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Optics Express

Odd-order quantum noise-like stream cipher scheme based on joint index modulation constellation shaping

Dongxu Zhu, Bo Liu, Jianxin Ren, Shuaidong Chen, Yaya Mao, xiumin song, Jianye Zhao, Lilong Zhao, Xue Tang, Mengtong Yin, Wei Dai

Published Mar 24, 2025• 28 citations
Publisher

Abstract

This paper proposes an odd-order quantum noise-like stream cipher scheme based on joint index modulation (JIM) constellation shaping. By utilizing subcarrier index modulation and dual-mode index techniques, additional information is transmitted through the combination distribution of silent subcarrier positions and constellation modes associated with subcarriers. An odd-order 9QAM signal is constructed, and by optimizing the index rule, constellation shaping is achieved while transmitting more information, increasing the distribution of constellation points within the signal. A 4D hyper-chaotic system is employed to implement multi-dimensional disturbances, including bitwise XOR of the original signal, subcarriers, symbols, and elevate the constellation order. Furthermore, the scheme performs upsampling on the chaotic system's initial values and actively introduces noise bits, which are appended to the initial signal as a basis state to enable key-accompanying transmission. Ultimately, the constellation-shaped 9QAM signal is escalated to a 576QAM signal with constellation shaping features. Experimental results demonstrate the successful transmission of a 2.94 Gb/s quantum noise stream signal over a 25 km single-mode fiber intensity modulation direct detection (IMDD) system. The experimental results show that the proposed JIM-576QAM1 signal provides a 0.7 dB gain at Forward error correction (FEC) = 3.8 × 10 −3 compared to random distribution of the two constellation modes. The proposed scheme maintains a bit error rate (BER) of 0 for key transmission, and abruptly increases to 0.5 in the event of misalignment, indicating a high sensitivity and accuracy of the system with respect to the key. At varying received optical power, the number of masked signal power remain consistent at 20480, and the detection failure probability stays around 1, demonstrating the stability and security of the proposed quantum noise stream encryption scheme. With a key space as large as 10 149 , the scheme can effectively counter brute-force attacks from unauthorized receivers. The proposed scheme exhibits high reliability and security, making it a promising candidate for future optical access applications.

DOI
10.1364/oe.558376

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Journal of Lightwave Technology•Apr 10, 2020•61 citations
This paper proposes an odd-order quantum noise-like stream cipher scheme based on joint index modulation (JIM) constellation shaping. By utilizing subcarrier index modulation and dual-mode index techniques, additional information is transmitted through the combination distribution of silent subcarrier positions and constellation modes associated with subcarriers. An odd-order 9QAM signal is constructed, and by optimizing the index rule, constellation shaping is achieved while transmitting more information, increasing the distribution of constellation points within the signal. A 4D hyper-chaotic system is employed to implement multi-dimensional disturbances, including bitwise XOR of the original signal, subcarriers, symbols, and elevate the constellation order. Furthermore, the scheme performs upsampling on the chaotic system's initial values and actively introduces noise bits, which are appended to the initial signal as a basis state to enable key-accompanying transmission. Ultimately, the constellation-shaped 9QAM signal is escalated to a 576QAM signal with constellation shaping features. Experimental results demonstrate the successful transmission of a 2.94 Gb/s quantum noise stream signal over a 25 km single-mode fiber intensity modulation direct detection (IMDD) system. The experimental results show that the proposed JIM-576QAM1 signal provides a 0.7 dB gain at Forward error correction (FEC) = 3.8 × 10 −3 compared to random distribution of the two constellation modes. The proposed scheme maintains a bit error rate (BER) of 0 for key transmission, and abruptly increases to 0.5 in the event of misalignment, indicating a high sensitivity and accuracy of the system with respect to the key. At varying received optical power, the number of masked signal power remain consistent at 20480, and the detection failure probability stays around 1, demonstrating the stability and security of the proposed quantum noise stream encryption scheme. With a key space as large as 10 149 , the scheme can effectively counter brute-force attacks from unauthorized receivers. The proposed scheme exhibits high reliability and security, making it a promising candidate for future optical access applications.
A quantum noise stream cipher scheme (QNSC) based on triangular quadrature amplitude modulation (TQAM) and the secret probabilistic shaping (SPS) is studied. Compared with rectangular quadrature amplitude modulation (QAM), TQAM is a more compact symmetrical structure, which results in better transmission performance and greater noise masking number. Then, SPS is realized, where the probabilistic shaping information as the secret key is masked into noise and transmitted with the encrypted signal simultaneously. The combination of SPS and QNSC makes it impossible for an attacker to obtain the ciphertext, which enhances the security of QNSC scheme without introducing additional key. TQAM and probabilistic shaping improve the transmission performance of QNSC scheme. Under 7% forward error correction (FEC) threshold in back-to-back system, compared with QAM/QNSC systems, TQAM/QNSC provides an OSNR gain of ∼ 0.6 dB, and SPS-TQAM/QNSC provides an OSNR gain of ∼ 1.2 dB. The proposed scheme is demonstrated with the net data rate of 34.28 Gbit/s over 140 km single-span standard single mode fiber.
A probabilistic shaping (PS) quadrature amplitude modulation (QAM) based on Y-00 quantum noise stream cipher (QNSC) has been proposed. We experimentally demonstrated this scheme with data rate of 201.6Gbit/s over a 1200-km standard single mode fiber (SSMF) under a 20% SD-FEC threshold. Accounting for the 20% FEC and 6.25% pilot overhead, the achieved net data rate is ∼160Gbit/s. In the proposed scheme, a mathematical cipher (Y-00 protocol) is utilized to convert the original low-order modulation PS-16 (2 2 × 2 2 ) QAM into ultra-dense high-order modulation PS-65536 (2 8 × 2 8 ) QAM. Then, the physical randomness of quantum (shot) noise at photodetection and amplified spontaneous emission (ASE) noise from optical amplifiers are employed to mask the encrypted ultra-dense high-order signal for further improving the security. We further analyze the security performance by two metrics known in the reported QNSC systems, namely the number of masked signals (NMS) of noise and the detection failure probability (DFP). Experimental results show it is difficult or even impossible to extract transmission signals from quantum or ASE noise for an eavesdropper (Eve). We believe that the proposed PS-QAM/QNSC secure transmission scheme has the potential to be compatible with existing high-speed long-distance optical fiber communication systems.
An ultra-high-order QAM quantum noise stream cipher (QNSC) scheme assisted by intensity and phase chaotic encryption is proposed. In this scheme, the legal transmitter (Alice) first encrypts the original low-order QAM signal into an ultra-high-order QAM signal according to the pre-shared seed key based on the Y-00 protocol, and then conceals the intensity and phase information of the ultra-high-order QAM signal through the intensity and phase chaos generated from a nonlinear delay chaotic source for enhancing the security. The intensity and phase chaotic carrier can be eliminated by the open-loop chaotic synchronization module at the legal receiver (Bob). The scheme was numerically verified in 112 Gbit/s (28 GBaud 16QAM plaintext) and 168 Gbit/s (28 GBaud 64QAM plaintext) 65536QAM/QNSC systems, which can achieve 600 km and 150 km transmission at 7% HD-FEC threshold, and 1000 km and 350 km transmission at 20% SD-FEC threshold, respectively. Meanwhile, the number of masked signals (NMS) and the detection failure probability (DFP) in the scheme are obviously higher than in the original QAM/QNSC system. We believe that the proposed scheme is a promising strategy for enhancing the security of QAM/QNSC transmission systems.
【Objective】To further enhance the security of the Intensity Modulated (IM) / Quantum Noise Stream Cipher (QNSC) system, this paper proposes a security enhancement scheme for the IM/QNSC system assisted by chaotic encryption.【Methods】In this scheme, the legitimate transmitter encrypts the low-order 4-level Pulse Amplitude Modulation (PAM-4) signal into an ultra-high-order PAM-256 signal. Then it uses the intensity chaos generated by a nonlinear delayed chaos source to encrypt the ultra-high-order PAM signal, so as to enhance the security of the IM/QNSC system.【Results】This scheme was numerically verified in IM/QNSC dispersion-managed transmission systems with rates of 56 and 112 Gbit/s. The results show that under the 7% Hard Decision-Forward Error Correction (HD-FEC) threshold, the 56 and 112 Gbit/s encrypted systems achieve transmissions of 400 and 300 km. Under the 20% Soft Decision-Forward Error Correction (SD-FEC) threshold, they achieve transmissions of 700 and 600 km. The security analysis of the scheme shows that the Number of Masked Symbols (NMS) and Detection Failure Probability (DFP) of the scheme are higher than those of the original IM/QNSC system.【Conclusion】Chaotic encryption assistance amplifies the eavesdropping noise in the QNSC system. Compared with the original IM/QNSC system, it improves the system security.
A lossless key-accompanying transmission method based on noise-masked three-dimensional (3D) index mapping over four-core fiber is proposed. This scheme utilizes a four-dimensional (4D) chaotic model to mask the bits of the original data and orthogonal frequency division multiplexing (OFDM) symbols. Its initial value key is transformed into binary bits, and the error-free transmission of the key is ensured by periodic key repetition. And the masking of the key is achieved by introducing noise bits. In the process of constellation mapping, the 16 constellation points are divided into inner constellations and outer constellations. The traceless loading of the key is achieved by controlling the mapping rule using noisy key bits. A 115-kilometer four-core fiber transmission experiment of the noise-masked 3D index mapping method was successfully verified. The experimental results show that the difference between different cores of the four-core fiber is no more than 0.35 dB. There is almost no signal-noise ratio (SNR) penalty before and after signal encryption. The difference in sensitivity at the receiver is only 0.05 dB, which proves that this scheme can achieve lossless key transmission. As this scheme adopts the method of key repetition, it can ensure the correct demodulation of the key and the precise index of the constellation B. Compared with the traditional 16 quadrature amplitude modulation (QAM) signal, a sensitivity gain of 0.75 dB can be achieved. As for the illegal receiver, due to the lack of correct keys and encryption methods, the accuracy rate of key extraction is 0%, and the bit error rate (BER) remains at around 0.5. Even if the key index position is displaced by one bit, the BER will soar above 0.48. And through five repetitions, 100% correct recovery of the key at the legitimate receiver can be guaranteed. This scheme has excellent transmission effect and security, and can effectively guarantee the performance of the next-generation communication system.
The Internet plays an essential role in modern societies and in the amount of sensitive data transported over the optical networks that shows its' importance has increased drastically. Therefore, it is critical to develop data protection schemes for optical fiber communications to provide user security. The Y-00 quantum-noise randomized stream cipher that employs extremely high-order modulation and restricts an attacker's interception of ciphertext is a practical candidate for providing data protection. In this article, we introduce the operation principle of the Y-00 cipher with respect to data encryption and decryption. The Y-00 cipher combines the mathematical encryption of multi-level signaling and physical randomness, and provides a high level of security to the physical layer of optical communications and a high communication performance. We also present the noise masking phenomenon of the Y-00 cipher with intensity modulation (IM). This noise masking is generated by shot noise, i.e., quantum noise and additive noise such as amplified spontaneous emission noise. The noise masking phenomenon fails an attacker's interception of the ciphertext. The secrecy of the IM Y-00 cipher is also discussed, and an approximate analytical solution is introduced for evaluating the probability of the attackers accurately guessing the ciphertext. Finally, the secrecy of a 1,000-km transmission system is experimentally demonstrated with the Y-00 cipher transceiver at data rate of 1.5-Gb/s using the derived analytical solution to deduce the high secrecy of the entire transmission system.