Highly Secure Physically Unclonable Cryptographic Primitives Based

Subscriber access provided by NORTH CAROLINA A&T UNIV

Communication

Highly secure physically unclonable cryptographic primitives based on interfacial magnetic anisotropy Huiming Chen, Min Song, Zhe Guo, Ruofan Li, Qi Ming Zou, Shijiang Luo, Shuai Zhang, Qiang Luo, Jeongmin Hong, and Long You Nano Lett., Just Accepted Manuscript • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Highly secure physically unclonable cryptographic primitives based on interfacial magnetic anisotropy Huiming Chen1†, Min Song2†, Zhe Guo1†, Ruofan Li1, Qiming Zou3, Shijiang Luo1, Shuai Zhang1, Qiang Luo1, Jeongmin Hong1, Long You1,4* 1School

of Optical and Electronic Information, Huazhong University of Science and Technology,

Wuhan 430074, China 2Hubei

Key Laboratory of Ferro &Piezoelectric Materials and Devices, Faculty of Physics and

Electronic Science, Hubei University, Wuhan 430062, China 3Department

of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln,

NE 68588-0511, USA 4Wuhan

National Lab for Optoelectronics, Huazhong University of Science and Technology,

Wuhan 430074, China

†These

authors contributed equally to this work.

*Correspondence

and requests for materials should be addressed to L. Y (email:

[email protected])

ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 22

Abstract: Information security is of great importance for the approaching internet of things (IoT) era. Physically unclonable functions (PUFs) have been intensively studied for information security. However, silicon PUFs are vulnerable to hazards such as modelling and side-channel attacks. Here we demonstrate a magnetic analogue PUF based on perpendicularly magnetized Ta/CoFeB/MgO heterostructures. The perpendicular magnetic anisotropy originates from the CoFeB/MgO interface, which is sensitive to the subnanometre variation of MgO thickness within a certain range (0.6–1.3 nm). By thinning the MgO layer, a thickness variation resulting from ion milling non-uniformity induces unclonable

random

distributions

of

easy-axis

magnetization

orientations

in

heterostructures. The analogue PUF can provide a much larger key size than a conventional binary-bit counterpart. Moreover, after the thinning process, the unique easy-axis magnetization orientation in each single device was formed, which can avoid setting random states to realize low power consumption and high-density integration. This magnetic PUF is a promising innovative primitive for secret key generation and storage with high security in the IoT era. Keywords: physically unclonable function (PUF), interfacial magnetic anisotropy, information security, analogue PUF


Page 3 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

The effective certification of physical entities is a basic problem to ensure information security. Physically unclonable functions (PUFs) that can be used for authentication and secret key storage have become a hot topic in the hardware security field over the last decade1-4. Compared with conventional encryption methods such as a secret key programmed into a non-volatile erasable read-only memory or static random-access memory, a PUF is almost impossible to duplicate because of its intrinsic random physical nature5. The most widely used PUFs in current integrated circuits are silicon-based semiconductor PUFs6, 7. However, silicon PUFs are vulnerable to modelling and side channel attacks. For example, it has been reported that machine learning can efficiently predict challenge–response pairs (CRPs) by utilizing the linear behaviour of the arbiter PUF8. A magnetic PUF based on magnetic random-access memory (MRAM) has also been demonstrated, which used fabrication variations to provide random geometric MRAM units with different switching currents or coercive fields9-11. This kind of PUF is resistant to attack and insensitive to environmental variations. However, practical implementation of the previously proposed MRAM-PUF was limited by the need to apply a magnetic field or current to randomly set cell states during application. Such a requirement complicates the cell structure, limiting the circuit scalability, and creates a large dissipative overhead that dominates the energy cost. An analogue PUF has the advantage of providing a higher level of security with a limited amount of PUF cells. It is therefore desirable to construct a magnetic analogue PUF that does not need an external magnetic field or writing current.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

In this paper, we demonstrate such a device in which we thinning the MgO layer in a patterned Ta/CoFeB/MgO heterostructure via a non-uniform etching process. This process provides CoFeB/MgO interface anisotropy that varies randomly spatially within the device. This variation induces the random distribution of effective anisotropy, and consequently magnetic easy-axis orientation, once the etching process is complete. Experimental results show that the developed interfacial anisotropy energy (IAE)-PUF is capable of generating response bits with desire randomness without applying an external magnetic field or writing current. The essential idea of the IAE-PUF is depicted in Figure 1. Imagine a magnet composed of a ferromagnet (FM)/oxide layered heterostructure that has an easy-axis orientation perpendicular to the film (perpendicular magnetic anisotropy, PMA) as shown in Figure 1a. Here, the actual device is made of a heterostructure consisting of Ta/CoFeB/MgO. The effective anisotropy is determined by the competition between the CoFeB/MgO interfacial anisotropy energy, which favours out-of-plane (OOP) magnetization, and demagnetization energy, which supports magnetization in the in-plane (IP) direction. If the former energy term is larger than the latter, a positive effective anisotropy energy can be obtained and the easy axis is aligned OOP12, 13. By tuning the two energy terms, for example, by decreasing the interface anisotropy while keep demagnetization anisotropy fixed, it is possible to lower the effective anisotropy energy, even to a negative value14-18. As a result, the magnetization orientation may rotate from an OOP to IP direction. In this heterostructure, the CoFeB/MgO interfacial anisotropy energy can be decreased by thinning the MgO layer via


Page 4 of 22

Page 5 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

etching18. Because the non-uniformity of the etching process causes thickness variations of the remaining MgO, the magnetization orientation of each device varies with a random distribution after etching. Thus, an analogue IAE-PUF can be achieved without a write operation by an external magnetic field or switching current.

Figure 1. Magnetic analogue IAE-PUF based on fabrication variations of a Ta/CoFeB/MgO magnet. (a) Schematic of the etching-induced variations of magnetization orientations in the 2D ferromagnet array. (b) Challenge and analogue response of the IAEPUF. The challenges are the PUF unit addresses and responses are the unit data. In the Ta/CoFeB/MgO heterostructure, the Hall resistances of each device corresponding to the anomalous Hall effect (AHE) are collected as the unit data. The CRPs gathered from the PUF are the references for the verification. The PUF unit address and data are the challenge and response of the IAE-PUF, respectively, as shown in Figure 1b. To harness the random magnetization orientations, the anomalous Hall


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

resistance (RAHE), which is proportional to the OOP magnetization of a Ta/CoFeB/MgO heterostructure19, was collected at zero field (remanence resistance Rr) as the analogue response. The raw responses were further processed through a comparison method (see Supporting Information for details) to generate a cryptographic key.

Figure 2. Dependence of the effective magnetic anisotropy of a Ta/CoFeB/MgO heterostructure on MgO thickness (tMgO). (a) Optical image of a Hall bar structure and the measurement set-up. (b) AHE resistance (RAHE) vs. perpendicular magnetic field (H) for different tMgO. TEM images of stacks with tMgO of (c) 1.6 nm and (d) 0.6 nm. We started by investigating the dependence of the magnetization orientation in an individual device on MgO thickness (tMgO). The devices were fabricated from a stack of


Page 6 of 22

Page 7 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

thermally oxidized Si (substrate)/Ta (10 nm)/CoFeB (1.2 nm)/MgO (1.6 nm)/Ta (5 nm) (see Methods). All measurements in this work were performed at room temperature. An optical image of a typical Hall bar structure with a magnetic device (6 × 6 µm2) at the cross section is shown in Figure 2a. In this configuration, one can obtain RAHE by applying a current along the x axis and measuring the voltage along the y axis. The black line in Figure 2b is a typical AHE loop, which has high PMA with anisotropy field HK = 2000 Oe (see Figure S2) and a remanence ratio (Rr/Rs; Rs is the saturated Hall resistance) of around 1. The large PMA originated from the high CoFeB/MgO interfacial anisotropy energy around the tMgO of 1.6 nm used here20. The corresponding transmission electron microscopy (TEM) image in Figure 2c exhibits the multilayers of the stack and the distinct interface between CoFeB and MgO. The Ta capping layer was removed by etching and the underlying MgO layer was successively thinned to different tMgO (1.3, 1.0, and 0.6 nm) by Ar-ion milling. RAHE normalized by Rs is plotted as a function of the perpendicular magnetic field in Figure 2b and the corresponding RAHE resistance values are shown in Figure S3a. To discern the easy-magnetization orientations of devices from each other more easily, we use the normalized RAHE hereafter. The data clearly show that the loop becomes more inclined as tMgO decreases. In addition, the normalized-remanence Hall resistance (Rnr) decreases with tMgO, which indicates that the interfacial anisotropy energy decreases, and the demagnetization energy begins to dominate. Typically, when tMgO decreased to 0.6 nm, the easy-axis orientation changed from OOP to IP. The TEM image in Figure 2d reveals that at tMgO = 0.6 nm, the interface between CoFeB and MgO is vague. The change of the lattice


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

structure at the CoFeB/MgO interface caused by ion milling might also account for the decreased interfacial anisotropy energy18,20,21. Accordingly, it can be concluded that the magnetization orientation of the heterostructure, determined by the effective anisotropy, can be readily tuned by varying tMgO. We next demonstrate a conceptual PUF chip consisting of 24 fabricated units each with 8 devices, as shown in Figure 3a. After patterning the Ta/CoFeB/MgO/Ta multilayer into the Hall bar structure, the MgO layer of the chip sample was precisely etched. The normalized AHE loops with a magnetic field range of (−800–800 Oe) were collected from the 192 (24 × 8) devices. For clear observation, a magnified view of −40–40 Oe is illustrated in Figure 3b and the inset shows the full view (see RAHE resistance loops in Figure S3b). The results clearly reveal that the simultaneously etched devices have different normalized AHE loops, along with different Rnr, which reflect the magnetization orientation of each device (see SI). The random distribution of tMgO (around 0.6–0.8 nm) induced by the non-uniform etching caused the variation of the effective anisotropy. To verify the PUF stability, repeated tests were conducted; another set of tests result are shown in Figure 3c. We then extracted Rnr from the normalized AHE loops as the analogue responses of the IAE-PUF. The data for unit #1, unit #2, and unit #24 are presented in Figure 3d. The Rnr values of the 8 devices in each unit vary randomly from each other, but the values for the two tests for the same device resemble each other. The results for other units showed similar behaviour (see Figure S4).


Page 8 of 22

Page 9 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3. Structure of IAE-PUF devices and AHE measurements for each device. (a) Optical image of the fabricated PUF chip consisting of 24 units. Each unit has 8 devices. (b), (c) Magnified views of the AHE loops for two tests. The insets show the full AHE loops. (d) Rnr of unit #1, unit #2, and unit #24. The Rnr values were extracted from the AHE loops for each device. For the statistical analysis, the parameters used to assess the quality of the PUF were statistical distances, including 1) the inter-hamming distance (inter-HD), which is the difference of the tests between different devices, and 2) the intra-hamming distance (intraHD), which is denoted as the difference between two test results for the same device22. The specific method to obtain these distances is to compare binary sequences bit by bit. The extracted Rr values were converted to binary sequence through a comparison method mentioned above, and a proposed hardware implementation was shown in Figure S1b and c. Accordingly, one PUF unit with 8 devices can produce 28 (𝐶28) binary bits. Then the random bitmaps of 24 (rows) × 28 (columns) were constructed as shown in Figure 4a and b for two tests, respectively. In contrast, the digital counterpart with 8 devices can only


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

generate 8 binary bits. As the device number in a unit increases to n, the key size of the unit would rapidly increase as 𝐶2𝑛, whereas the binary counterpart can only generate an nbit key size, as shown in Figure 4c. This leads to a higher security level in the analogue unit than in the corresponding digital one. The distribution of normalized inter-distance is approximated with Gaussian distribution that is centred at 0.49782 with a variance of 0.16587, as shown in Figure 4d. The mean inter-distance is close to 0.5, which means that the magnetization orientation distributions in the IAE-PUF are completely random and it has high anti-cloning and anti-replication performance. The small intra-distance of 0.107 indicates the good repeatability of the IAE-PUF.

Figure 4. Bitmaps and statistical analysis of an IAE-PUF. (a), (b) 28×24 binary bits generated from AHE measurements by a comparative method. (c) Key sizes of the analogue IAE-PUF unit with n devices and a binary counterpart. (d) Distributions of the


Page 10 of 22

Page 11 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

normalized intra- and inter-distances. The normalized inter-hamming distance is a Gaussian distribution with a mean and standard deviation of 0.49782 and 0.16587, respectively. The intra-HD reflects the bit error rate, which needs to be close to zero for a high-quality PUF. The intra-HD of 0.107 for the IAE-PUF may be caused by the non-ideal contact present during testing. When the PUF is integrated in circuits for actual application, the influence of such external factors will be eliminated and thereby the bit error rate will be greatly lowered. When using the Ta/CoFeB/MgO structure as the free layer of a magnetic tunnel junction23-25, which consists of two FM electrodes (a free layer and a reference layer) separated by an ultrathin tunnelling layer, the external factors would also be suppressed because of the much larger resistance change than that of AHE (relative to the same variation of magnetization orientations). The dependence of the resistance changes on the angle of tunnelling magnetoresistance (TMR)26,27 can be expressed as follows: R(θ)=Rmin+Rmin×TMR×(1−cos(θF−θR))/2, where θF and θR are the magnetization orientations with respect to the substrate normal for the free and reference layers, respectively28. Rmin is the resistance in parallel and TMR is the magnetoresistance ratio. If the

reference

layer

is

perpendicular

to

the

substrate,

we

can

obtain

R(θ)=Rmin+Rmin×TMR×(1−cosθF)/2. Thereby, the resistance variation caused by the small change of the free layer magnetization orientation Δθ can be described as ΔR=Rmin×TMR×Δθ (see SI). The TMR values can be very high23, resulting in a large change of resistance caused by the small variation of magnetization orientations.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A high-performance PUF should tolerate harsh environmental conditions. silicon-based PUFs have a narrow working temperature range (

Highly Secure Physically Unclonable Cryptographic Primitives Based

Recommend Documents