Threshold Implementation Research Articles

Low-Latency and Low-Randomness Second-Order Masked Cubic Functions

Masking schemes are the most popular countermeasure to mitigate Side-Channel Analysis (SCA) attacks. Compared to software, their hardware implementations require certain considerations with respect to physical defaults, such as glitches. To counter this extended leakage effect, the technique known as Threshold Implementation (TI) has proven to be a reliable solution. However, its efficiency, namely the number of shares, is tied to the algebraic degree of the target function. As a result, the application of TI may lead to unaffordable implementation costs. This dependency is relaxed by the successor schemes where the minimum number of d + 1 shares suffice for dth-order protection independent of the function’s algebraic degree. By this, although the number of input shares is reduced, the implementation costs are not necessarily low due to their high demand for fresh randomness. It becomes even more challenging when a joint low-latency and low-randomness cost is desired. In this work, we provide a methodology to realize the second-order glitch-extended probing-secure implementation of cubic functions with three shares while allowing to reuse fresh randomness. This enables us to construct low-latency second-order secure implementations of several popular lightweight block ciphers, including Skinny, Midori, and Prince, with a very limited number of fresh masks. Notably, compared to state-of-the-art equivalent implementations, our designs lower the latency in terms of the number of clock cycles while keeping randomness costs low.

Algebraic Persistent Fault Analysis of SKINNY_64 Based on S_Box Decomposition

Algebraic persistent fault analysis (APFA), which combines algebraic analysis with persistent fault attacks, brings new challenges to the security of lightweight block ciphers and has received widespread attention since its introduction. Threshold Implementation (TI) is one of the most widely used countermeasures for side channel attacks. Inspired by this method, the SKINNY block cipher adopts the S_box decomposition to reduce the number of variables in the set of algebraic equations and the number of Conjunctive Normal Form (CNF) equations in this paper, thus speeding up the algebraic persistent fault analysis and reducing the number of fault ciphertexts. In our study, we firstly establish algebraic equations for full-round faulty encryption, and then analyze the relationship between the number of fault ciphertexts required and the solving time in different scenarios (decomposed S_boxes and original S_box). By comparing the two sets of experimental results, the success rate and the efficiency of the attack are greatly improved by using S_box decomposition. In this paper, We can recover the master key in a minimum of 2000s using 11 pairs of plaintext and fault ciphertext, while the key recovery cannot be done in effective time using the original S_box expression equations. At the same time, we apply S_box decomposition to another kind of algebraic persistent fault analysis, and the experimental results show that using S_box decomposition can effectively reduce the solving time and solving success rate under the same conditions.

Power Side-Channel Leakage Assessment Framework at Register-Transfer Level

Power side-channel (PSC) attacks received significant attention over the past two decades due to their effectiveness in breaking mathematically strong cryptographic implementations. However, most existing PSC assessment frameworks apply only to post-silicon implementations; this is unfavorable to the industry due to the lack of flexibility in fixing the design and the high cost/time penalty incurred in redoing the entire design cycle. This article presents the register transfer level (RTL)-power analysis tool (PAT) framework to perform a technology-independent PSC assessment of cryptographic (pre- and post-quantum) hardware at the RTL stage. Performing assessment at the RTL gives designers the utmost flexibility to quickly apply the countermeasures locally. RTL-PAT can also serve as a front-end sign-off framework for PSC leakage, allowing a designer to make changes in the early design stage, which would otherwise be difficult/time-consuming to perform in subsequent design stages. Furthermore, RTL-PAT can analyze both FPGA and ASIC design flows for standalone IPs and SoCs. In this article, we present the efficacy of RTL-PAT on several cryptographic implementations. The results are presented for standalone IPs, which include different AES implementations (Galois field, lookup table, pipelined, and threshold implementation) and <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PRESENT</monospace> cipher. We also analyze a large-scale SoC, which includes the post-quantum SABER implementation and AES. The results show that the framework effectively identifies the leaky modules and validates the efficacy of PSC countermeasures implemented in the RTL. The obtained RTL-PAT assessment results are validated with the post-silicon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> -statistics assessment as well.

Boolean Masking for Arithmetic Additions at Arbitrary Order in Hardware

Modular addition is an important component of many cryptographic algorithms such as ARX-ciphers and lattice-based post-quantum secure schemes. In order to protect devices that execute these algorithms against side-channel attacks, countermeasures such as masking must be applied. However, if an implementation needs to be secured against multivariate attacks, univariately secure masking schemes do not suffice. In this work, we focus on hardware architectures for higher-order masked addition circuits. We present and discuss three adder designs that are protected with a provably secure masking scheme. Concretely, we discuss Kogge–Stone, Sklansky and Brent–Kung adders regarding their suitability for high-order masking and their performance in this setting. All architectures are fully pipelined and achieve a throughput of one addition per cycle. In order to achieve multivariate security at arbitrary orders, we use HPC2 Gadgets that satisfy the PINI security notion. Additionally, we apply a first-order secure threshold implementation scheme to the adder variants and compare their performance in the univariate case.

Optimized threshold implementations: securing cryptographic accelerators for low-energy and low-latency applications

Threshold implementations have emerged as one of the most popular masking countermeasures for hardware implementations of cryptographic primitives. In this work, we provide three TI optimization techniques: First, a generic construction for \(d+1\) TI sharing achieves the minimal number of output shares for any n-input Boolean function of degree \(t=n-1\) and for any d. Next, we present a methodology for finding minimal number of output shares in \(d+1\) TI when \(t<n-1\). Third, a heuristic for minimizing the number of output shares for higher-order \(td + 1\) TI for any n, any t and \(d \le 2\) is proposed. In addition, we describe an optimization for the secure AES schedule which achieves maximum throughput for a serial implementation. Then, we demonstrate the applicability of our results on \(d+1\) and \(td+1\) TI versions, for first- and second-order secure, low-latency and low-energy implementations of the PRINCE block cipher. We show the fastest and the most energy efficient known TI-protected implementations of PRINCE.

Curse of Re-encryption: A Generic Power/EM Analysis on Post-Quantum KEMs

This paper presents a side-channel analysis (SCA) on key encapsulation mechanism (KEM) based on the Fujisaki–Okamoto (FO) transformation and its variants. The FO transformation has been widely used in actively securing KEMs from passively secure public key encryption (PKE), as it is employed in most of NIST post-quantum cryptography (PQC) candidates for KEM. The proposed attack exploits side-channel leakage during execution of a pseudorandom function (PRF) or pseudorandom number generator (PRG) in the re-encryption of KEM decapsulation as a plaintext-checking oracle that tells whether the PKE decryption result is equivalent to the reference plaintext. The generality and practicality of the plaintext-checking oracle allow the proposed attack to attain a full-key recovery of various KEMs when an active attack on the underlying PKE is known. This paper demonstrates that the proposed attack can be applied to most NIST PQC third-round KEM candidates, namely, Kyber, Saber, FrodoKEM, NTRU, NTRU Prime, HQC, BIKE, and SIKE (for BIKE, the proposed attack achieves a partial key recovery). The applicability to Classic McEliece is unclear because there is no known active attack on this cryptosystem. This paper also presents a side-channel distinguisher design based on deep learning (DL) for mounting the proposed attack on practical implementation without the use of a profiling device. The feasibility of the proposed attack is evaluated through experimental attacks on various PRF implementations (a SHAKE software, an AES software, an AES hardware, a bit-sliced masked AES software, and a masked AES hardware based on threshold implementation). Although it is difficult to implement the oracle using the leakage from the TI-based masked hardware, the success of the proposed attack against these implementations (even except for the masked hardware), which include masked software, confirms its practicality.

Impact of a New Cost-Effectiveness Threshold Implementation on Cancer Formulary Decisions in Jordan.

Rising prices of novel cancer medications are increasing the economic burden from cancer in Jordan, risking the ability of cancer patients to access lifesaving and life-extending treatments. Furthermore, in the absence of a national health technology assessment (HTA) framework, medication prices in Jordan are set based on manufacturers’ pricing considerations and not a value proposition. In response to these challenges, King Hussein Cancer Center (KHCC), the de facto national cancer institute, developed a first-in-country, cancer-specific, cost-effectiveness threshold (CET) to aid institutional decision makers in approving only cost-effective medications. Over the past 10 years, cost-effectiveness analyses based on this CET have led to the introduction of > 70% of requested novel cancer medications after manufacturers agreed to lower prices, beyond registration prices, to meet the CET. Future work is warranted to empirically derive a CET for Jordan to better guide reimbursement decisions.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41669-021-00293-4.

Resilient uniformity: applying resiliency in masking

Threshold Implementations are known countermeasures defending against side-channel attacks via the use of masking techniques. While sufficient properties are known to defend against first-order side-channel attacks, it is not known how to achieve higher-order security. This work generalizes the Threshold Implementation notion of uniformity and proves it achieves second-order protection. The notion is applied to create a second-order masking of the Present cipher with a low randomness cost.

Second-Order SCA Security with almost no Fresh Randomness

Masking schemes are among the most popular countermeasures against Side-Channel Analysis (SCA) attacks. Realization of masked implementations on hardware faces several difficulties including dealing with glitches. Threshold Implementation (TI) is known as the first strategy with provable security in presence of glitches. In addition to the desired security order d, TI defines the minimum number of shares to also depend on the algebraic degree of the target function. This may lead to unaffordable implementation costs for higher orders.For example, at least five shares are required to protect the smallest nonlinear function against second-order attacks. By cuttingsuch a dependency, the successor schemes are able to achieve the same security level by just d + 1 shares, at the cost of high demand for fresh randomness, particularly at higher orders. In this work, we provide a methodology to realize the second-order glitch-extended probing-secure implementation of a group of quadratic functions with three shares and no fresh randomness. This allows us to construct second-order secure implementations of several cryptographic primitives with very limited number of fresh masks, including Keccak, SKINNY, Midori, PRESENT, and PRINCE.

Countermeasures against Static Power Attacks

In recent years it has been demonstrated convincingly that the standby power of a CMOS chip reveals information about the internally stored and processed data. Thus, for adversaries who seek to extract secrets from cryptographic devices via side-channel analysis, the static power has become an attractive quantity to obtain. Most works have focused on the destructive side of this subject by demonstrating attacks. In this work, we examine potential solutions to protect circuits from silently leaking sensitive information during idle times. We focus on countermeasures that can be implemented using any common digital standard cell library and do not consider solutions that require full-custom or analog design flow. In particular, we evaluate and compare a set of five distinct standard-cell-based hiding countermeasures, including both, randomization and equalization techniques. We then combine the hiding countermeasures with state-of-the-art hardware masking in order to amplify the noise level and achieve a high resistance against attacks. An important part of our contribution is the proposal and evaluation of the first ever standard-cell-based balancing scheme which achieves perfect data-independence on paper, i.e., in absence of intra-die process variations and aging effects. We call our new countermeasure Exhaustive Logic Balancing (ELB). While this scheme, applied to a threshold implementation, provides the highest level of resistance in our experiments, it may not be the most cost effective option due to the significant resource overhead associated. All evaluated countermeasures and combinations thereof are applied to a serialized hardware implementation of the PRESENT block cipher and realized as cryptographic co-processors on a 28nm CMOS ASIC prototype. Our experimental results are obtained through real-silicon measurements of a fabricated die of the ASIC in a temperature-controlled environment using a source measure unit (SMU). We believe that our elaborate comparison serves as a useful guideline for hardware designers to find a proper tradeoff between security and cost for almost any application.

Monomial evaluation of polynomial functions protected by threshold implementations—with an illustration on AES—

Monomial evaluation of polynomial functions protected by threshold implementations—with an illustration on AES—

RAIN: A Lightweight Block Cipher Towards Software, Hardware and Threshold Implementations

RAIN: A Lightweight Block Cipher Towards Software, Hardware and Threshold Implementations

Unbalanced sharing: a threshold implementation of SM4

Unbalanced sharing: a threshold implementation of SM4

Thresholdizing HashEdDSA: MPC to the Rescue

Following recent comments in a NIST document related to threshold cryptographic standards, we examine the case of thresholdizing the HashEdDSA signature scheme. This is a deterministic signature scheme based on Edwards elliptic curves. Unlike DSA, it has a Schnorr-like signature equation, which is an advantage for threshold implementations, but it has the disadvantage of having the ephemeral secret obtained by hashing the secret key and the message. We show that one can obtain relatively efficient implementations of threshold HashEdDSA with no modifications to the behaviour of the signing algorithm; we achieve this using a doubly authenticated bit (daBit) generation protocol tailored for $$\mathcal {Q}_2$$ access structures that is more efficient than prior work. However, if one was to modify the standard algorithm to use an MPC-friendly hash function, such as Rescue, the performance becomes very fast indeed.

LLTI: Low-Latency Threshold Implementations

With the enormous increase in portable cryptographic devices, physical attacks are becoming similarly popular. One of the most common physical attacks is Side-Channel Analysis (SCA), extremely dangerous due to its non-invasive nature. Threshold Implementations (TI) was proposed as the first countermeasure to provide provable security in masked hardware implementations. While most works on hardware masking are focused on optimizing the area requirements, with the newer and smaller technologies area is taking a backseat, and low-latency is gaining importance. In this work, we revisit the scheme proposed by Arribas et al. in TCHES 2018 to secure unrolled implementations. We formalize and expand this methodology, to devise a masking scheme, derived from TI, designed to secure hardware implementations optimized for latency named Low-Latency Threshold Implementations (LLTI). By applying the distributive property and leveraging a divide-and-conquer strategy, we split a non-linear operation in layers which are masked separately. The result is a more efficient scheme than the former TI for any operation of algebraic degree greater than two, achieving great optimizations both in terms of speed and area. We compare the performance of first-order LLTI with first-order TI in securing a cubic gate and a degree-7 AND gate without using any registers in between. We achieve a 137% increase in maximum frequency and a 60% reduction in area for the cubic gate, and 3131 times reduction in area in the case of a degree-7 AND gate compared to TI. To further illustrate the power of our scheme we take a low-latency PRINCE implementation from the literature and, by simply changing the secure S-box with the LLTI version, we achieve a 46% max. frequency improvement and a 38% area reduction. Moreover, we apply LLTI to a secure a low-latency AES implementation and compare it with the TI version, achieving a 6.9 times max. freq. increase and a 47.2% area reduction.

On the Parity of Power Permutations

Side-channel analysis (SCA) attacks and many countermeasures to foil these attacks have been the subject of a large body of research. Different masking schemes have been proposed as countermeasures, one of which is Threshold Implementation (TI), which carries proof of security against DPA even in the presence of glitches. At the same time, it requires a smaller area and uses much less randomness than the other secure masking methods. One of the methods to have an efficient TI of high degree S-boxes is the decomposition method. Our goal in this paper is to analyze the nonlinear components of symmetric cryptographic algorithms. To minimize the area of the protected implementation of cryptographic algorithms, we show the conditions to decompose the substitutions boxes, which are permutations, of high algebraic degree into the ones of lower degree. To find the conditions, we target the decomposition of permutations into quadratic or cubic permutations by considering the power permutations and their parities, which help us determine whether the higher degree permutations are decomposable power permutations or not. Finally, the decomposition results about the finite fields and corresponding lower degree power permutations are presented.

Diffusional Side-Channel Leakage From Unrolled Lightweight Block Ciphers: A Case Study of Power Analysis on PRINCE

This study investigates a new side-channel leakage observed in the inner rounds of an unrolled hardware implementation of block ciphers in a chosen-input attack scenario. The side-channel leakage occurs in the first round and it can be observed in the later inner rounds because it arises from path activation bias caused by the difference between two consecutive inputs. Therefore, a new attack that exploits the leakage is possible even for unrolled implementations equipped with countermeasures (masking and/or deglitchers that separate the circuit in terms of glitch propagation) in the round involving the leakage. We validate the existence of such a unique side-channel leakage through a set of experiments with a fully unrolled PRINCE cipher hardware, implemented on a field-programmable gate array (FPGA). In addition, we verify the validity and evaluate the hardware cost of a countermeasure for the unrolled implementation, namely the Threshold Implementation (TI) countermeasure.

Detection Algorithm for Cellular Synchronization Signals in Airborne Applications

Cellular to air communication is critical for the booming aerial package delivery and transportation business. Detecting cellular signals in airborne applications is challenging because it requires receiving and processing waveforms that are subject to significantly more interference than those experienced in terrestrial settings. This paper highlights and tackles the complexity of 4G Long Term Evolution (LTE) signal synchronization in high altitude applications, e.g., cell access onboard an aircraft. Specifically, we design a novel cell detector that operates efficiently under high interference levels found in airborne applications, maintains a constant false alarm rate using an optimized threshold implementation for Zadoff Chu sequences, and monitors multiple towers with different time delays simultaneously. We validate our cell detector through simulation and experimentation. Lastly, the cell detector is used to estimate the interference in live waveforms taken from an aircraft at 2 to 2.5 km altitude and velocities of 200–400 km/h. Our cell detection model can be adapted to support 5G New Radio (NR) synchronization signals as NR deploys aerial support in the future. The threshold implementation to handle correlation spurs can be applied directly to other Zadoff Chu based signals such as random access signals found in both LTE and NR.

The DICOM CT Image Compression Based On Enhanced Lossless Prediction And Multilevel Thresholding Based Hybrid Cuckoo Search With Hill Climbing (CS-HC) Algorithm Based Segmentation

In computer vision applications, image segmentation is a common image processing step. It is used to separate pixels into different groups. The rise in the threshold count would hinder the segmentation phase of images. At the same time, in the field of threshold implementation in the image, it becomes an NT concern. This thesis suggests a multilevel threshold based on optimization techniques to remove ROI and uses enhanced lossless prediction algorithm to compress DICOM images in telemedicine applications. The hybrid Cuckoo search with hill climbing (CS-HC) algorithm strengthens the process used by the search agent to update the optimal solution. This algorithm calculates the threshold value. The superior results are produced by the proposed multilevel level thresholding based on CS-HC, as seen by the simulation results. Optimization is efficient and it has a high degree of convergence. Effective results are provided by the proposed lossless compression algorithm based on classification and blending estimation as compared with JPEG lossless and lossy compression techniques. With various threshold values, the algorithm 's efficiency is checked. To apply this algorithm, Matlab2010a is used and DICOM photos are used to validate it.

LM-DAE: Low-Memory Deterministic Authenticated Encryption for 128-bit Security

This paper proposes a new lightweight deterministic authenticated encryption (DAE) scheme providing 128-bit security. Lightweight DAE schemes are practically important because resource-restricted devices sometimes cannot afford to manage a nonce properly. For this purpose, we first design a new mode LM-DAE that has a minimal state size and uses a tweakable block cipher (TBC). The design can be implemented with low memory and is advantageous in threshold implementations (TI) as a side-channel attack countermeasure. LM-DAE further reduces the implementation cost by eliminating the inverse tweak schedule needed in the previous TBC-based DAE modes. LM-DAE is proven to be indistinguishable from an ideal DAE up to the O(2n) query complexity for the block size n. To achieve 128-bit security, an underlying TBC must handle a 128-bit block, 128-bit key, and 128+4-bit tweak, where the 4-bit tweak comes from the domain separation. To satisfy this requirement, we extend SKINNY-128-256 with an additional 4-bit tweak, by applying the elastic-tweak proposed by Chakraborti et al. We evaluate the hardware performances of the proposed scheme with and without TI. Our LM-DAE implementation achieves 3,717 gates, roughly 15% fewer than state-of-the-art nonce-based schemes, thanks to removing the inverse tweak schedule.