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Applied Physics Letters

Generation of information theoretic secure keys using a chaotic semiconductor laser

Atsushi Uchida, Peter Davis, Shunsuke Itaya

Published Oct 13, 2003• 37 citations
Publisher

Abstract

We demonstrate a method for information theoretic secure key generation based on practical physical limits of continuous data acquisition from a rapidly fluctuating random signal generated by a chaotic semiconductor laser and transmitted over an optical fiber. Users independently and randomly grab sections of the chaotic waveform, separate into tag and key parts, and exchange tag parts to identify the common key parts which can be used to make secure keys. The frequency of trigger pulses in the waveform is used to control the security of the scheme which depends on the small probability of a third party coincidentally acquiring samples acquired by two other users.

DOI
10.1063/1.1619215

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We demonstrate a method for information theoretic secure key generation based on practical physical limits of continuous data acquisition from a rapidly fluctuating random signal generated by a chaotic semiconductor laser and transmitted over an optical fiber. Users independently and randomly grab sections of the chaotic waveform, separate into tag and key parts, and exchange tag parts to identify the common key parts which can be used to make secure keys. The frequency of trigger pulses in the waveform is used to control the security of the scheme which depends on the small probability of a third party coincidentally acquiring samples acquired by two other users.
It has been proposed that a secure key distribution scheme using correlated random bit sequences can be implemented using common random-signal induced synchronization of semiconductor laser systems. In this scheme it is necessary to use laser systems consisting of multiple cascaded lasers to be secure against a powerful eavesdropper. In this paper, we report the results of an experimental study that demonstrate that the common random-signal induced synchronization is possible in cascaded semiconductor laser systems. We also show that the correlated random bit sequences generated in the synchronized cascaded laser systems can be used to create an information-theoretically secure key between two legitimate users.
Random numbers have great application value in the fields of secure communications, which are commonly used as secret keys to encrypt the information. To guarantee that the information is absolutely secure in the current high-speed communication, the applied random keys should possess a generation speed not less than the encrypted data rate, according to one-time pad theory found by Shannon (Shannon C E 1949 Bell.Syst.Tech.J. 28 656) Pseudo-random numbers generated by algorithm may easily reach a fast speed, but a certain periodicity makes them difficult to meet the aforementioned demand of information security. Utilizing physical stochastic phenomena can provide reliable random numbers, called physical random number generators (RNGs). However, limited by the bandwidth of the conventional physical sources such as electronic noise, frequency jitter of oscillator and quantum randomness, the traditional physical RNG has a generation speed at a level of Mb/s typically. Therefore, real-time and ultrafast physical random number generation is urgently required from the view of absolute security for high-speed communication today. With the advent of wideband photonic entropy sources, in recent years lots of schemes for high-speed random number generation are proposed. Among them, chaotic laser has received great attention due to its ultra-wide bandwidth and large random fluctuation of intensity. The real-time speed of physical RNG based on chaotic laser is now limited under 5 Gb/s, although the reported RNG claims that an ultrafast speed of Tb/s is possible in theory. The main issues that restrict the real-time speed of RNG based on chaotic laser are from two aspects. The first aspect is electrical jitter bottleneck confronted by the electrical analog-to-digital converter (ADC). Specifically, most of the methods of extracting random numbers are first to convert the chaotic laser into an electrical signal by a photo-detector, then use an electrical ADC driven by radio frequency (RF) clock to sample and quantify the chaotic signal in electronic domain. Unfortunately, the response rate of ADC is below Gb/s restricted by the aperture jitter (several picoseconds) of RF clock in the sample and hold circuit. The second aspect comes from the complex post-processes, which are fundamental in current RNG techniques to realize a good randomness. The strict synchronization among post-processing components (e.g., XOR gates, memory buffers, high-order difference) is controlled by an RF clock. Similarly, it is also an insurmountable obstacle to achieve an accurate synchronization due to the electronic jitter of the RF clock. In this paper, we propose a method of ultrafast multi-bit physical RNG based on chaotic laser without any post-process. In this method, a train of optical pulses generated by a GHz mode-locked laser with low temporal jitter at a level of fs is used as an optical sampling clock. The chaotic laser is sampled in the optical domain through a low switching energy and high-linearity terahertz optical asymmetric demultiplexer (TOAD) sampler, which is a fiber loop with an asymmetrical nonlinear semiconductor optical amplifier. Then, the peak amplitude of each sampled chaotic pulse is digitized by a multi-bit comparator (i.e., a multi-bit ADC without sample and hold circuit) and converted into random numbers directly. Specifically, a proof-of-principle experiment is executed to demonstrate the aforementioned proposed method. In this experiment, an optical feedback chaotic laser is used, which has a bandwidth of 6 GHz. Through setting a sampling rate to be 5 GSa/s and selecting 4 LSBs outputs of the 8-bit comparator, 20 Gb/s (=5 GSa/s4 LSBs) physical random number sequences are obtained. Considering the ultrafast response rate of TOAD sampler, the speed of random numbers generated by this method has the potential to reach several hundreds of Gb/s as long as the used chaotic laser has a sufficient bandwidth.
We propose and experimentally demonstrate a physical-layer key distribution scheme using commonly-driven laser synchronization with random modulation of drive light. Two parameter-matched semiconductor lasers injected by a common complex drive light are used as entropy sources for legitimate users. Legitimate users generate their own random signal by randomly time-division multiplexing of two random sequences with a certain duration according to individual control codes, and then independently modulate the drive light. Laser synchronization is achieved during time slots when the modulation sequences of two users are identical, and thus provide highly correlated randomness for extracting random numbers as shared keys. Experimental results show that the random modulation of the drive light reduces the correlation between the drive light and laser outputs. In addition, laser synchronization is sensitive to the modulation delay and then the latter can be used as an additional hardware parameter. These mean that security is enhanced. In addition, the proposed method has a short laser synchronization recovery time of lower than 1.1 ns, meaning a high rate of key distribution. The upper limit of final key rate of 2.55 Gb/s with a criterion of bit error rate of 1.68 × 10 −3 is achieved in experiments. Our results provide a promising candidate for protecting the security of optical fiber communication.
Secure fiber-optic communication systems are an important area of research and development in the IT industry. In this work, we report the development of a promising fiber laser system for physical-layer secure key generation and distribution. This is a pulsed ultra-long Erbium fiber laser in which pulse shaping is symmetrically split between two communicating parties (Alice and Bob). The proposed protocol for the physical-layer secure key generation and distribution is based on control of the duration of generated laser pulses. Alice and Bob contribute random binary values to the secure key generation by making independent choices of their states in the split pulse shaping every bit cycle. The key exchange is secured whenever different choices lead to the same pulse duration, thereby confusing an eavesdropper (Eve). Two strong algorithms for the transmitted data encryption at the physical layer are proposed and discussed as well. One of them uses a private key to encrypt the message entered by one of the communicating parties, and the other uses a meaningful message entered synchronously by the other party.
We propose and numerically demonstrate a new scheme for key distribution on the physical layer based on the chaos synchronization and physical random bit generation. In this scheme, two chaotic semiconductor lasers are commonly driven by a third semiconductor laser, their output chaotic signals are employed as the physical sources of the random bit generators (RBGs). Under symmetry operation scenario, the two RBGs are well synchronized and the random bits generated by them are used to generate identical secret keys for Alice and Bob by the way of a dynamic post-processing technology. The feasibility and security of the proposed scheme are investigated by testing the parameters mismatch tolerance and the sensitivity to the systematic noise. The numerical results indicate that the dynamic and unpredictable post-processing can provide a great enhancement for the security of the secret key distribution. The security of the proposed scheme mainly determined by the post-processing, not confidential source, which provides a new potential way for implementing high-speed secure secret key distribution.