Secure and Efficient RNS Approach for Elliptic Curve Cryptography

Scalar multiplication, the main operation in elliptic curve cryptographic protocols, is vulnerable to side-channel (SCA) and fault injection (FA) attacks. An efficient countermeasure for scalar multiplication can be provided by using alternative number systems like the Residue Number System (RNS). In RNS, a number is represented as a set of smaller numbers, where each one is the result of the modular reduction with a given moduli basis. Under certain requirements, a number can be uniquely transformed from the integers to the RNS domain (and vice versa) and all arithmetic operations can be performed in RNS. This representation provides an inherent SCA and FA resistance to many attacks and can be further enhanced by RNS arithmetic manipulation or more traditional algorithmic countermeasures. In this paper, extending our previous work, we explore the potentials of RNS as an SCA and FA countermeasure and provide an description of RNS based SCA and FA resistance means. We propose a secure and efficient Montgomery Power Ladder based scalar multiplication algorithm on RNS and discuss its SCAFA resistance. The proposed algorithm is implemented on an ARM Cortex A7 processor and its SCA-FA resistance is evaluated by collecting preliminary leakage trace results that validate our initial assumptions

Methods increasing inherent resistance of ECC designs against horizontal attacks

Due to the nature of applications such as critical infrastructure and the Internet of Things etc. side channel analysis attacks are becoming a serious threat. Side channel analysis attacks take advantage from the fact that the behaviour of crypto implementations can be observed and provides hints that simplify revealing keys. A new type of SCA is the so called horizontal differential SCA. In this paper we investigate two different approaches to increase the inherent resistance of our hardware accelerator for the kP operation. The first approach aims at reducing the impact of the addressing in our design by realizing a regular schedule of the addressing. In the second approach, we investigated how the formula used to implement the multiplication of GF(2n)-elements influences the results of horizontal DPA attacks against a Montgomery kP-implementation. We implemented 5 designs with different partial multipliers, i.e. based on different multiplication formulae. We used two different technologies, i.e. a 130 and a 250 nm technology, to simulate power traces for our analysis. We show that the implemented multiplication formula influences the success of horizontal attacks significantly. The combination of these two approaches leads to the most resistant design. For the 250 nm technology only 2 key candidates could be revealed with a correctness of about 70% which is a huge improvement given the fact that for the original design 7 key candidates achieved a correctness of more than 90%. For our 130 nm technology no key candidate was revealed with a correctness of more than 60%

Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

The Montgomery kP algorithm i.e. the Montgomery ladder is reported in literature as resistant against simple SCA due to the fact that the processing of each key bit value of the scalar k is done using the same sequence of operations. We implemented the Montgomery kP algorithm using Lopez-Dahab projective coordinates for the NIST elliptic curve B-233. We instantiated the same VHDL code for a wide range of clock frequencies for the same target FPGA and using the same compiler options. We measured electromagnetic traces of the kP executions using the same input data, i.e. scalar k and elliptic curve point P, and measurement setup. Additionally, we synthesized the same VHDL code for two IHP CMOS technologies, for a broad spectrum of frequencies. We simulated the power consumption of each synthesized design during an execution of the kP operation, always using the same scalar k and elliptic curve point P as inputs. Our experiments clearly show that the success of simple electromagnetic analysis attacks against FPGA implementations as well as the one of simple power analysis attacks against synthesized ASIC designs depends on the target frequency for which the design was implemented and at which it is executed significantly. In our experiments the scalar k was successfully revealed via simple visual inspection of the electromagnetic traces of the FPGA for frequencies from 40 to 100 MHz when standard compile options were used as well as from 50 MHz up to 240 MHz when performance optimizing compile options were used. We obtained similar results attacking the power traces simulated for the ASIC. Despite the significant differences of the here investigated technologies the designs’ resistance against the attacks performed is similar: only a few points in the traces represent strong leakage sources allowing to reveal the key at very low and very high frequencies. For the “middle” frequencies the number of points which allow to successfully reveal the key increases when increasing the frequency

Circuit-Variant Moving Target Defense for Side-Channel Attacks on Reconfigurable Hardware

With the emergence of side-channel analysis (SCA) attacks, bits of a secret key may be derived by correlating key values with physical properties of cryptographic process execution. Power and Electromagnetic (EM) analysis attacks are based on the principle that current flow within a cryptographic device is key-dependent and therefore, the resulting power consumption and EM emanations during encryption and/or decryption can be correlated to secret key values. These side-channel attacks require several measurements of the target process in order to amplify the signal of interest, filter out noise, and derive the secret key through statistical analysis methods. Differential power and EM analysis attacks rely on correlating actual side-channel measurements to hypothetical models. This research proposes increasing resistance to differential power and EM analysis attacks through structural and spatial randomization of an implementation. By introducing randomly located circuit variants of encryption components, the proposed moving target defense aims to disrupt side-channel collection and correlation needed to successfully implement an attac

Improving Security and Reliability of Physical Unclonable Functions Using Machine Learning

Physical Unclonable Functions (PUFs) are promising security primitives for device authenti-cation and key generation. Due to the noise influence, reliability is an important performance metric of PUF-based authentication. In the literature, lots of efforts have been devoted to enhancing PUF reliability by using error correction methods such as error-correcting codes and fuzzy extractor. Ho-wever, one property that most of these prior works overlooked is the non-uniform distribution of PUF response across different bits. This wok proposes a two-step methodology to improve the reliability of PUF under noisy conditions. The first step involves acquiring the parameters of PUF models by using machine lear-ning algorithms. The second step then utilizes these obtained parameters to improve the reliability of PUFs by selectively choosing challenge-response pairs (CRPs) for authentication. Two distinct algorithms for improving the reliability of multiplexer (MUX) PUF, i.e., total delay difference thresholding and sensitive bits grouping, are presented. It is important to note that the methodology can be easily applied to other types of PUFs as well. Our experimental results show that the relia-bility of PUF-based authentication can be significantly improved by the proposed approaches. For example, in one experimental setting, the reliability of an MUX PUF is improved from 89.75% to 94.07% using total delay difference thresholding, while 89.30% of generated challenges are stored. As opposed to total delay difference thresholding, sensitive bits grouping possesses higher efficiency, as it can produce reliable CRPs directly. Our experimental results show that the reliability can be improved to 96.91% under the same setting, when we group 12 bits in the challenge vector of a 128-stage MUX PUF. Besides, because the actual noise varies greatly in different conditions, it is hard to predict the error of of each individual PUF response bit. This wok proposes a novel methodology to improve the efficiency of PUF response error correction based on error-rates. The proposed method first obtains the PUF model by using machine learning techniques, which is then used to predict the error-rates. Intuitively, we are inclined to tolerate errors in PUF response bits with relatively higher error-rates. Thus, we propose to treat different PUF response bits with different degrees of error tolerance, according to their estimated error-rates. Specifically, by assigning optimized weights, i.e., 0, 1, 2, 3, and infinity to PUF response bits, while a small portion of high error rates responses are truncated; the other responses are duplicated to a limited number of bits according to error-rates before error correction and a portion of low error-rates responses bypass the error correction as direct keys. The hardware cost for error correction can also be reduced by employing these methods. Response weighting is capable of reducing the false negative and false positive simultaneously. The entropy can also be controlled. Our experimental results show that the response weighting algorithm can reduce not only the false negative from 20.60% to 1.71%, but also the false positive rate from 1.26 × 10−21 to 5.38 × 10−22 for a PUF-based authentication with 127-bit response and 13-bit error correction. Besides, three case studies about the applications of the proposed algorithm are also discussed. Along with the rapid development of hardware security techniques, the revolutionary gro-wth of countermeasures or attacking methods developed by intelligent and adaptive adversaries have significantly complicated the ability to create secure hardware systems. Thus, there is a critical need to (re)evaluate existing or new hardware security techniques against these state-of-the-art attacking methods. With this in mind, this wok presents a novel framework for incorporating active learning techniques into hardware security field. We demonstrate that active learning can significantly im-prove the learning efficiency of PUF modeling attack, which samples the least confident and the most informative challenge-response pair (CRP) for training in each iteration. For example, our ex-perimental results show that in order to obtain a prediction error below 4%, 2790 CRPs are required in passive learning, while only 811 CRPs are required in active learning. The sampling strategies and detailed applications of PUF modeling attack under various environmental conditions are also discussed. When the environment is very noisy, active learning may sample a large number of mis-labeled CRPs and hence result in high prediction error. We present two methods to mitigate the contradiction between informative and noisy CRPs. At last, it is critical to design secure PUF, which can mitigate the countermeasures or modeling attacking from intelligent and adaptive adversaries. Previously, researchers devoted to hiding PUF information by pre- or post processing of PUF challenge/response. However, these methods are still subject to side-channel analysis based hybrid attacks. Methods for increasing the non-linearity of PUF structure, such as feedforward PUF, cascade PUF and subthreshold current PUF, have also been proposed. However, these methods significantly degrade the reliability. Based on the previous work, this work proposes a novel concept, noisy PUF, which achieves modeling attack resistance while maintaining a high degree of reliability for selected CRPs. A possible design of noisy PUF along with the corresponding experimental results is also presented

ASSESSING AND IMPROVING THE RELIABILITY AND SECURITY OF CIRCUITS AFFECTED BY NATURAL AND INTENTIONAL FAULTS

The reliability and security vulnerability of modern electronic systems have emerged as concerns due to the increasing natural and intentional interferences. Radiation of high-energy charged particles generated from space environment or packaging materials on the substrate of integrated circuits results in natural faults. As the technology scales down, factors such as critical charge, voltage supply, and frequency change tremendously that increase the sensitivity of integrated circuits to natural faults even for systems operating at sea level. An attacker is able to simulate the impact of natural faults and compromise the circuit or cause denial of service. Therefore, instead of utilizing different approaches to counteract the effect of natural and intentional faults, a unified countermeasure is introduced. The unified countermeasure thwarts the impact of both reliability and security threats without paying the price of more area overhead, power consumption, and required time. This thesis first proposes a systematic analysis method to assess the probability of natural faults propagating the circuit and eventually being latched. The second part of this work focuses on the methods to thwart the impact of intentional faults in cryptosystems. We exploit a power-based side-channel analysis method to analyze the effect of the existing fault detection methods for natural faults on fault attack. Countermeasures for different security threats on cryptosystems are investigated separately. Furthermore, a new micro-architecture is proposed to thwart the combination of fault attacks and side-channel attacks, reducing the fault bypass rate and slowing down the key retrieval speed. The third contribution of this thesis is a unified countermeasure to thwart the impact of both natural faults and attacks. The unified countermeasure utilizes dynamically alternated multiple generator polynomials for the cyclic redundancy check (CRC) codec to resist the reverse engineering attack

Machine-Learning assisted Side-Channel Attacks on RNS-based Elliptic Curve Implementations using Hybrid Feature Engineering

Side-channel attacks based on machine learning have recently been introduced to recover the secret information from software and hardware implementations of mathematically secure algorithms. Convolutional Neural Networks (CNNs) have proven to outperform the template attacks due to their ability of handling misalignment in the symmetric algorithms leakage data traces. However, one of the limitations of deep learning algorithms is the requirement of huge datasets for model training. For evaluation scenarios, where limited leakage trace instances are available, simple machine learning with the selection of proper feature engineering, data splitting, and validation techniques, can be more effective. Moreover, limited analysis exists for public-key algorithms, especially on non-traditional implementations like those using Residue Number System (RNS). Template attacks are successful on RNS-based Elliptic Curve Cryptography (ECC), only if the aligned portion is used in templates. In this study, we present a systematic methodology for the evaluation of ECC cryptosystems with and without countermeasures against machine learning side-channel attacks using two attack models. RNS-based ECC datasets have been evaluated using four machine learning classifiers and comparison is provided with existing state-of-the-art template attacks. Moreover, we analyze the impact of raw features and advanced hybrid feature engineering techniques, along with the effect of splitting ratio. We discuss the metrics and procedures that can be used for accurate classification on the imbalance datasets. The experimental results demonstrate that, for ECC RNS datasets, the efficiency of simple machine learning algorithms is better than the complex deep learning techniques when such datasets are not so huge

Envisioning the Future of Cyber Security in Post-Quantum Era: A Survey on PQ Standardization, Applications, Challenges and Opportunities

The rise of quantum computers exposes vulnerabilities in current public key cryptographic protocols, necessitating the development of secure post-quantum (PQ) schemes. Hence, we conduct a comprehensive study on various PQ approaches, covering the constructional design, structural vulnerabilities, and offer security assessments, implementation evaluations, and a particular focus on side-channel attacks. We analyze global standardization processes, evaluate their metrics in relation to real-world applications, and primarily focus on standardized PQ schemes, selected additional signature competition candidates, and PQ-secure cutting-edge schemes beyond standardization. Finally, we present visions and potential future directions for a seamless transition to the PQ era

Implementation Attacks on Post-Quantum Cryptographic Schemes

Post-quantum cryptographic schemes have been developed in the last decade in response to the rise of quantum computers. Fortunately, several schemes have been developed with quantum resistance. However, there is very little effort in evaluating and comparing these schemes in the embedded settings. Low cost embedded devices represents a highly-constraint environment that challenges all post-quantum cryptographic schemes. Moreover, there are even fewer efforts in evaluating the security of these schemes against implementation attacks including side-channel and fault attacks. It is commonly accepted that, any embedded cryptographic module that is built without a sound countermeasure, can be easily broken. Therefore, we investigate the question: Are we ready to implement post-quantum cryptographic schemes on embedded systems? We present an exhaustive survey of research efforts in designing embedded modules of post-quantum cryptographic schemes and the efforts in securing these modules against implementation attacks. Unfortunately, the study shows that: we are not ready yet to implement any post-quantum cryptographic scheme in practical embedded systems. There is still a considerable amount of research that needs to be conducted before reaching a satisfactory level of security

Designing Novel Hardware Security Primitives for Smart Computing Devices

Smart computing devices are miniaturized electronics devices that can sense their surroundings, communicate, and share information autonomously with other devices to work cohesively. Smart devices have played a major role in improving quality of the life and boosting the global economy. They are ubiquitously present, smart home, smart city, smart girds, industry, healthcare, controlling the hazardous environment, and military, etc. However, we have witnessed an exponential rise in potential threat vectors and physical attacks in recent years. The conventional software-based security approaches are not suitable in the smart computing device, therefore, hardware-enabled security solutions have emerged as an attractive choice. Developing hardware security primitives, such as True Random Number Generator (TRNG) and Physically Unclonable Function (PUF) from electrical properties of the sensor could be a novel research direction. Secondly, the Lightweight Cryptographic (LWC) ciphers used in smart computing devices are found vulnerable against Correlation Power Analysis (CPA) attack. The CPA performs statistical analysis of the power consumption of the cryptographic core and reveals the encryption key. The countermeasure against CPA results in an increase in energy consumption, therefore, they are not suitable for battery operated smart computing devices. The primary goal of this dissertation is to develop novel hardware security primitives from existing sensors and energy-efficient LWC circuit implementation with CPA resilience. To achieve these. we focus on developing TRNG and PUF from existing photoresistor and photovoltaic solar cell sensors in smart devices Further, we explored energy recovery computing (also known as adiabatic computing) circuit design technique that reduces the energy consumption compared to baseline CMOS logic design and same time increasing CPA resilience in low-frequency applications, e.g. wearable fitness gadgets, hearing aid and biomedical instruments. The first contribution of this dissertation is to develop a TRNG prototype from the uncertainty present in photoresistor sensors. The existing sensor-based TRNGs suffer a low random bit generation rate, therefore, are not suitable in real-time applications. The proposed prototype has an average random bit generation rate of 8 kbps, 32 times higher than the existing sensor-based TRNG. The proposed lightweight scrambling method results in random bit entropy close to ideal value 1. The proposed TRNG prototype passes all 15 statistical tests of the National Institute of Standards and Technology (NIST) Statistical Test Suite with quality performance. The second contribution of this dissertation is to develop an integrated TRNG-PUF designed using photovoltaic solar cell sensors. The TRNG and PUF are mutually independent in the way they are designed, therefore, integrating them as one architecture can be beneficial in resource-constrained computing devices. We propose a novel histogram-based technique to segregate photovoltaic solar cell sensor response suitable for TRNG and PUF respectively. The proposed prototype archives approximately 34\% improvement in TRNG output. The proposed prototype achieves an average of 92.13\% reliability and 50.91\% uniformity performance in PUF response. The proposed sensor-based hardware security primitives do not require additional interfacing hardware. Therefore, they can be ported as a software update on existing photoresistor and photovoltaic sensor-based devices. Furthermore, the sensor-based design approach can identify physically tempered and faulty sensor nodes during authentication as their response bit differs. The third contribution is towards the development of a novel 2-phase sinusoidal clocking implementation, 2-SPGAL for existing Symmetric Pass Gate Adiabatic Logic (SPGAL). The proposed 2-SPGAL logic-based LWC cipher PRESENT shows an average of 49.34\% energy saving compared to baseline CMOS logic implementation. Furthermore, the 2-SPGAL prototype has an average of 22.76\% better energy saving compared to 2-EE-SPFAL (2-phase Energy-Efficient-Secure Positive Feedback Adiabatic Logic). The proposed 2-SPGAL was tested for energy-efficiency performance for the frequency range of 50 kHz to 250 kHz, used in healthcare gadgets and biomedical instruments. The proposed 2-SPGAL based design saves 16.78\% transistor count compared to 2-EE-SPFAL counterpart. The final contribution is to explore Clocked CMOS Adiabatic Logic (CCAL) to design a cryptographic circuit. Previously proposed 2-SPGAL and 2-EE-SPFAL uses two complementary pairs of the transistor evaluation network, thus resulting in a higher transistor count compared to the CMOS counterpart. The CCAL structure is very similar to CMOS and unlike 2-SPGAL and 2-EE-SPFAL, it does not require discharge circuitry to improve security performance. The case-study implementation LWC cipher PRESENT S-Box using CCAL results into 45.74\% and 34.88\% transistor count saving compared to 2-EE-SPFAL and 2-SPGAL counterpart. Furthermore, the case-study implementation using CCAL shows more than 95\% energy saving compared to CMOS logic at frequency range 50 kHz to 125 kHz, and approximately 60\% energy saving at frequency 250 kHz. The case study also shows 32.67\% and 11.21\% more energy saving compared to 2-EE-SPFAL and 2-SPGAL respectively at frequency 250 kHz. We also show that 200 fF of tank capacitor in the clock generator circuit results in optimum energy and security performance in CCAL