Efficient Error detection Architectures for Low-Energy Block Ciphers with the Case Study of Midori Benchmarked on FPGA

Achieving secure, high performance implementations for constrained applications such as implantable and wearable medical devices is a priority in efficient block ciphers. However, security of these algorithms is not guaranteed in presence of malicious and natural faults. Recently, a new lightweight block cipher, Midori, has been proposed which optimizes the energy consumption besides having low latency and hardware complexity. This algorithm is proposed in two energy-efficient varients, i.e., Midori64 and Midori128, with block sizes equal to 64 and 128 bits. In this thesis, fault diagnosis schemes for variants of Midori are proposed. To the best of the our knowledge, there has been no fault diagnosis scheme presented in the literature for Midori to date. The fault diagnosis schemes are provided for the nonlinear S-box layer and for the round structures with both 64-bit and 128-bit Midori symmetric key ciphers. The proposed schemes are benchmarked on field-programmable gate array (FPGA) and their error coverage is assessed with fault-injection simulations. These proposed error detection architectures make the implementations of this new low-energy lightweight block cipher more reliable

On the Construction of Near-MDS Matrices

The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer, compared to MDS matrices. In this paper, we study NMDS matrices, exploring their construction in both recursive and nonrecursive settings. We provide several theoretical results and explore the hardware efficiency of the construction of NMDS matrices. Additionally, we make comparisons between the results of NMDS and MDS matrices whenever possible. For the recursive approach, we study the DLS matrices and provide some theoretical results on their use. Some of the results are used to restrict the search space of the DLS matrices. We also show that over a field of characteristic 2, any sparse matrix of order $n\geq 4$ with fixed XOR value of 1 cannot be an NMDS when raised to a power of $k\leq n$. Following that, we use the generalized DLS (GDLS) matrices to provide some lightweight recursive NMDS matrices of several orders that perform better than the existing matrices in terms of hardware cost or the number of iterations. For the nonrecursive construction of NMDS matrices, we study various structures, such as circulant and left-circulant matrices, and their generalizations: Toeplitz and Hankel matrices. In addition, we prove that Toeplitz matrices of order $n>4$ cannot be simultaneously NMDS and involutory over a field of characteristic 2. Finally, we use GDLS matrices to provide some lightweight NMDS matrices that can be computed in one clock cycle. The proposed nonrecursive NMDS matrices of orders 4, 5, 6, 7, and 8 can be implemented with 24, 50, 65, 96, and 108 XORs over $\mathbb{F}_{2^4}$, respectively

Optimizing Implementations of Lightweight Building Blocks

We study the synthesis of small functions used as building blocks in lightweight cryptographic designs in terms of hardware implementations. This phase most notably appears during the ASIC implementation of cryptographic primitives. The quality of this step directly affects the output circuit, and while general tools exist to carry out this task, most of them belong to proprietary software suites and apply heuristics to any size of functions. In this work, we focus on small functions (4- and 8-bit mappings) and look for their optimal implementations on a specific weighted instructions set which allows fine tuning of the technology. We propose a tool named LIGHTER, based on two related algorithms, that produces optimized implementations of small functions. To demonstrate the validity and usefulness of our tool, we applied it to two practical cases: first, linear permutations that define diffusion in most of SPN ciphers; second, non-linear 4-bit permutations that are used in many lightweight block ciphers. For linear permutations, we exhibit several new MDS diffusion matrices lighter than the state-of-the-art, and we also decrease the implementation cost of several already known MDS matrices. As for non-linear permutations, LIGHTER outperforms the area-optimized synthesis of the state-of-the-art academic tool ABC. Smaller circuits can also be reached when ABC and LIGHTER are used jointly

A reduced set of submatrices for a faster evaluation of the MDS property of a circulant matrix with entries that are powers of two

In this paper a reduced set of submatrices for a faster evaluation of the MDS property of a circulant matrix, with entries that are powers of two, is proposed. A proposition is made that under the condition that all entries of a t × t circulant matrix are powers of 2, it is sufficient to check only its 2x2 submatrices in order to evaluate the MDS property in a prime field. Although there is no theoretical proof to support this proposition at this point, the experimental results conducted on a sample of 100 thousand randomly generated matrices indicate that this proposition is true. There are benefits of the proposed MDS test on the efficiency of search methods for the generation of circulant MDS matrices, regardless of the correctness of this proposition. However, if this proposition is correct, its impact on the speed of search methods for circulant MDS matrices will be huge, which will enable generation of MDS matrices of large sizes. Also, a modified version of the make_binary_powers function is presented. Based on this modified function and the proposed MDS test, some examples of efficient 16 x 16 MDS matrices are presented. Also, an examples of efficient 24 x 24 matrices are generated, whose MDS property should be further validated

Improved Heuristics for Low-latency Implementations of Linear Layers

In many applications, low area and low latency are required for the chip-level implementation of cryptographic primitives. The low-cost implementations of linear layers usually play a crucial role for symmetric ciphers. Some heuristic methods, such as the forward search and the backward search, minimize the number of XOR gates of the linear layer under the minimum latency limitation. For the sake of achieving further optimization for such implementation of the linear layer, we put forward a new general search framework attaching the division optimization and extending base techniques in this paper. In terms of the number of XOR gates and the searching time, our new search algorithm is better than the previous heuristics, including the forward search and the backward search when testing matrices provided by them. We obtain an improved implementation of AES MixColumns requiring only 102 XORs under minimum latency, which outdoes the previous best record provided by the forward search

Midori: A Block Cipher for Low Energy (Extended Version)

In the past few years, lightweight cryptography has become a popular research discipline with a number of ciphers and hash functions proposed. The designers\u27 focus has been predominantly to minimize the hardware area, while other goals such as low latency have been addressed rather recently only. However, the optimization goal of low energy for block cipher design has not been explicitly addressed so far. At the same time, it is a crucial measure of goodness for an algorithm. Indeed, a cipher optimized with respect to energy has wide applications, especially in constrained environments running on a tight power/energy budget such as medical implants. This paper presents the block cipher Midori that is optimized with respect to the energy consumed by the circuit per bit in encryption or decryption operation. We deliberate on the design choices that lead to low energy consumption in an electrical circuit, and try to optimize each component of the circuit as well as its entire architecture for energy. An added motivation is to make both encryption and decryption functionalities available by small tweak in the circuit that would not incur significant area or energy overheads. We propose two energy-efficient block ciphers Midori128 and Midori64 with block sizes equal to 128 and 64 bits respectively. These ciphers have the added property that a circuit that provides both the functionalities of encryption and decryption can be designed with very little overhead in terms of area and energy. We compare our results with other ciphers with similar characteristics: it was found that the energy consumptions of Midori64 and Midori128 are by far better when compared ciphers like PRINCE and NOEKEON

Construction of MDS Matrices from Generalized Feistel Structures

This paper investigates the construction of MDS matrices with generalized Feistel structures (GFS). The approach developed by this paper consists in deriving MDS matrices from the product of several sparser ones. This can be seen as a generalization to several matrices of the recursive construction which derives MDS matrices as the powers of a single companion matrix. The first part of this paper gives some theoretical results on the iteration of GFS. In second part, using GFS and primitive matrices, we propose some types of sparse matrices that are called extended primitive GFS (EGFS) matrices. Then, by applying binary linear functions to several round of EGFS matrices, lightweight $4\times 4$, $6\times 6$ and $8\times 8$ MDS matrices are proposed which are implemented with $67$, $156$ and $260$ XOR for $8$-bit input, respectively. The results match the best known lightweight $4\times 4$ MDS matrix and improve the best known $6\times 6$ and $8\times 8$ MDS matrices. Moreover, we propose $8\times 8$ Near-MDS matrices such that the implementation cost of the proposed matrices are $108$ and $204$ XOR for 4 and $8$-bit input, respectively. Although none of the presented matrices are involutions, the implementation cost of the inverses of the proposed matrices is equal to the implementation cost of the given matrices. Furthermore, the construction presented in this paper is relatively general and can be applied for other matrix dimensions and finite fields as well

SCFI: State Machine Control-Flow Hardening Against Fault Attacks

Fault injection (FI) is a powerful attack methodology allowing an adversary to entirely break the security of a target device. As finite-state machines (FSMs) are fundamental hardware building blocks responsible for controlling systems, inducing faults into these controllers enables an adversary to hijack the execution of the integrated circuit. A common defense strategy mitigating these attacks is to manually instantiate FSMs multiple times and detect faults using a majority voting logic. However, as each additional FSM instance only provides security against one additional induced fault, this approach scales poorly in a multi-fault attack scenario. In this paper, we present SCFI: a strong, probabilistic FSM protection mechanism ensuring that control-flow deviations from the intended control-flow are detected even in the presence of multiple faults. At its core, SCFI consists of a hardened next-state function absorbing the execution history as well as the FSM's control signals to derive the next state. When either the absorbed inputs, the state registers, or the function itself are affected by faults, SCFI triggers an error with no detection latency. We integrate SCFI into a synthesis tool capable of automatically hardening arbitrary unprotected FSMs without user interaction and open-source the tool. Our evaluation shows that SCFI provides strong protection guarantees with a better area-time product than FSMs protected using classical redundancy-based approaches. Finally, we formally verify the resilience of the protected state machines using a pre-silicon fault analysis tool

More results on Shortest Linear Programs

At the FSE conference of ToSC 2018, Kranz et al. presented their results on shortest linear programs for the linear layers of several well known block ciphers in literature. Shortest linear programs are essentially the minimum number of 2-input xor gates required to completely describe a linear system of equations. In the above paper the authors showed that the commonly used metrics like d-xor/s-xor count that are used to judge the ``lightweightedness\u27\u27 do not represent the minimum number of xor gates required to describe a given MDS matrix. In fact they used heuristic based algorithms of Boyar/Peralta and Paar to find implementations of MDS matrices with even fewer xor gates than was previously known. They proved that the AES mixcolumn matrix can be implemented with as little as 97 xor gates. In this paper we show that the values reported in the above paper are not optimal. By suitably including random bits in the instances of the above algorithms we can achieve implementations of almost all matrices with lesser number of gates than were reported in the above paper. As a result we report an implementation of the AES mixcolumn matrix that uses only 95 xor gates. In the second part of the paper, we observe that most standard cell libraries contain both 2 and 3-input xor gates, with the silicon area of the 3-input xor gate being smaller than the sum of the areas of two 2-input xor gates. Hence when linear circuits are synthesized by logic compilers (with specific instructions to optimize for area), most of them would return a solution circuit containing both 2 and 3-input xor gates. Thus from a practical point of view, reducing circuit size in presence of these gates is no longer equivalent to solving the shortest linear program. In this paper we show that by adopting a graph based heuristic it is possible to convert a circuit constructed with 2-input xor gates to another functionally equivalent circuit that utilizes both 2 and 3-input xor gates and occupies less hardware area. As a result we obtain more lightweight implementations of all the matrices listed in the ToSC paper

A Generalization of the Subfield Construction

The subfield construction is one of the most promising methods to construct maximum distance separable (MDS) diffusion layers for block ciphers and cryptographic hash functions. In this paper, we give a generalization of this method and investigate the efficiency of our generalization. As a result, we provide several best MDS diffusions with respect to the number of XORs that the diffusion needs. For instance, we give (i) an involutory MDS diffusion $\mathbb{F}_{2^8}^{3} \rightarrow \mathbb{F}_{2^8}^{3}$ by 85 XORs and (ii) an involutory MDS diffusion $\mathbb{F}_{2^8}^{4} \rightarrow \mathbb{F}_{2^8}^{4}$ by 122 XORs, and hence present new records to the literature. Furthermore, we interpret the coding theoretical background of our generalization