Algorithms for switching between block-wise and arithmetic masking

The task of ensuring the required level of security of information systems in the adversary models with additional data obtained through side channels (a striking example of implementing threats in such a model is a differential power analysis) has become increasingly relevant in recent years. An effective protection method against side-channel attacks is masking all intermediate variables used in the algorithm with random values. At the same time, many algorithms use masking of different kinds, for example, Boolean, byte-wise, and arithmetic; therefore, a problem of switching between masking of different kinds arises. Switching between Boolean and arithmetic masking is well studied, while no solutions have been proposed for switching between masking of other kinds. This article recalls the requirements for switching algorithms and presents algorithms for switching between block-wise and arithmetic masking, which includes the case of switching between byte-wise and arithmetic masking

Provably Secure Countermeasures against Side-channel Attacks

Side-channel attacks exploit the fact that the implementations of cryptographic algorithms leak information about the secret key. In power analysis attacks, the observable leakage is the power consumption of the device, which is dependent on the processed data and the performed operations.\ignore{While Simple Power Analysis (SPA) attacks try to recover the secret value by directly interpreting the power measurements with the corresponding operations, Differential Power Analysis (DPA) attacks are more sophisticated and aim to recover the secret value by applying statistical techniques on multiple measurements from the same operation.} Masking is a widely used countermeasure to thwart the powerful Differential Power Analysis (DPA) attacks. It uses random variables called masks to reduce the correlation between the secret key and the obtained leakage. The advantage with masking countermeasure is that one can formally prove its security under reasonable assumptions on the device leakage model. This thesis proposes several new masking schemes along with the analysis and improvement of few existing masking schemes. The first part of the thesis addresses the problem of converting between Boolean and arithmetic masking. To protect a cryptographic algorithm which contains a mixture of Boolean and arithmetic operations, one uses both Boolean and arithmetic masking. Consequently, these masks need to be converted between the two forms based on the sequence of operations. The existing conversion schemes are secure against first-order DPA attacks only. This thesis proposes first solution to switch between Boolean and arithmetic masking that is secure against attacks of any order. Secondly, new solutions are proposed for first-order secure conversion with logarithmic complexity (${\cal O}(\log k)$ for $k$-bit operands) compared to the existing solutions with linear complexity (${\cal O}(k)$). It is shown that this new technique also improves the complexity of the higher-order conversion algorithms from ${\cal O}(n^2 k)$ to ${\cal O}(n^2 \log k)$ secure against attacks of order $d$, where $n = 2d+1$. Thirdly, for the special case of second-order masking, the running times of the algorithms are further improved by employing lookup tables. The second part of the thesis analyzes the security of two existing Boolean masking schemes. Firstly, it is shown that a higher-order masking scheme claimed to be secure against attacks of order $d$ can be broken with an attack of order $d/2+1$. An improved scheme is proposed to fix the flaw. Secondly, a new issue concerning the problem of converting the security proofs from one leakage model to another is examined. It is shown that a second-order masking scheme secure in the Hamming weight model can be broken with a first-order attack on a device leaking in the Hamming distance model. This result underlines the importance of re-evaluating the security proofs for devices leaking in different models

Efficient Masking of ARX-Based Block Ciphers Using Carry-Save Addition on Boolean Shares

Masking is a widely-used technique to protect block ciphers and other symmetric cryptosystems against Differential Power Analysis (DPA) attacks. Applying masking to a cipher that involves both arithmetic and Boolean operations requires a conversion between arithmetic and Boolean masks. An alternative approach is to perform the required arithmetic operations (e.g. modular addition or subtraction) directly on Boolean shares. At FSE 2015, Coron et al. proposed a logarithmic-time algorithm for modular addition on Boolean shares based on the Kogge-Stone carry-lookahead adder. We revisit their addition algorithm in this paper and present a fast implementation for ARM processors. Then, we introduce a new technique for direct modular addition/subtraction on Boolean shares using a simple Carry-Save Adder (CSA) in an iterative fashion. We show that the average complexity of CSA-based addition on Boolean shares grows logarithmically with the operand size, similar to the Kogge-Stone carry-lookahead addition, but consists of only a single AND, an XOR, and a left-shift per iteration. A 32-bit CSA addition~on Boolean shares has an average execution time of 162 clock cycles on an ARM Cortex-M3 processor, which is approximately 43% faster than the Kogge-Stone adder. The performance gain increases to over 55% when comparing the average subtraction times. We integrated both addition techniques into a masked implementation of the block cipher Speck and found that the CSA-based variant clearly outperforms its Kogge-Stone counterpart by a factor of 1.70 for encryption and 2.30 for decryption

A Hybrid Approach to Formal Verification of Higher-Order Masked Arithmetic Programs

Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by removing the statistical dependence between secrecy and power consumption via randomization. However, designing efficient and effective masked implementations turns out to be an error-prone task. Current techniques for verifying whether masked programs are secure are limited in their applicability and accuracy, especially when they are applied. To bridge this gap, in this article, we first propose a sound type system, equipped with an efficient type inference algorithm, for verifying masked arithmetic programs against higher-order attacks. We then give novel model-counting based and pattern-matching based methods which are able to precisely determine whether the potential leaky observable sets detected by the type system are genuine or simply spurious. We evaluate our approach on various implementations of arithmetic cryptographicprograms.The experiments confirm that our approach out performs the state-of-the-art base lines in terms of applicability, accuracy and efficiency

Orthogonal Direct Sum Masking: A Smartcard Friendly Computation Paradigm in a Code, with Builtin Protection against Side-Channel and Fault Attacks

Secure elements, such as smartcards or trusted platform modules (TPMs), must be protected against implementation-level attacks. Those include side-channel and fault injection attacks. We introduce ODSM, Orthogonal Direct Sum Masking, a new computation paradigm that achieves protection against those two kinds of attacks. A large vector space is structured as two supplementary orthogonal subspaces. One subspace (called a code $\mathcal{C}$) is used for the functional computation, while the second subspace carries random numbers. As the random numbers are entangled with the sensitive data, ODSM ensures a protection against (monovariate) side-channel attacks. The random numbers can be checked either occasionally, or globally, thereby ensuring a fine or coarse detection capability. The security level can be formally detailed: it is proved that monovariate side-channel attacks of order up to $d_\mathcal{C}-1$, where $d_\mathcal{C}$ is the minimal distance of $\mathcal{C}$, are impossible, and that any fault of Hamming weight strictly less than $d_\mathcal{C}$ is detected. A complete instantiation of ODSM is given for AES. In this case, all monovariate side-channel attacks of order strictly less than $5$ are impossible, and all fault injections perturbing strictly less than $5$ bits are detected

Efficient Conversion Method from Arithmetic to Boolean Masking in Constrained Devices

A common technique employed for preventing a side channel analysis is boolean masking. However, the application of this scheme is not so straightforward when it comes to block ciphers based on Addition-Rotation-Xor structure. In order to address this issue, since 2000, scholars have investigated schemes for converting Arithmetic to Boolean (AtoB) masking and Boolean to Arithmetic (BtoA) masking schemes. However, these solutions have certain limitations. The time performance of the AtoB scheme is extremely unsatisfactory because of the high complexity of $\mathcal{O}(k)$ where $k$ is the size of addition bit. At the FSE 2015, an improved algorithm with time complexity $\mathcal{O}(\log k)$ based on the Kogge-Stone carry look-ahead adder was suggested. Despite its efficiency, this algorithm cannot consider for constrained environments. Although the original algorithm naturally extends to low-resource devices, there is no advantage in time performance; we call this variant as the generic variant. In this study, we suggest an enhanced variant algorithm to apply to constrained devices. Our solution is based on the principle of the Kogge-Stone carry look-ahead adder, and it uses a divide and conquer approach. In addition, we prove the security of our new algorithm against first-order attack. In implementation results, when $k=64$ and the register bit size of a chip is $8$, $16$ or $32$, we obtain $58$\%, $72$\%, or $68$\% improvement, respectively, over the results obtained using the generic variant. When applying those algorithms to first-order SPECK, we also achieve about $40$\% improvement. Moreover, our proposal extends to higher-order countermeasures as previous study

A Lightweight Implementation of Saber Resistant Against Side-Channel Attacks

The field of post-quantum cryptography aims to develop and analyze algorithms that can withstand classical and quantum cryptanalysis. The NIST PQC standardization process, now in its third round, specifies ease of protection against side-channel analysis as an important selection criterion. In this work, we develop and validate a masked hardware implementation of Saber key encapsulation mechanism, a third-round NIST PQC finalist. We first design a baseline lightweight hardware architecture of Saber and then apply side-channel countermeasures. Our protected hardware implementation is significantly faster than previously reported protected software and software/hardware co-design implementations. Additionally, applying side-channel countermeasures to our baseline design incurs approximately 2.9x and 1.4x penalty in terms of the number of LUTs and latency, respectively, in modern FPGAs