Introduction

With the rapid development of artificial intelligence and IoT, greater demands are being placed on the security by growing hacking incidents. To implement cryptographic remote control, two general types of key-based algorithms, public-key and symmetric, are being widely investigated. Public-key algorithms use two different keys for encryption and decryption, and are often based on computational complexity; while they are imperfect in the real world for being slow, and vulnerable to chosen-plaintext attacks1. Conventional symmetric algorithms require that communication parties share matched and secret keys in advance; while the security of such algorithms relies on the shared keys. One-time pad2, as a powerful symmetric algorithm, has been proved by Claude Shannon to be impossible to crack3, as long as crucial problems of generating and sharing real random sequences are settled.

Randomness is a fundamental resource with significant applications in cryptography and numerical simulation. Real random sequences, however, are hard to generate mathematically4, but have to rely on unpredictable physical processes5,6,7,8,9. Although different mechanics, such as chaotic effects10,11, thermal noise12, biometric parameters13 and free-running oscillators14 are employed in the generation of physical random number, they are faced with some problems like hard to detect failure15. The inherent uncertainty of quantum mechanics makes quantum systems an excellent stochastic source, with the fact that a single photon incident on a 50:50 beam splitter be transmitted or reflected is intrinsically random. More importantly, the randomness is precisely balanced and immune to environmental perturbations.

Sharing randomness is another crucial problem to be settled for realizing symmetric algorithms. One best-known scheme is quantum key distribution (QKD), which is quite mature so far for applications, with enormous progresses16,17,18,19 and is even ready for constructing secure networks20,21,22,23,24. Nevertheless, many situations of IoT control are not compatible with QKD schemes. For example, sensor networks require low cost, low power and miniature devices, which is hard to be met by QKD systems25, especially for large-scale and distributed sensor networks.

Interestingly, in many situations, real-time sharing of randomness is not really necessary in practice. For instance, UAVs or satellites are essentially well identified before being launched, and are well isolated with other parties during their missions. For all these situations, we could precharge quantum keys into controllers and controlees, and implement cryptographic remote control with quantum enhancement in a straightforward and practical way. In this work, we present this quantum-enhanced cryptographic remote control scheme that combines quantum randomness and one-time pad algorithm for delivering commands remotely, and experimentally demonstrate this on a UAV control system.

The cryptographic system is composed of three subsystems: key management unit, controller unit and controlee unit, as is shown in Fig. 1(a). The randomness derived from quantum nature of single photons is charged into IoT devices through secure key storage (SKS) chips to perform one-time pad encryption and decryption. The connection of flexible small-scale SKS chips to QRN generator is realized by a home-built key management unit. SKS chips are planted into controllers and controlees before they are detached. Commands are encrypted by one-time pad algorithm with a certain section of keys, which can only be decrypted correctly by the controlee with corresponding keys. On the controller side, with QRN keys, a bitwise exclusive OR is performed on commands before being sent; and conversely, with identical keys, commands can be deciphered and executed on the controlee’s side, as is shown in Fig. 1(b).

Figure 1
figure 1

Quantum-enhanced cryptographic remote control. (a) A schematic diagram of quantum-enhanced cryptographic remote control system and the potential applications. The quantum random number generator utilized here is the “Quantis USB” of ID Quantique company. Scenarios applicable to our direct-charging scheme: remote control of UAV, high-speed rail scheduling, vessel movement, airport dispatch and smart grid control. (b) A specific example that combines QRN keys and one-time pad algorithm for delivering commands remotely.

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The data transmission diagram of our UAV control system is illustrated in Fig. 2(a). Encryption keys are generated by Quantis, which is a reliable QRN generator, employing a quantum process as the source of randomness, and producing random sequences at a bit rate of 4 Mb/s. To be specific, a photon incident on a semi-transparent mirror will be reflected with half the probability, leading to a “0”; or transmitted with half the probability, leading to an “1”. A microcontroller is dedicated for charging or updating quantum keys into SKS chips.

Figure 2
figure 2

Signal flow diagram and NIST tests of quantum randomness. (a) Signal flow diagram of the quantum-enhanced cryptographic control system. (b) NIST statistical randomness tests performance of quantum keys. The experimental results are obtained from 1,638,400 bits samples with a significance level of α = 0.01. In the histogram, the value of each test that exceeds the red dashed line turns out a successful pass.

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The successful execution of one-time pad algorithm depends on the synchronization of keys. Unfortunately, it happens that commands get lost or make mistakes, leading to key mismatch between controllers and controlees. Any minor key mismatch may cause control system failure. To solve this problem, we assign unique address information to each command, so that each command with quantum keys is independent and well labeled. Once error happens, the corresponding command will be discarded directly together with its encryption and decryption keys to maintain the synchronization. Such address information doesn’t have to be encrypted, because they include no information about commands.

The randomness of quantum keys is a crucial parameter that determines system security. Quantum random number based on the uncertainty principle of quantum mechanics provides the honest-to-goodness randomness in the world, with the properties of unpredictable and unreproducible1. We use NIST suites to perform statistical tests26, and the final results are shown in Fig. 2(b). The results are P–values of all 15 tests: indicating how a sequence is identical to purely random number, ideally P–values equal to one. The results of NIST tests prove an excellent statistical randomness of our quantum keys.

Furthermore, according to one-time pad algorithm, where ciphertexts are the XOR values of quantum keys and plaintexts, the randomness of quantum keys determines that of ciphertexts. We intercept a section of commands in the air sent by the controller, and test them with three characteristics of random binary sequences proposed by Gobomb: balance property, runs property and auto-correlation property27. The good properties of balance, runs (see Table 1), and auto-correlation (see Fig. 3) indicate that our ciphertexts are statistically random. Meanwhile, since the quantum keys are unpredictable and unrepeatable, the ciphertexts intercepted here are expected and experimentally observed to be truly random, which is impossible to be deciphered without matched quantum keys.

Table 1 Balance and runs properties.
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Figure 3
figure 3

The auto-correlation function measured among long commands ciphertexts. The auto-correlation function of ideal random sequence is close to delta function. The sharp auto-correlation peak in the center indicates that the encrypted binary sequence has excellent independence on each part. The insets show auto-correlation details in the near- and far-field regime.

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Experimental commands between the remote control and the aircraft are shown in Fig. 4. We intercept five pieces of different functional commands, both with and without one-time pad encryption for comparison. For plaintexts, we can see that five repeating commands share exactly identical values; while for ciphertexts, five repeating commands are bought into chaos, and there is no correlation between any two commands or even any two bytes, which guarantees the security as have been proved statistically in Table 1 and Fig. 3, according to three postulates proposed by Golomb27.

Figure 4
figure 4

Experimental results of intercepted commands. (a) Intercepted five pieces of typical commands both with (blue lines) and without (red lines) one-time pad encryption for comparison. (b) Details of each functional command. The last four bytes of ciphertexts represent the assigned address information of quantum keys. One command is combined with 32 bytes, and each byte represents for an integer whose value ranges from 0 to 255, stored with eight binaries. See Supplementary Materials for details.

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Since the security of the commands depends on the one-time pad, the communication capacity in this cryptographic control scheme is mainly limited by the number of precharged QRNs. To extend the key updating period, on one hand, the capacity of secure key storage device should be large enough, while it might take more bytes in the commands for storing keys’ address information. On the other hand, the encryption commands can be optimized according to different structures, and some trivial information in a certain command could be ignored to save keys, as well as to increase decryption speed.

In summary, we have proposed and experimentally demonstrated a quantum-enhanced cryptographic remote control scheme that combines quantum randomness and one-time pad algorithm for delivering commands remotely. The quantum-enhanced cryptographic scheme is expected to be generalized to bidirectional systems: controlees can be securely controlled and also be able to send encrypted recorded flight data back to controllers, such as position, direction and speed. Besides, the point-to-point solution can be extended to point-to-multipoint or distributed networks. More importantly, such scheme can be combined with fixed QKD channels23,28,29,30 for long-distance quantum keys charging, providing a flexible solution for control security of artificial intelligence and IoT in large scale.