Memristive fingerprints prove key destruction

The physical fingerprinting of a memristor crossbar array can be used to prove whether a digital key stored in the array is securely destroyed.

Digital keys are central to the security of digital systems. Using encryption and message authentication, they protect digital information from unauthorized access and modification. Data being transmitted over a network can, for example, be encrypted using a key known only to the communicating parties, thus preventing eavesdroppers from deciphering any intercepted data. Traditional computer security techniques involve the secure distribution and storage of digital keys to ensure only legitimate users or devices have access to the digital key. However, once a device has the key, it is challenging to remove the key securely and prove that the key has been completely erased from the device1. For instance, fully erasing data on a hard disk is challenging due to remanent magnetization. New approaches to verify whether certain digital keys are erased from a device are therefore needed. Writing in Nature Electronics, J. Joshua Yang, Daniel Holcomb, Qiangfei Xia and colleagues show that the physical fingerprint of a memristor crossbar array can be used to prove that keys stored in the array have been completely erased2.

Memristors in a crossbar array can be used in non-volatile memory applications3,4, where information is stored in the resistance of the cells in the array — a cell can either be in a low-resistance state or a high-resistance state to store one bit of information. The resistance of the cells in the low-resistance state are not exactly the same, however, due to variations in the fabrication process. Thus, a ‘fingerprint’ of the crossbar array — commonly known as a physically unclonable function (PUF)4,5 — can be generated by comparing the resistances of pairs of neighbouring cells in the crossbar array. All of the cells in the crossbar array need to be in the low-resistance state in order to extract the fingerprint of the memristor crossbar array, so the memristor crossbar array cannot store any information, including any digital keys. Therefore, if a device containing a memristor crossbar array is able to generate the correct fingerprint, it proves that any digital key that was stored in that array has been erased (Fig. 1).

Fig. 1: Provable key destruction using memristor crossbar array fingerprints.

a, During the key distribution, the key owner registers the memristor crossbar array fingerprint, and then loads the key into the array. b, When the owner wants to revoke the key, they request the user to extract the fingerprint of the memristor crossbar array and send it back to them. Since this process requires zeroing out the data in the memristor crossbar array to extract the fingerprint, the ability to send the correct fingerprint to the owner is proof of key destruction.

The researchers — who are based at the University of Massachusetts, Amherst — demonstrate that the fingerprint of the memristor crossbar array is unique to each crossbar array and stable across measurements. Furthermore, they designed an integrated system and protocol to prove the removal of keys in the crossbar as a result of measuring the fingerprint. Before the key distribution, the fingerprint of the device is collected. Next, the key is stored in the memristor crossbar array. When the owner wants to revoke the key, the device extracts the fingerprint again, and in the process proves the device erased the key (Fig. 1). The researchers designed their system to ensure that the key is either in the memristor crossbar array or is being used on the fly for encryption or decryption — and thus, in their design, the key cannot be copied to any other location.

The security of the integrated system is based on the fact that an attacker cannot extract the same fingerprint from a different memristor crossbar array. If the attacker could do so, they could store the key in one crossbar array, and return the fingerprint of a different crossbar, in order to fool the owner into believing that the key had been removed. But Xia and colleagues experimentally demonstrate that the fingerprint is unique and reliable on 128 × 64 hafnium oxide memristor crossbar arrays. Five crossbar arrays were tested and, for each, a 128-bit fingerprint was extracted 200 times to evaluate the reliability using a metric known as the fractional intraclass Hamming distance: the difference between each pair of fingerprints from the same crossbar array. The fingerprints from different crossbar arrays were also compared to calculate the fractional interclass Hamming distance. The results show that there is no overlap between the fractional intraclass Hamming distance and fractional interclass Hamming distance, indicating that even when the noise in the measurement is considered, the fingerprint is unique to each device.

Traditional cryptographic approaches base security on the hardness of mathematical problems. The approach adopted by Xia and colleagues is distinct, as the security lies in the uniqueness of the physical properties of memristive devices in a crossbar array configuration: that is, the fingerprint of the memristor crossbar array. Further work is still required in order to actually deploy the secure integrated system they propose. This will require computer engineers to work together with device researchers to develop practical memristor crossbar arrays to store the key and the related digital logic needed to use the key securely. Crucially, the fingerprint of the memristor crossbar arrays needs to be evaluated on more sample chips to ensure that the system is secure enough for mass production. Furthermore, possible attacks leveraging the timing, power consumption or electromagnetic emanations of the system to obtain an illegal copy of the key or the fingerprint — so-called side-channel attacks — require further investigation6. Nevertheless, the work provides a new approach to computer security that is anchored in the physical features of the underlying device. And in the future, it is likely that similar approaches to computer security, which rely on the physical properties of the devices used to build the computers, will be developed and used.


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Correspondence to Wenjie Xiong or Jakub Szefer.

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Xiong, W., Szefer, J. Memristive fingerprints prove key destruction. Nat Electron 1, 527–528 (2018). https://doi.org/10.1038/s41928-018-0149-2

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