Algebraic Security Analysis of Key Generation with Physical Unclonable Functions

Physical Unclonable Functions (PUFs) provide cryptographic keys for embedded systems without secure non-volatile key storage. Several error correction schemes for key generation with PUFs were introduced, analyzed and implemented over the last years. This work abstracts from the typical algorithmic level and provides an algebraic view to reveal fundamental similarities and differences in the security of these error correction schemes. An algebraic core is introduced for key generation with Physical Unclonable Functions (PUFs). It computes the secret key through the helper data from the input PUF response and an optional random number. For nearly uniformly distributed PUF responses, the leakage of the secret key and the helper data can be brought to zero if and only if the rank of the algebraic core is equal to the sum of the ranks of the key generating part and the rank of the helper data generating part. This rank criterion has the practical advantage that a security check can be performed for linear codes at an early design stage of an algorithm. The criterion is applied to state-of-the-art approaches to show that fuzzy commitment and systematic low leakage coding are the only analyzed schemes that achieve zero leakage

Design, Fabrication, and Run-time Strategies for Hardware-Assisted Security

Today, electronic computing devices are critically involved in our daily lives, basic infrastructure, and national defense systems. With the growing number of threats against them, hardware-based security features offer the best chance for building secure and trustworthy cyber systems. In this dissertation, we investigate ways of making hardware-based security into a reality with primary focus on two areas: Hardware Trojan Detection and Physically Unclonable Functions (PUFs). Hardware Trojans are malicious modifications made to original IC designs or layouts that can jeopardize the integrity of hardware and software platforms. Since most modern systems critically depend on ICs, detection of hardware Trojans has garnered significant interest in academia, industry, as well as governmental agencies. The majority of existing detection schemes focus on test-time because of the limited hardware resources available at run-time. In this dissertation, we explore innovative run-time solutions that utilize on-chip thermal sensor measurements and fundamental estimation/detection theory to expose changes in IC power/thermal profile caused by Trojan activation. The proposed solutions are low overhead and also generalizable to many other sensing modalities and problem instances. Simulation results using state-of-the-art tools on publicly available Trojan benchmarks verify that our approaches can detect Trojans quickly and with few false positives. Physically Unclonable Functions (PUFs) are circuits that rely on IC fabrication variations to generate unique signatures for various security applications such as IC authentication, anti-counterfeiting, cryptographic key generation, and tamper resistance. While the existence of variations has been well exploited in PUF design, knowledge of exactly how variations come into existence has largely been ignored. Yet, for several decades the Design-for-Manufacturability (DFM) community has actually investigated the fundamental sources of these variations. Furthermore, since manufacturing variations are often harmful to IC yield, the existing DFM tools have been geared towards suppressing them (counter-intuitive for PUFs). In this dissertation, we make several improvements over current state-of-the-art work in PUFs. First, our approaches exploit existing DFM models to improve PUFs at physical layout and mask generation levels. Second, our proposed algorithms reverse the role of standard DFM tools and extend them towards improving PUF quality without harming non-PUF portions of the IC. Finally, since our approaches occur after design and before fabrication, they are applicable to all types of PUFs and have little overhead in terms of area, power, etc. The innovative and unconventional techniques presented in this dissertation should act as important building blocks for future work in cyber security

PUF for the Commons: Enhancing Embedded Security on the OS Level

Security is essential for the Internet of Things (IoT). Cryptographic operations for authentication and encryption commonly rely on random input of high entropy and secure, tamper-resistant identities, which are difficult to obtain on constrained embedded devices. In this paper, we design and analyze a generic integration of physically unclonable functions (PUFs) into the IoT operating system RIOT that supports about 250 platforms. Our approach leverages uninitialized SRAM to act as the digital fingerprint for heterogeneous devices. We ground our design on an extensive study of PUF performance in the wild, which involves SRAM measurements on more than 700 IoT nodes that aged naturally in the real-world. We quantify static SRAM bias, as well as the aging effects of devices and incorporate the results in our system. This work closes a previously identified gap of missing statistically significant sample sizes for testing the unpredictability of PUFs. Our experiments on COTS devices of 64 kB SRAM indicate that secure random seeds derived from the SRAM PUF provide 256 Bits-, and device unique keys provide more than 128 Bits of security. In a practical security assessment we show that SRAM PUFs resist moderate attack scenarios, which greatly improves the security of low-end IoT devices.Comment: 18 pages, 12 figures, 3 table

Secret-key rates and privacy leakage in biometric systems

In this thesis both the generation of secret keys from biometric data and the binding of secret keys to biometric data are investigated. These secret keys can be used to regulate access to sensitive data, services, and environments. In a biometric secrecy system a secret key is generated or chosen during an enrollment procedure in which biometric data are observed for the first time. This key is to be reconstructed after these biometric data are observed for the second time when authentication is required. Since biometric measurements are typically noisy, reliable biometric secrecy systems also extract so-called helper data from the biometric observation at the time of enrollment. These helper data facilitate reliable reconstruction of the secret key in the authentication process. Since the helper data are assumed to be public, they should not contain information about the secret key. We say that the secrecy leakage should be negligible. Important parameters of biometric key-generation and key-binding systems include the size of the generated or chosen secret key and the information that the helper data contain (leak) about the biometric observation. This latter parameter is called privacy leakage. Ideally the privacy leakage should be small, to prevent the biometric data of an individual from being compromised. Moreover, the secret-key length (also characterized by the secret-key rate) should be large to minimize the probability that the secret key is guessed and unauthorized access is granted. The first part of this thesis mainly focuses on the fundamental trade-off between the secret-key rate and the privacy-leakage rate in biometric secret-generation and secretbinding systems. This trade-off is studied from an information-theoretical perspective for four biometric settings. The first setting is the classical secret-generation setting as proposed by Maurer [1993] and Ahlswede and Csiszár [1993]. For this setting the achievable secret-key vs. privacy-leakage rate region is determined in this thesis. In the second setting the secret key is not generated by the terminals, but independently chosen during enrollment (key binding). Also for this setting the region of achievable secret-key vs. privacy-leakage rate pairs is determined. In settings three and four zero-leakage systems are considered. In these systems the public message should contain only a negligible amount of information about both the secret key and the biometric enrollment sequence. To achieve this, a private key is needed, which can be observed only by the two terminals. Again both the secret generation setting and chosen secret setting are considered. For these two cases the regions of achievable secret-key vs. private-key rate pairs are determined. For all four settings two notions of leakage are considered. Depending on whether one looks at secrecy and privacy leakage separately or in combination, unconditional or conditional privacy leakage is considered. Here unconditional leakage corresponds to the mutual information between the helper data and the biometric enrollment sequence, while the conditional leakage relates to the conditional version of this mutual information, given the secret. The second part of the thesis focuses on the privacy- and secrecy-leakage analysis of the fuzzy commitment scheme. Fuzzy commitment, proposed by Juels and Wattenberg [1999], is, in fact, a particular realization of a binary biometric secrecy system with a chosen secret key. In this scheme the helper data are constructed as a codeword from an error-correcting code, used to encode a chosen secret, masked with the biometric sequence that has been observed during enrollment. Since this scheme is not privacy preserving in the conditional privacy-leakage sense, the unconditional privacy-leakage case is investigated. Four cases of biometric sources are considered, i.e. memoryless and totally-symmetric biometric sources, memoryless and input-symmetric biometric sources, memoryless biometric sources, and stationary and ergodic biometric sources. For the first two cases the achievable rate-leakage regions are determined. In these cases the secrecy leakage rate need not be positive. For the other two cases only outer bounds on achievable rate-leakage regions are found. These bounds, moreover, are sharpened for fuzzy commitment based on systematic parity-check codes. Using the fundamental trade-offs found in the first part of this thesis, it is shown that fuzzy commitment is only optimal for memoryless totally-symmetric biometric sources and only at the maximum secret-key rate. Moreover, it is demonstrated that for memoryless and stationary ergodic biometric sources, which are not input-symmetric, the fuzzy commitment scheme leaks information on both the secret key and the biometric data. Biometric sequences have an often unknown statistical structure (model) that can be quite complex. The last part of this dissertation addresses the problem of finding the maximum a posteriori (MAP) model for a pair of observed biometric sequences and the problem of estimating the maximum secret-key rate from these sequences. A universal source coding procedure called the Context-TreeWeighting (CTW) method [1995] can be used to find this MAP model. In this thesis a procedure that determines the MAP model, based on the so-called beta-implementation of the CTW method, is proposed. Moreover, CTW methods are used to compress the biometric sequences and sequence pairs in order to estimate the mutual information between the sequences. However, CTW methods were primarily developed for compressing onedimensional sources, while biometric data are often modeled as two-dimensional processes. Therefore it is proved here that the entropy of a stationary two-dimensional source can be expressed as a limit of a series of conditional entropies. This result is also extended to the conditional entropy of one two-dimensional source given another one. As a consequence entropy and mutual information estimates can be obtained from CTW methods using properly-chosen templates. Using such techniques estimates of the maximum secret-key rate for physical unclonable functions (PUFs) are determined from a data-set of observed sequences. PUFs can be regarded as inanimate analogues of biometrics

Variable-Length Bit Mapping and Error-Correcting Codes for Higher-Order Alphabet PUFs

Device-specific physical characteristics provide the foundation for PUFs, a hardware primitive for secure storage of cryptographic keys. So far, they have been implemented by either directly evaluating a binary output or by mapping outputs from a higher-order alphabet to a fixed-length bit sequence. However, the latter causes a significant bias in the derived key when combined with an equidistant quantization. To overcome this limitation, we propose a variable-length bit mapping that reflects the properties of a Gray code in a different metric, namely the Levenshtein metric instead of the classical Hamming metric. Subsequent error-correction is therefore based on a custom insertion/deletion correcting code. This new approach effectively counteracts the bias in the derived key already at the input side. We present the concept for our scheme and demonstrate its feasibility based on an empirical PUF distribution. As a result, we increase the effective output bit length of the secret by over 40% compared to state-of-the-art approaches while at the same time obtaining additional advantages, e.g., an improved tamper-sensitivity. This opens up a new direction of Error-Correcting Codes (ECCs) for PUFs that output responses with symbols of higher-order output alphabets

Secure and Reliable Key Agreement with Physical Unclonable Functions

Different transforms used in binding a secret key to correlated physical-identifier outputs are compared. Decorrelation efficiency is the metric used to determine transforms that give highly-uncorrelated outputs. Scalar quantizers are applied to transform outputs to extract uniformly distributed bit sequences to which secret keys are bound. A set of transforms that perform well in terms of the decorrelation efficiency is applied to ring oscillator (RO) outputs to improve the uniqueness and reliability of extracted bit sequences, to reduce the hardware area and information leakage about the key and RO outputs, and to maximize the secret-key length. Low-complexity error-correction codes are proposed to illustrate two complete key-binding systems with perfect secrecy, and better secret-key and privacy-leakage rates than existing methods. A reference hardware implementation is also provided to demonstrate that the transform-coding approach occupies a small hardware area.Comment: An extra term in the last page due to the mismatch between the Arxiv compiler and MDPI template is eliminated. No other change