret keys expanded into pseudo-random running keys unlike One-Time Pad. However, it may offer information-theoretic security beyond the Shannon limit of cryptography.
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.
A quantum stream cipher by Yuen 2000 protocol (so-called Y00 protocol or $\ensuremath{\alpha}\ensuremath{\eta}$ scheme) consisting of linear feedback shift register of short key is very attractive in implementing secure 40 Gbits/s optical data transmission, which is expected as a next-generation network. However, a basic model of the Y00 protocol with a very short key needs a careful design against fast correlation attacks as pointed out by Donnet et al. This Brief Report clarifies an effectiveness of irregular mapping between running key and physical signals in the driver for selection of MMM-ary basis in the transmitter, and gives a design method. Consequently, quantum stream cipher by the Y00 protocol with our mapping has immunity against the proposed fast correlation attacks on a basic model of the Y00 protocol even if the key is very short.
Abstract As past works have shown, information‐theoretically secure implementations transmitters of Y00 quantum noise randomised cypher are possible. An advance to the provably secure Y00 protocol by bridging gaps between experimental results and theoretical analyses under so‐called quantum collective measurement attacks with known plaintexts is aimed. It would be the strongest attack on the Y00 protocol in the context of quantum key distribution protocols. However, recently proposed security evaluations under the attacks were too abstract to apply to experiments. Therefore, security analyses directly evaluable with the equipped Y00 transmitters under attack are offered. Thus, new security indices are proposed instead of ordinary security measures, such as the bit‐error‐rate guarantee between optical signals or a masking size. Contrarily, unsolved problems are also listed.
Although quantum key distribution is regarded as promising secure communication, security of Y00 protocol proposed by Yuen in 2000 for the affinity to conventional optical communication is not well-understood yet; its security has been evaluated only by the eavesdropper’s error probabilities of detecting individual signals or masking size, the number of hidden signal levels under quantum and classical noise. Our study is the first challenge of evaluating the guessing probabilities on shared secret keys for pseudorandom number generators in a simplified Y00 communication system based on quantum multiple hypotheses testing theory. The result is that even unlimitedly long known-plaintext attack only lets the eavesdropper guess the shared secret keys of limited lengths with a probability strictly <1. This study will give some insights for detailed future works on this quantum communication protocol.
There exists a great gap between one-time pad with perfect secrecy and conventional mathematical encryption. The Yuen 2000 (Y00) protocol or $\ensuremath{\alpha}\ensuremath{\eta}$ scheme may provide a protocol which covers from the conventional security to the ultimate one, depending on implementations. This paper presents the complexity-theoretic security analysis on some models of the Y00 protocol with nonlinear pseudo-random-number-generator and quantum noise diffusion mapping (QDM). Algebraic attacks and fast correlation attacks are applied with a model of the Y00 protocol with nonlinear filtering like the Toyocrypt stream cipher as the running key generator, and it is shown that these attacks in principle do not work on such models even when the mapping between running key and quantum state signal is fixed. In addition, a security property of the Y00 protocol with QDM is clarified. Consequently, we show that the Y00 protocol has a potential which cannot be realized by conventional cryptography and that it goes beyond mathematical encryption with physical encryption.