Boolean Masking Research Articles

Provably Secure and Area-Efficient Modular Addition over Boolean Shares

Several cryptographic schemes, including lattice-based cryptography and the SHA-2 family of hash functions, involve both integer arithmetic and Boolean logic. Each of these classes of operations, considered separately, can be efficiently implemented under the masking countermeasure when resistance against vertical attacks is required. However, protecting interleaved arithmetic and logic operations is much more expensive, requiring either additional masking conversions to switch between masking schemes, or implementing arithmetic functions as nonlinear operations over a Boolean masking. Both solutions can be achieved by providing masked arithmetic addition over Boolean shares, which is an operation with relatively long latency and usually high area utilization in hardware. A further complication arises when the arithmetic performed by the scheme is over a prime modulus, which is common in lattice-based cryptography. In this work, we propose a first-order masked implementation of arithmetic addition over Boolean shares occupying a very small area, while still having reasonable latency. Our proposal is specifically tuned for efficient addition and subtraction modulo an arbitrary integer, but it can also be configured at runtime for power-of-two arithmetic. To the best of our knowledge, we propose the first such construction whose security is formally proven in the glitch+transition-robust probing model.

An Efficient Masked White-Box Implementation of SM4

Differential computation analysis (DCA) is a powerful method for extracting secret information from carefully designed white-box schemes without reverse engineering. Consequently, white-box solutions typically require substantial storage and computing resources to withstand DCAs, as demonstrated by the schemes proposed by Zhang et al. and Yuan et al. for the ISO/IEC standard algorithm SM4. Our approach employs Boolean masking to obscure the correlation between the key and intermediate states. Additionally, we introduce nonlinear permutations to reuse random mask values, thereby reducing space consumption. Experimental results indicate that DCAs against both the simplified version and the algebraic enhancement version of our scheme fail to retrieve the correct keys. Moreover, the former version can be implemented with approximately 1.62 MB of memory and the latter with 7.8 MB, which is much less than 24.3 MB (Zhang et al.) and 34.5 MB (Yuan et al.). Consequently, our design can thwart first-order DCA with lower overhead.

A Low-Latency High-Order Arithmetic to Boolean Masking Conversion

Masking, an effective countermeasure against side-channel attacks, is commonly applied in modern cryptographic implementations. Considering cryptographic algorithms that utilize both Boolean and arithmetic masking, the conversion algorithm between arithmetic masking and Boolean masking is required. Conventional high-order arithmetic masking to Boolean masking conversion algorithms based on Boolean circuits suffer from performance overhead, especially in terms of hardware implementation. In this work, we analyze high latency for the conversion and propose an improved high-order A2B conversion algorithm. For the conversion of 16-bit variables, the hardware latency can be reduced by 47% in the best scenario. For the case study of second-order 32-bit conversion, the implementation results show that the improved scheme reduces the clock cycle latency by 42% in hardware and achieves a 30% speed performance improvement in software. Theoretically, a security proof of arbitrary order is provided for the proposed high-order A2B conversion. Experimental validations are performed to verify the second-order DPA resistance of second-order implementation. The Test Vector Leakage Assessment does not observe side-channel leakage for hardware and software implementations.

Prime-Field Masking in Hardware and its Soundness against Low-Noise SCA Attacks

A recent study suggests that arithmetic masking in prime fields leads to stronger security guarantees against passive physical adversaries than Boolean masking. Indeed, it is a common observation that the desired security amplification of Boolean masking collapses when the noise level in the measurements is too low. Arithmetic encodings in prime fields can help to maintain an exponential increase of the attack complexity in the number of shares even in such a challenging context. In this work, we contribute to this emerging topic in two main directions. First, we propose novel masked hardware gadgets for secure squaring in prime fields (since squaring is non-linear in non-binary fields) which prove to be significantly more resource-friendly than corresponding masked multiplications. We then formally show their local and compositional security for arbitrary orders. Second, we attempt to >experimentally evaluate the performance vs. security tradeoff of prime-field masking. In order to enable a first comparative case study in this regard, we exemplarily consider masked implementations of the AES as well as the recently proposed AESprime. AES-prime is a block cipher partially resembling the standard AES, but based on arithmetic operations modulo a small Mersenne prime. We present cost and performance figures for masked AES and AES-prime implementations, and experimentally evaluate their susceptibility to low-noise side-channel attacks. We consider both the dynamic and the static power consumption for our low-noise analyses and emulate strong adversaries. Static power attacks are indeed known as a threat for side-channel countermeasures that require a certain noise level to be effective because of the adversary’s ability to reduce the noise through intra-trace averaging. Our results show consistently that for the noise levels in our practical experiments, the masked prime-field implementations provide much higher security for the same number of shares. This compensates for the overheads prime computations lead to and remains true even if / despite leaking each share with a similar Signal-to-Noise Ratio (SNR) as their binary equivalents. We hope our results open the way towards new cipher designs tailored to best exploit the advantages of prime-field masking.

Design and Implementation of a Secure RISC-V Microprocessor

Secret keys can be extracted from the power consumption or electromagnetic emanations of unprotected devices. Traditional countermeasures have a limited scope of protection and impose several restrictions on how sensitive data must be manipulated. We demonstrate a bit-serial RISC-V microprocessor implementation with no plain-text data. All values are protected using Boolean masking. Software can run with little to no countermeasures, reducing code size and performance overheads. Unlike previous literature, our methodology is fully automated and can be applied to designs of arbitrary size or complexity. We also provide details on other key components, such as clock randomizer, memory protection, and random number generator (RNG). The microprocessor was implemented in 65-nm CMOS technology. Its implementation was evaluated using NIST tests and side-channel attacks. Random numbers generated with our RNG pass on all NIST tests. The side-channel analysis on the baseline implementation extracted the advanced encryption system (AES) key using only 375 traces, while our secure microprocessor was able to withstand attacks using 20M traces.

Bitslicing Arithmetic/Boolean Masking Conversions for Fun and Profit

The performance of higher-order masked implementations of lattice-based based key encapsulation mechanisms (KEM) is currently limited by the costly conversions between arithmetic and Boolean masking. While bitslicing has been shown to strongly speed up masked implementations of symmetric primitives, its use in arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets has never been thoroughly investigated. In this paper, we first show that bitslicing can indeed accelerate existing conversion gadgets. We then optimize these gadgets, exploiting the degrees of freedom offered by bitsliced implementations. As a result, we introduce new arbitrary-order Boolean masked addition, arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets, each in two variants: modulo 2k and modulo p (for any integers k and p). Practically, our new gadgets achieve a speedup of up to 25x over the state of the art. Turning to the KEM application, we develop the first open-source embedded (Cortex-M4) implementations of Kyber768 and Saber masked at arbitrary order. The implementations based on the new bitsliced gadgets achieve a speedup of 1.8x for Kyber and 3x for Saber, compared to the implementation based on state-of-the-art gadgets. The bottleneck of the bitslice implementations is the masked Keccak-f[1600] permutation.

Guarding Machine Learning Hardware Against Physical Side-channel Attacks

Machine learning (ML) models can be trade secrets due to their development cost. Hence, they need protection against malicious forms of reverse engineering (e.g., in IP piracy). With a growing shift of ML to the edge devices, in part for performance and in part for privacy benefits, the models have become susceptible to the so-called physical side-channel attacks. ML being a relatively new target compared to cryptography poses the problem of side-channel analysis in a context that lacks published literature. The gap between the burgeoning edge-based ML devices and the research on adequate defenses to provide side-channel security for them thus motivates our study. Our work develops and combines different flavors of side-channel defenses for ML models in the hardware blocks. We propose and optimize the first defense based on Boolean masking . We first implement all the masked hardware blocks. We then present an adder optimization to reduce the area and latency overheads. Finally, we couple it with a shuffle-based defense. We quantify that the area-delay overhead of masking ranges from 5.4× to 4.7× depending on the adder topology used and demonstrate a first-order side-channel security of millions of power traces. Additionally, the shuffle countermeasure impedes a straightforward second-order attack on our first-order masked implementation.

A relation calculus for reasoning about t-probing security

In the context of side-channel attacks against cryptographic circuits, t-probing security characterizes the amount of information derivable about sensitive values (e.g., keys) by observing t output/internal values. Non-interference is a useful mathematical tool used by researchers to assess the probing security of a circuit which employs Boolean masking to protect itself from attacks. However, reasoning about non-interference still requires either difficult ratiocination or complex automatic tools. In this work, we propose a novel point of view to reason about non-interference, by exploiting the Walsh transform of a Boolean function. To this end, we introduce a calculus for mechanically reasoning about the shares of a variable and show that this formalism provides a lean algebraic explanation of known compositional patterns allowing for the discovery of new ones. Eventually, we show how this formalism can be applied to study the probing security of known cryptographic gadgets.

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.

High-order Table-based Conversion Algorithms and Masking Lattice-based Encryption

Masking is the main countermeasure against side-channel attacks on embedded devices. For cryptographic algorithms that combine Boolean and arithmetic masking, one must therefore convert between the two types of masking, without leaking additional information to the attacker. In this paper we describe a new high-order conversion algorithm between Boolean and arithmetic masking, based on table recomputation, and provably secure in the ISW probing model. We show that our technique is particularly efficient for masking structured LWE encryption schemes such as Kyber and Saber. In particular, for Kyber IND-CPA decryption, we obtain an order of magnitude improvement compared to existing techniques.

A Low-Overhead Countermeasure against Differential Power Analysis for AES Block Cipher

This paper presents the employment of a DPA attack on the NIST (National Institute of Standards and Technology) standardized AES (advance encryption standard) protocol for key retrieval and prevention. Towards key retrieval, we applied the DPA attack on AES to obtain a 128-bit secret key by measuring the power traces of the computations involved in the algorithm. In resistance to the DPA attack, we proposed a countermeasure, or a new modified masking scheme, comprising (i) Boolean and (ii) multiplicative masking, for linear and non-linear operations of AES, respectively. Furthermore, we improved the complexity involved in Boolean masking by introducing Rebecca’s approximation. Moreover, we provide a novel solution to tackle the zero mask problem in multiplicative masking. To evaluate the power traces, we propose our custom correlation technique, which results in a decrease in the calculation time. The synthesis results for original implementation (without countermeasure) and inclusion of countermeasure are given on a Zynq 7020 FPGA (Artix-7 device). It takes 424 FPGA slices when implemented without considering the countermeasure, whereas 714 slices are required to implement AES with the inclusion of the proposed countermeasure. Consequently, the implementation results provide the acceptability of this work for area-constrained applications that require prevention against DPA attacks.

High-level synthesis, cryptography, and side-channel countermeasures: A comprehensive evaluation

Side-channel attacks pose a severe threat to both software and hardware cryptographic implementations. Current literature presents various countermeasures against these kinds of attacks, based on approaches such as hiding or masking, implemented either in software, or on register–transfer level or gate level in hardware. However, emerging trends in hardware design lean towards a system-level approach, allowing for faster, less error-prone, design process, an efficient hardware/software co-design, or sophisticated validation, verification, and (co)simulation strategies. In this paper, we propose a Boolean masking scheme suitable for high-level synthesis of substitution–permutation network-based encryption. We implement both unprotected and protected PRESENT, AES/Rijndael and Serpent encryption in C language, utilizing the concept of dynamic logic reconfiguration, synthesize it for Xilinx FPGA, and we compare our results regarding time and area utilization. We evaluate the effectiveness of proposed countermeasures using both specific and non-specific t-test leakage assessment methodology. We discuss the leakage assessment results, and we identify and discuss the related limitations of the system-level approach and the high-level synthesis.

Analysis and Comparison of Table-based Arithmetic to Boolean Masking

Masking is a popular technique to protect cryptographic implementations against side-channel attacks and comes in several variants including Boolean and arithmetic masking. Some masked implementations require conversion between these two variants, which is increasingly the case for masking of post-quantum encryption and signature schemes. One way to perform Arithmetic to Boolean (A2B) mask conversion is a table-based approach first introduced by Coron and Tchulkine, and later corrected and adapted by Debraize in CHES 2012. In this work, we show both analytically and experimentally that the table-based A2B conversion algorithm proposed by Debraize does not achieve the claimed resistance against differential power analysis due to a non-uniform masking of an intermediate variable. This non-uniformity is hard to find analytically but leads to clear leakage in experimental validation. To address the non-uniform masking issue, we propose two new A2B conversions: one that maintains efficiency at the cost of additional memory and one that trades efficiency for a reduced memory footprint. We give analytical and experimental evidence for their security, and will make their implementations, which are shown to be free from side-channel leakage in 100.000 power traces collected on the ARM Cortex-M4, available online. We conclude that when designing side-channel protection mechanisms, it is of paramount importance to perform both a theoretical analysis and an experimental validation of the method.

A Persistent Fault-Based Collision Analysis Against the Advanced Encryption Standard

A transient fault-based collision attack always requires to inject fault multiple times. We present the first attack that uses collision information caused by a persistent fault in the substitution box (S-box) to recover the entire 128-bit key of the advanced encryption standard (AES). Moreover, a relatively relaxed fault model is required; i.e., the attacker does not know any information about the position, the length (i.e., the number of bytes), or the value of the injected fault. At most, 4096 chosen plaintexts are required for a persistent fault-based collision attack (PFCA), and the computational complexity is O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">23</sup> ) in the worst case in the single-byte fault setting. A filtering algorithm is presented in the multibyte fault setting, and we theoretically prove that the complexity can be reduced to O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> ) in more than half of cases if the number of collision ciphertexts follows a uniform distribution. In addition, PFCAs against a software implementation of AES are simulated on a laptop, and the results show that the success probability of the attack either with online key searching or with offline key searching approaches 100%. In particular, more than 97% of all experiments output the right key with complexity O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> ) in the multibyte fault setting. Therefore, the attack is more efficient in this scenario. Furthermore, the attack works on an AES implementation protected by Boolean masking. Finally, PFCAs against AES implementations separately protected by two widely used countermeasures-the inverse S-box and the parity-1 matrix-are performed. The experimental results illustrate that only a 10-round protection using the first method can completely defeat the attack.

Analysis of Multiplicative Low Entropy Masking Schemes Against Correlation Power Attack

Low Entropy Masking Schemes (LEMS) had been proposed to mitigate the high-performance overhead results from the Full Entropy Masking Schemes (FEMS) while offering good protection against side-channel attacks. The masking schemes usually rely on Boolean masking, however, splitting sensitive variables in a multiplicative way is more amenable to non-linear functions and it had been applied to both software and hardware with a competitive alternative to state-of-the-art masked design. Compared to the comprehensive analysis done for Boolean LEMS, the specific leakage characteristics of Multiplicative LEMS have not yet been analyzed. In this paper, we introduce security models for LEMS to characterize the balance of the mask set. Based on the security model, we present an inherent weakness of Multiplicative LEMS. We prove that this defect of Multiplicative LEMS cannot be compensated by choosing a proper mask set, and the security of FEMS is guaranteed thanks to the Dirac function which is used to resist zero-value attack. Then, we exhibit the leakages in the implementation of Multiplicative LEMS. In particular, we propose a new attack against Multiplicative LEMS more efficient by utilizing the distribution of masked intermediate values. The feasibility of the attack is verified by both simulation and practical experiments.

Redundant Code-based Masking Revisited

Masking schemes are a popular countermeasure against side-channel attacks. To mask bytes, the two classical options are Boolean masking and polynomial masking. The latter lends itself to redundant masking, where leakage emanates from more shares than are strictly necessary to reconstruct, raising the obvious question how well such “redundant” leakage can be exploited by a side-channel adversary. We revisit the recent work by Chabanne et al. (CHES’18) and show that, contrary to their conclusions, said leakage can—in theory—always be exploited. For the Hamming weight scenario in the low-noise regime, we heuristically determine how security degrades in terms of the number of redundant shares for first and second order secure polynomial masking schemes.Furthermore, we leverage a well-established link between linear secret sharing schemes and coding theory to determine when different masking schemes will end up with essentially equivalent leakage profiles. Surprisingly, we conclude that for typical field sizes and security orders, Boolean masking is a special case of polynomial masking. We also identify quasi-Boolean masking schemes as a special class of redundant polynomial masking and point out that the popular “Frobenius-stable” sets of interpolations points typically lead to such quasi-Boolean masking schemes, with subsequent degraded leakage performance.

Maskara: Compilation of a Masking Countermeasure With Optimized Polynomial Interpolation

Side-channel attacks are amongst the major threats for embedded systems and IoT devices. Masking is one of the most used countermeasure against such attacks, but its application remains a difficult process. We propose a target-independent approach for applying a first-order Boolean masking countermeasure during compilation, on the static single assignment (SSA) form. Contrary to the state-of-the art automated approaches that require to simplify the control flow of the input program, our approach supports regular control-flow program structures. Moreover, our compiler is the first to automatically mask table lookups using a polynomial interpolation approach. We also present new optimizations to speedup the evaluation of polynomials: we reduce the number of terms of the polynomial, and we accelerate finite-field multiplication. We show that our approach is faster than the standard masked table approach with mask refresh after each access, with speedups up to ×2.4 in our experiments. Finally, using a formal verification approach, we show that the compiled machine code is secure, i.e., that all intermediate computations are statistically independent of the secrets.

Optimizing Inner Product Masking Scheme by a Coding Theory Approach

Masking is one of the most popular countermeasures to protect cryptographic implementations against side-channel analysis since it is provably secure and can be deployed at the algorithm level. To strengthen the original Boolean masking scheme, several works have suggested using schemes with high algebraic complexity. The Inner Product Masking (IPM) is one of those. In this paper, we propose a unified framework to quantitatively assess the side-channel security of the IPM in a coding-theoretic approach. Specifically, starting from the expression of IPM in a coded form, we use two defining parameters of the code to characterize its side-channel resistance. In order to validate the framework, we then connect it to two leakage metrics (namely signal-to-noise ratio and mutual information, from an information-theoretic aspect) and one typical attack metric (success rate, from a practical aspect) to build a firm foundation for our framework. As an application, our results provide ultimate explanations on the observations made by Balasch et al. at EUROCRYPT'15 and at ASIACRYPT'17, Wang et al. at CARDIS'16 and Poussier et al. at CARDIS'17 regarding the parameter effects in IPM, like higher security order in bounded moment model. Furthermore, we show how to systematically choose optimal codes (in the sense of a concrete security level) to optimize IPM by using this framework. Eventually, we present a simple but effective algorithm for choosing optimal codes for IPM, which is of special interest for designers when selecting optimal parameters for IPM.

Toward Improving Secret Sharing Scheme Based on Encryption in Cloud Computing Environment

Flexibility, acceptance of hire of Cloud Computing, control facilities originates a number of challenges. In precise, safety has been widely conveyed to create the key issues which stop movement to the cloud. Shamir’s Secret Sharing Scheme splits the secret message into n shares with threshold k and distribution of shares to n participants and each participant has unique share of secret message. For reconstructing the secret message, minimum k fragments are required. Threshold scheme which requires only k shares to re-construct the secret message is implemented, as collection of shares from all the n participants to reconstruct the secret message may be unfeasible. AES encryption turns out to be totally inappropriate if a password is used as an alternative of providing the key. The attacker finds file, downloads Ax crypt, and brute force/dictionary attacks it until it’s cracked. An additional security can provided to user password which of varying length by splitting the password into n shares. Advance Encryption Standard (AES) procedure is implemented to encipher the produced shares. AES with 256-bit key is applied to encode the share for every member. Covering arrangement alternative to Boolean masking established on Shamir’s Secret Sharing arrangement is suggested.

Efficient and Private Computations with Code-Based Masking

Code-based masking is a very general type of masking scheme that covers Boolean masking, inner product masking, direct sum masking, and so on. The merits of the generalization are twofold. Firstly, the higher algebraic complexity of the sharing function decreases the information leakage in “low noise conditions” and may increase the “statistical security order” of an implementation (with linear leakages). Secondly, the underlying error-correction codes can offer improved fault resistance for the encoded variables. Nevertheless, this higher algebraic complexity also implies additional challenges. On the one hand, a generic multiplication algorithm applicable to any linear code is still unknown. On the other hand, masking schemes with higher algebraic complexity usually come with implementation overheads, as for example witnessed by inner-product masking. In this paper, we contribute to these challenges in two directions. Firstly, we propose a generic algorithm that allows us (to the best of our knowledge for the first time) to compute on data shared with linear codes. Secondly, we introduce a new amortization technique that can significantly mitigate the implementation overheads of code-based masking, and illustrate this claim with a case study. Precisely, we show that, although performing every single code-based masked operation is relatively complex, processing multiple secrets in parallel leads to much better performances. This property enables code-based masked implementations of the AES to compete with the state-of-the-art in randomness complexity. Since our masked operations can be instantiated with various linear codes, we hope that these investigations open new avenues for the study of code-based masking schemes, by specializing the codes for improved performances, better side-channel security or improved fault tolerance.