Twin physically unclonable functions based on aligned carbon nanotube arrays

Aligned carbon nanotube arrays have random characteristics, such as chirality and position, perpendicular to the growth direction and identical characteristics along the growth direction. We proposed and realized twin physically unclonable functions based on CNTs for secure communication.

In the information age, the omnipresent smart devices and human-machine interactions have created an explosion of massive data, which not only demands significant improvements in the handling, storage and communication abilities of hardware but also requires higher security in the storage and communication of personal or sensitive information. Classical cryptography uses cryptographic algorithms and keys to authenticate electronic devices and encrypt or decrypt information. The most popular asymmetric algorithm for secure communication is Rivest, Shamir, and Adleman (RSA) encryption, which is predicated on the difficulty for a classical computer of factoring a very large number. This task has, however, been shown mathematically to be accomplishable in polynomial time using a quantum computer. Another strategy is symmetric encryption where all communication participants possess the same secret keys for encryption or decryption, and secret keys are stored in non-volatile memory, which are vulnerable to physical and side-channel attacks. Quantum key distribution can exhibit higher security than classical methods by exploiting quantum theory— specifically, the feature of quantum systems to be intrinsically disturbed by the process of measuring them — but this technology requires expensive equipment.

To achieve a low-cost and hardware-based secure communication, in our recent work in Nature Electronics, we proposed and realized a new technology, twin physically unclonable functions (PUFs) based on aligned carbon nanotube (CNT) arrays (Fig. 1a). Firstly, we grew aligned CNT arrays on quartz substrate (Fig. 1b). On one hand, induced by the quartz lattice-CNT interaction, CNT arrays grew along the [2 -1 -1 0] crystal orientation for several hundred microns, which ensured that the properties of CNT arrays were identical parallel to the growth direction. On another hand, CNT arrays have random characteristics, such as chirality and position, perpendicular to the CNT growth direction. Then, we fabricated two rows of field-effect transistors on CNT arrays (Fig. 1c). These transistors showed three channel types with distinct electrical properties — channels containing some metallic CNTs (M), purely semiconducting CNTs (S), and no CNTs at all (O) (Fig. 1d). Since the location and type of CNTs in the channel are determined by the stochastic nucleation and random catalyst distribution, FETs fabricated on the CNT arrays will show O, S, and M characteristics in a random manner perpendicular to the growth direction. The random nature neither predictable nor unclonable; therefore, in principle one row of FETs meets the requirement of PUFs. Meanwhile, two rows of FETs fabricated in parallel on the same CNT array show O, S, and M types with the same order (Fig. 1e), so two identical PUFs (twin PUFs) can be fabricated together.

Figure 1 | Twin physically unclonable functions based on aligned CNT arrays. a, Schematic of twin PUFs based on CVD-grown CNT arrays. The letters ‘m’ and ‘s’ represent metallic or semiconducting CNT, while letter ‘P’ represents interspacing between two adjacent CNTs. b, Schematic of three distinct types of devices according to their conduction type. Letter ‘O’ represents device with open channel, and ‘S’ and ‘M’ represent devices channel with semiconducting or metallic CNT, respectively. c, SEM image of aligned CNT array. d, False-coloured SEM image showing a group of 24 pairs of twin PUF devices. e, Transfer characteristics measured from the three pairs of devices in (d).

To improve the randomness and entropy of our PUFs, we built a model to study the relation of PUFs with CNT array and device dimension. We found the CNT pitches (CPs) meet the lognormal distribution (Fig. 2a), which was verified by other CNT samples we grew with different densities and those published by other groups. Based on the simulation and optimization, CNT arrays with a CP of 0.65±0.58 μm and a metallic/semiconducting CNT ratio of approximately 0.4 were selected to demonstrate PUFs with ideal ternary bits, and the experimental result is in good agreement with simulation (Fig. 2b). A total of 1600 FETs with a Wch of 600 nm were fabricated to generate a 40×40 ternary bit map (Fig. 2c), in which 532, 516, and 552 O-, S- and M-bits were counted, respectively. With this, our PUFs also exhibited high randomness, uniformity, uniqueness, unpredictability, and reliability.

Figure 2 | Performance of CNT twin PUFs and demonstration of secure communication. a, Distribution of CNT pitch and lognormal fit of the data. b, Ratios of three types of devices versus channel width of PUF devices. The squares and lines represent experimental and simulation data, respectively. c, CNT PUF-generated ternary keys including 1600 bits. The green, red and blue circles represent open (0,0), semiconducting (1,0) and metallic (1,1) bits or devices, respectively. d, Twin binary bit maps generated from twin PUFs using double-binary bits. The solid green and solid red circles represent bit ‘1’ and bit ‘0’, respectively. The hollow black circles represent in-consistent or “wrong” bits. e, Schematic of secure communication using a fault-tolerant design. f, BER versus fault-tolerant number with different consistencies.

Figure 2 | Performance of CNT twin PUFs and demonstration of secure communication. a, Distribution of CNT pitch and lognormal fit of the data. b, Ratios of three types of devices versus channel width of PUF devices. The squares and lines represent experimental and simulation data, respectively. c, CNT PUF-generated ternary keys including 1600 bits. The green, red and blue circles represent open (0,0), semiconducting (1,0) and metallic (1,1) bits or devices, respectively. d, Twin binary bit maps generated from twin PUFs using double-binary bits. The solid green and solid red circles represent bit ‘1’ and bit ‘0’, respectively. The hollow black circles represent in-consistent or “wrong” bits. e, Schematic of secure communication using a fault-tolerant design. f, BER versus fault-tolerant number with different consistencies.

For traditional PUFs, unclonability ensures the safety of keys inside, but also makes them hard to implement secure communication. Since we can make two identical PUFs, so we can directly use them to encrypt or decrypt information without key pre-extraction, which makes our twin PUFs possess higher security. Because of the imperfection during CNT growth, including chirality transition, the existence of broken tubes between catalyst stripes and misalignment, twin PUFs showed a non-perfect consistency (Fig. 2d), so the encryption and decryption process could introduce wrong bits, which is generally measured using BER. To reduce BER, we designed fault-tolerant cryptography in which multiple key bits (3, odd) are used to encrypt one plain text bit into multiple cipher text bits, and the multiple cipher text bits are decrypted and then generate one plain text bit through a majority vote (Fig. 2e). The BER will be exponentially reduced with increasing fault-tolerant number for consistency greater than 80 % (Fig. 2f). For our twin PUFs with a consistency of 95 %, the BER can be reduced to one in a trillion when the fault-tolerant number is up to 29; therefore, the accuracy of communication can be greatly strengthened.

If you are interested in more details of our work, please refer to the paper published in Nature Electronics: “Twin physically unclonable functions based on aligned carbon nanotube arrays” following the link: https://www.nature.com/articles/s41928-022-00787-x