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Transactions on Cryptographic Hardware and Embedded Systems
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  This is an Open Access Journal Open Access journal
ISSN (Online) 2569-2925
Published by Ruhr-Universit├Ąt Bochum Homepage  [4 journals]
  • Automatic Search of Meet-in-the-Middle Differential Fault Analysis on
           AES-like Ciphers

    • Authors: Qingyuan Yu, Xiaoyang Dong, Lingyue Qin, Yongze Kang, Keting Jia, Xiaoyun Wang, Guoyan Zhang
      Pages: 1 - 31
      Abstract: Fault analysis is a powerful technique to retrieve secret keys by exploiting side-channel information. Differential fault analysis (DFA) is one of the most powerful threats utilizing differential information between correct and faulty ciphertexts and can recover keys for symmetric-key cryptosystems efficiently. Since DFA usually targets the first or last few rounds of the block ciphers, some countermeasures against DFA only protect the first and last few rounds for efficiency. Therefore, to explore how many rounds DFA can affect is very important to make sure how many rounds to protect in practice. At CHES 2011, Derbez et al. proposed an improved DFA on AES based on MitM approach, which covers one more round than previous DFAs. To perform good (or optimal) MitM DFA on block ciphers, the good (or optimal) attack configurations should be identified, such as the location where the faults inject, the matching point with differential relationship, and the two independent computation paths where two independent subsets of the key are involved. In this paper, we formulate the essential ideas of the construction of the attack, and translate the problem of searching for the best MitM DFA into optimization problems under constraints in Mixed-Integer-Linear-Programming (MILP) models. With the models, we achieve more powerful and practical DFA attacks on SKINNY, CRAFT, QARMA, PRINCE, PRINCEv2, and MIDORI with faults injected in 1 to 9 earlier rounds than the best previous DFAs.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.1-31
  • BASALISC: Programmable Hardware Accelerator for BGV Fully Homomorphic

    • Authors: Robin Geelen, Michiel Van Beirendonck, Hilder V. L. Pereira, Brian Huffman, Tynan McAuley, Ben Selfridge, Daniel Wagner, Georgios Dimou, Ingrid Verbauwhede, Frederik Vercauteren, David W. Archer
      Pages: 32 - 57
      Abstract: Fully Homomorphic Encryption (FHE) allows for secure computation on encrypted data. Unfortunately, huge memory size, computational cost and bandwidth requirements limit its practicality. We present BASALISC, an architecture family of hardware accelerators that aims to substantially accelerate FHE computations in the cloud. BASALISC is the first to implement the BGV scheme with fully-packed bootstrapping – the noise removal capability necessary for arbitrary-depth computation. It supports a customized version of bootstrapping that can be instantiated with hardware multipliers optimized for area and power.
      BASALISC is a three-abstraction-layer RISC architecture, designed for a 1 GHz ASIC implementation and underway toward 150mm2 die tape-out in a 12nm GF process. BASALISC’s four-layer memory hierarchy includes a two-dimensional conflict-free inner memory layer that enables 32 Tb/s radix-256 NTT computations without pipeline stalls. Its conflict-resolution permutation hardware is generalized and re-used to compute BGV automorphisms without throughput penalty. BASALISC also has a custom multiply-accumulate unit to accelerate BGV key switching.
      The BASALISC toolchain comprises a custom compiler and a joint performance and correctness simulator. To evaluate BASALISC, we study its physical realizability, emulate and formally verify its core functional units, and we study its performance on a set of benchmarks. Simulation results show a speedup of more than 5,000× over HElib – a popular software FHE library.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.32-57
  • Protecting Dilithium against Leakage

    • Authors: Melissa Azouaoui, Olivier Bronchain, Gaëtan Cassiers, Clément Hoffmann, Yulia Kuzovkova, Joost Renes, Tobias Schneider, Markus Schönauer, François-Xavier Standaert, Christine van Vredendaal
      Pages: 58 - 79
      Abstract: CRYSTALS-Dilithium has been selected by the NIST as the new standard for post-quantum digital signatures. In this work, we revisit the side-channel countermeasures of Dilithium in three directions. First, we improve its sensitivity analysis by classifying intermediate computations according to their physical security requirements. Second, we provide improved gadgets dedicated to Dilithium, taking advantage of recent advances in masking conversion algorithms. Third, we combine these contributions and report performance for side-channel protected Dilithium implementations. Our benchmarking results additionally put forward that the randomized version of Dilithium can lead to significantly more efficient implementations (than its deterministic version) when side-channel attacks are a concern.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.58-79
  • MMM: Authenticated Encryption with Minimum Secret State for Masking

    • Authors: Yusuke Naito, Yu Sasaki, Takeshi Sugawara
      Pages: 80 - 109
      Abstract: We propose a new authenticated encryption (AE) mode MMM that achieves the minimum memory size with masking. Minimizing the secret state is the crucial challenge in the low-memory AE suitable for masking. Here, the minimum secret state is s + b bits, composed of s bits for a secret key and b bits for a plaintext block. HOMA appeared in CRYPTO 2022 achieved this goal with b = 64, but choosing a smaller b was difficult because b = s/2 is bound to the block size of the underlying primitive, meaning that a block cipher with an unrealistically small block size (e.g., 8 bits) is necessary for further improvement. MMM addresses the issue by making b independent of the underlying primitive while achieving the minimum (s + b)-bit secret state. Moreover, MMM provides additional advantages over HOMA, including (i) a better rate, (ii) the security under the multi-user model, (iii) and a smaller transmission cost. We instantiate two variants, MMM-8 (with b = 8) and MMM-64 (with b = 64), using the standard tweakable block cipher SKINNY-64/192. With a (d + 1)-masking scheme, MMM-8 (resp. MMM-64) is smaller by 56d + 184 (resp. 128) bits compared with HOMA. As a result of hardware performance evaluation, MMM-8 and MMM-64 achieved smaller circuit areas than HOMA with all the examined protection orders d ∈ [0, 5]. MMM-8’s circuit area is only 81% of HOMA with d = 5, and MMM-64 achieves more than x3 speed-up with a smaller circuit area.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.80-109
  • Improved Gadgets for the High-Order Masking of Dilithium

    • Authors: Jean-Sébastien Coron, François Gérard, Matthias Trannoy, Rina Zeitoun
      Pages: 110 - 145
      Abstract: We present novel and improved high-order masking gadgets for Dilithium, a post-quantum signature scheme that has been standardized by the National Institute of Standards and Technologies (NIST). Our proposed gadgets include the ShiftMod gadget, which is used for efficient arithmetic shifts and serves as a component in other masking gadgets. Additionally, we propose a new algorithm for Boolean-to-arithmetic masking conversion of a μ-bit integer x modulo any integer q, with a complexity that is independent of both μ and q. This algorithm is used in Dilithium to mask the generation of the random variable y modulo q. Moreover, we describe improved techniques for masking the Decompose function in Dilithium. Our new gadgets are proven to be secure in the t-probing model.
      We demonstrate the effectiveness of our countermeasures by presenting a complete high-order masked implementation of Dilithium that utilizes the improved gadgets described above. We provide practical results obtained from a C implementation and compare the performance improvements provided by our new gadgets with those of previous work.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.110-145
  • Dlog is Practically as Hard (or Easy) as DH – Solving Dlogs via DH
           Oracles on EC Standards

    • Authors: Alexander May, Carl Richard Theodor Schneider
      Pages: 146 - 166
      Abstract: Assume that we have a group G of known order q, in which we want to solve discrete logarithms (dlogs). In 1994, Maurer showed how to compute dlogs in G in poly time given a Diffie-Hellman (DH) oracle in G, and an auxiliary elliptic curve ˆÊ (Fq) of smooth order. The problem of Maurer’s reduction of solving dlogs via DH oracles is that no efficient algorithm for constructing such a smooth auxiliary curve is known. Thus, the implications of Maurer’s approach to real-world applications remained widely unclear.
      In this work, we explicitly construct smooth auxiliary curves for 13 commonly used, standardized elliptic curves of bit-sizes in the range [204, 256], including e.g., NIST P-256, Curve25519, SM2 and GOST R34.10. For all these curves we construct a corresponding cyclic auxiliary curve ˆÊ(Fq), whose order is 39-bit smooth, i.e., its largest factor is of bit-length at most 39 bits.
      This in turn allows us to compute for all divisors of the order of ˆÊ(Fq) exhaustively a codebook for all discrete logarithms. As a consequence, dlogs on ˆÊ(Fq) can efficiently be computed in a matter of seconds. Our resulting codebook sizes for each auxiliary curve are less than 29 TByte individually, and fit on our hard disk.
      We also construct auxiliary curves for NIST P-384 and NIST P-521 with a 65-bit and 110-bit smooth order.
      Further, we provide an efficient implementation of Maurer’s reduction from the dlog computation in G with order q to the dlog computation on its auxiliary curve ˆÊ (Fq). Let us provide a flavor of our results, e.g., when G is the NIST P-256 group, the results for other curves are similar. With the help of our codebook for the auxiliary curve Ê(Fq), and less than 24,000 calls to a DH oracle in G (that we simulate), we can solve discrete logarithms on NIST P-256 in around 30 secs.
      From a security perspective, our results show that for current elliptic curve standards< the difficulty of solving DH is practically tightly related to the difficulty of computing dlogs. Namely, unless dlogs are easy to compute on these curves G, we provide a very concrete security guarantee that DH in G must also be hard. From a cryptanalytic perspective, our results show a way to efficiently solve discrete logarithms in the presence of a DH oracle.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.146-166
  • On Provable White-Box Security in the Strong Incompressibility Model

    • Authors: Estuardo Alpirez Bock, Chris Brzuska, Russell W. F. Lai
      Pages: 167 - 187
      Abstract: Incompressibility is a popular security notion for white-box cryptography and captures that a large encryption program cannot be compressed without losing functionality. Fouque, Karpman, Kirchner and Minaud (FKKM) defined strong incompressibility, where a compressed program should not even help to distinguish encryptions of two messages of equal length. Equivalently, the notion can be phrased as indistinguishability under chosen-plaintext attacks and key-leakage (LK-IND-CPA), where the leakage rate is high.
      In this paper, we show that LK-IND-CPA security with superlogarithmic-length leakage, and thus strong incompressibility, cannot be proven under standard (i.e. single-stage) assumptions, if the encryption scheme is key-fixing, i.e. a polynomial number of message-ciphertext pairs uniquely determine the key with high probability. Our impossibility result refutes a claim by FKKM that their big-key generation mechanism achieves strong incompressibility when combined with any PRG or any conventional encryption scheme, since the claim is not true for encryption schemes which are key-fixing (or for PRGs which are injective). In particular, we prove that the cipher block chaining (CBC) block cipher mode is key-fixing when modelling the cipher as a truly random permutation for each key. Subsequent to and inspired by our work, FKKM prove that their original big-key generation mechanism can be combined with a random oracle into an LK-IND-CPA-secure encryption scheme, circumventing the impossibility result by the use of an idealised model.
      Along the way, our work also helps clarifying the relations between incompressible white-box cryptography, big-key symmetric encryption, and general leakage resilient cryptography, and their limitations.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.167-187
  • Exploiting Intermediate Value Leakage in Dilithium: A Template-Based

    • Authors: Alexandre Berzati, Andersson Calle Viera, Maya Chartouny, Steven Madec, Damien Vergnaud, David Vigilant
      Pages: 188 - 210
      Abstract: This paper presents a new profiling side-channel attack on CRYSTALSDilithium, the new NIST primary standard for quantum-safe digital signatures. An open source implementation of CRYSTALS-Dilithium is already available, with constant-time property as a consideration for side-channel resilience. However, this implementation does not protect against attacks that exploit intermediate data leakage. We show how to exploit a new leakage on a vector generated during the signing process, for which the costly protection by masking is still a matter of debate. With a corpus of 700 000 messages, we design a template attack that enables us to efficiently predict whether a given coefficient in one coordinate of this vector is zero or not. By gathering signatures and being able to make the correct predictions for each index, and then using linear algebra methods, this paper demonstrates that one can recover part of the secret key that is sufficient to produce universal forgeries. While our paper deeply discusses the theoretical attack path, it also demonstrates the validity of the assumption regarding the required leakage model from practical experiments with the reference implementation on an ARM Cortex-M4. We need approximately a day to collect enough representatives and one more day to perform the traces acquisition on our target.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.188-210
  • Enhancing Quality and Security of the PLL-TRNG

    • Authors: Viktor Fischer, Florent Bernard, Quentin Dallison, Maciej Skórski
      Pages: 211 - 237
      Abstract: Field Programmable Gate Arrays (FPGAs) are used more and more frequently to implement cryptographic systems, which need random number generators (RNGs) to be embedded in the same device. The main challenge related to the implementation of a generator running inside FPGAs is that the physical source of randomness, such as jittered clock generator, is implemented in the configurable logic area, i.e. in the close vicinity of noisy running algorithms, which can have significant impact on generated numbers or even serve to attack the generator. A possible approach to prevent such influence is the use of Phase-Lock Loops (PLLs), which are separated from the re-configurable logic area inside the FPGA chip. In this paper, we propose a new architecture of the PLL-based TRNG including a method to avoid correlation in the output through control of timing in the sampling process, as well as new embedded tests based on the enhanced stochastic model. We also propose a workflow to help find the best parameters, such as output bitrate and entropy rate. We show that bitrates of around 400 kb/s or more can be achieved, while guaranteeing min-entropy rates per bit higher than 0.98 as required by the latest security standards.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.211-237
  • Silicon Echoes: Non-Invasive Trojan and Tamper Detection using
           Frequency-Selective Impedance Analysis

    • Authors: Tahoura Mosavirik, Saleh Khalaj Monfared, Maryam Saadat Safa, Shahin Tajik
      Pages: 238 - 261
      Abstract: The threat of chip-level tampering and its detection has been widely researched. Hardware Trojan insertions are prominent examples of such tamper events. Altering the placement and routing of a design or removing a part of a circuit for side-channel leakage/fault sensitivity amplification are other instances of such attacks. While semi- and fully-invasive physical verification methods can confidently detect such stealthy tamper events, they are costly, time-consuming, and destructive. On the other hand, virtually all proposed non-invasive side-channel methods suffer from noise and, therefore, have low confidence. Moreover, they require activating the tampered part of the circuit (e.g., the Trojan trigger) to compare and detect the modifications. In this work, we introduce a non-invasive post-silicon tamper detection technique applicable to different classes of tamper events at the chip level without requiring the activation of the malicious circuit. Our method relies on the fact that physical modifications (regardless of their physical, activation, or action characteristics) alter the impedance of the chip. Hence, characterizing the impedance can lead to the detection of the tamper events. To sense the changes in the impedance, we deploy known RF tools, namely, scattering parameters, in which we inject sine wave signals with high frequencies to the power distribution network (PDN) of the system and measure the “echo” of the signal. The reflected signals in various frequency bands reveal different tamper events based on their impact size on the die. To validate our claims, we performed measurements on several proof-ofconcept tampered hardware implementations realized on FPGAs manufactured with a 28 nm technology. We further show that deploying the Dynamic Time Warping (DTW) distance can distinguish between tamper events and noise resulting from manufacturing process variation of different chips/boards. Based on the acquired results, we demonstrate that stealthy hardware Trojans, as well as sophisticated modifications of P&R, can be detected.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.238-261
  • From MLWE to RLWE: A Differential Fault Attack on Randomized &
           Deterministic Dilithium

    • Authors: Mohamed ElGhamrawy, Melissa Azouaoui, Olivier Bronchain, Joost Renes, Tobias Schneider, Markus Schönauer, Okan Seker, Christine van Vredendaal
      Pages: 262 - 286
      Abstract: The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALSDilithium, and other post-quantum cryptography schemes, on embedded devices raises a new set of challenges, including ones related to performance in terms of speed and memory requirements, but also related to side-channel and fault injection attacks security. In this work, we investigated the latter and describe a differential fault attack on the randomized and deterministic versions of CRYSTALS-Dilithium. Notably, the attack requires a few instructions skips and is able to reduce the MLWE problem that Dilithium is based on to a smaller RLWE problem which can be practically solved with lattice reduction techniques. Accordingly, we demonstrated key recoveries using hints extracted on the secret keys from the same faulted signatures using the LWE with side-information framework introduced by Dachman-Soled et al. at CRYPTO’20. As a final contribution, we proposed algorithmic countermeasures against this attack and in particular showed that the second one can be parameterized to only induce a negligible overhead over the signature generation.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.262-286
  • Belief Propagation Meets Lattice Reduction: Security Estimates for
           Error-Tolerant Key Recovery from Decryption Errors

    • Authors: Julius Hermelink, Erik Mårtensson, Simona Samardjiska, Peter Pessl, Gabi Dreo Rodosek
      Pages: 287 - 317
      Abstract: In LWE-based KEMs, observed decryption errors leak information about the secret key in the form of equations or inequalities. Several practical fault attacks have already exploited such leakage by either directly applying a fault or enabling a chosen-ciphertext attack using a fault. When the leaked information is in the form of inequalities, the recovery of the secret key is not trivial. Recent methods use either statistical or algebraic methods (but not both), with some being able to handle incorrect information. Having in mind that integration of the side-channel information is a crucial part of several classes of implementation attacks on LWEbased schemes, it is an important question whether statistically processed information can be successfully integrated in lattice reduction algorithms.
      We answer this question positively by proposing an error-tolerant combination of statistical and algebraic methods that make use of the advantages of both approaches. The combination enables us to improve upon existing methods – we use both fewer inequalities and are more resistant to errors. We further provide precise security estimates based on the number of available inequalities.
      Our recovery method applies to several types of implementation attacks in which decryption errors are used in a chosen-ciphertext attack. We practically demonstrate the improved performance of our approach in a key-recovery attack against Kyber with fault-induced decryption errors.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.287-317
  • LPN-based Attacks in the White-box Setting

    • Authors: Alex Charlès, Aleksei Udovenko
      Pages: 318 - 343
      Abstract: In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner’s masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko (ASIACRYPT 2018) and Seker-Eisenbarth-Liskiewicz (CHES 2021) prevent LDA and force to use its higher-degree generalizations with much higher complexity.
      In this work, we study the relationship between the security of these and related schemes to the Learning Parity with Noise (LPN) problem and propose a new automated attack by applying an LPN-solving algorithm to white-box implementations. The attack effectively exploits strong linear approximations of the masking scheme and thus can be seen as a combination of the DCA and LDA techniques. Different from previous attacks, the complexity of this algorithm depends on the approximation error, henceforth allowing new practical attacks on masking schemes which previously resisted automated analysis. We demonstrate it theoretically and experimentally, exposing multiple cases where the LPN-based method significantly outperforms LDA and DCA methods, including their higher-order variants.
      This work applies the LPN problem beyond its usual post-quantum cryptography boundary, strengthening its interest for the cryptographic community, while expanding the range of automated attacks by presenting a new direction for breaking masking schemes in the white-box model.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.318-343
  • Low Trace-Count Template Attacks on 32-bit Implementations of ASCON AEAD

    • Authors: Shih-Chun You, Markus G. Kuhn, Sumanta Sarkar, Feng Hao
      Pages: 344 - 366
      Abstract: The recently adopted Ascon standard by NIST offers a lightweight authenticated encryption algorithm for use in resource-constrained cryptographic devices. To help assess side-channel attack risks of Ascon implementations, we present the first template attack based on analyzing power traces, recorded from an STM32F303 microcontroller board running Weatherley’s 32-bit implementations of Ascon-128. Our analysis combines a fragment template attack with belief-propagation and key-enumeration techniques. The main results are three-fold: (1) we reached 100% success rate from a single trace if the C compiler optimized the unmasked implementation for space, (2) the success rate was about 95% after three traces if the compiler optimized instead for time, and (3) we also attacked a masked version, where the success rate was over 90% with 20 traces of executions with the same key, all after enumerating up to 224 key candidates. These results show that suitably-designed template attacks can pose a real threat to Ascon implementations, even if protected by first-order masking, but we also learnt how some differences in programming style, and even compiler optimization settings, can significantly affect the result.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.344-366
  • Loop Aborts Strike Back: Defeating Fault Countermeasures in Lattice
           Signatures with ILP

    • Authors: Vincent Quentin Ulitzsch, Soundes Marzougui, Alexis Bagia, Mehdi Tibouchi, Jean-Pierre Seifert
      Pages: 367 - 392
      Abstract: At SAC 2016, Espitau et al. presented a loop-abort fault attack against lattice-based signature schemes following the Fiat–Shamir with aborts paradigm. Their attack recovered the signing key by injecting faults in the sampling of the commitment vector (also called masking vector) y, leaving its coefficients at their initial zero value. As possible countermeasures, they proposed to carry out the sampling of the coefficients of y in shuffled order, or to ensure that the masking polynomials in y are not of low degree. In this paper, we show that both of these countermeasures are insufficient. We demonstrate a new loop-abort fault injection attack against Fiat–Shamir with aborts lattice-based signatures that can recover the secret key from faulty signatures even when the proposed countermeasures are implemented. The key idea of our attack is that faulted signatures give rise to a noisy linear system of equations, which can be solved using integer linear programming. We present an integer linear program that recovers the secret key efficiently in practice, and validate the efficacy of our attack by conducting a practical end-to-end attack against a shuffled version of the Dilithium reference implementation, mounted on an ARM Cortex M4. We achieve a full (equivalent) key recovery in under 3 minutes total execution time (including signature generation), using only 5 faulted signatures. In addition, we conduct extensive theoretical simulations of the attack against Dilithium. We find that our method can achieve key recovery in under 5 minutes given a (sufficiently large) set of signatures where just one of the coefficients of y is zeroed out (or left at its initial value of zero). Furthermore, we find that our attack works against all security levels of Dilithium. Our attack shows that protecting Fiat–Shamir with aborts lattice-based signatures against fault injection attacks cannot be achieved using the simple countermeasures proposed by Espitau et al. and likely requires significantly more expensive countermeasures.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.367-392
  • Don’t Forget Pairing-Friendly Curves with Odd Prime Embedding

    • Authors: Yu Dai, Fangguo Zhang, Chang-an Zhao
      Pages: 393 - 419
      Abstract: Pairing-friendly curves with odd prime embedding degrees at the 128-bit security level, such as BW13-310 and BW19-286, sparked interest in the field of public-key cryptography as small sizes of the prime fields. However, compared to mainstream pairing-friendly curves at the same security level, i.e., BN446 and BLS12-446, the performance of pairing computations on BW13-310 and BW19-286 is usually considered inefficient. In this paper we investigate high performance software implementations of pairing computation on BW13-310 and corresponding building blocks used in pairing-based protocols, including hashing, group exponentiations and membership testings. Firstly, we propose efficient explicit formulas for pairing computation on this curve. Moreover, we also exploit the state-of-art techniques to implement hashing in G1 and G2, group exponentiations and membership testings. In particular, for exponentiations in G2 and GT , we present new optimizations to speed up computational efficiency. Our implementation results on a 64-bit processor show that the gap in the performance of pairing computation between BW13-310 and BN446 (resp. BLS12-446) is only up to 4.9% (resp. 26%). More importantly, compared to BN446 and BLS12-446, BW13-310 is about 109.1% − 227.3%, 100% − 192.6%, 24.5%−108.5% and 68.2%−145.5% faster in terms of hashing to G1, exponentiations in G1 and GT , and membership testing for GT , respectively. These results reveal that BW13-310 would be an interesting candidate in pairing-based cryptographic protocols.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.393-419
  • Provable Secure Parallel Gadgets

    • Authors: Francesco Berti, Sebastian Faust, Maximilian Orlt
      Pages: 420 - 459
      Abstract: Side-channel attacks are a fundamental threat to the security of cryptographic implementations. One of the most prominent countermeasures against side-channel attacks is masking, where each intermediate value of the computation is secret shared, thereby concealing the computation’s sensitive information. An important security model to study the security of masking schemes is the random probing model, in which the adversary obtains each intermediate value of the computation with some probability p. To construct secure masking schemes, an important building block is the refreshing gadget, which updates the randomness of the secret shared intermediate values. Recently, Dziembowski, Faust, and Zebrowski (ASIACRYPT’19) analyzed the security of a simple refreshing gadget by using a new technique called the leakage diagram. In this work, we follow the approach of Dziembowski et al. and significantly improve its methodology. Concretely, we refine the notion of a leakage diagram via so-called dependency graphs, and show how to use this technique for arbitrary complex circuits via composition results and approximation techniques. To illustrate the power of our new techniques, as a case study, we designed provably secure parallel gadgets for the random probing model, and adapted the ISW multiplication such that all gadgets can be parallelized. Finally, we evaluate concrete security levels, and show how our new methodology can further improve the concrete security level of masking schemes. This results in a compiler provable secure up to a noise level of O(1) for affine circuits and O(1/√n) in general.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.420-459
  • Pincering SKINNY by Exploiting Slow Diffusion

    • Authors: Nicolas Costes, Martijn Stam
      Pages: 460 - 492
      Abstract: Lightweight cryptography is an emerging field where designers are testing the limits of symmetric cryptography. We investigate the resistance against sidechannel attacks of a new class of lighter blockciphers, which use a classic substitution–permutation network with slow diffusion and many rounds.
      Among these ciphers, we focus on SKINNY, a primitive used up to the final round ofNIST’s recent lightweight standardisation effort. We show that the lack of diffusion in the key scheduler allows an attacker to combine leakage from the first and the last rounds, effectively pincering its target. Furthermore, the slow diffusion used by its partial key-absorption and linear layers enable, on both sides, to target S-Boxes from several rounds deep.
      As some of these S-boxes leak on the same part of the key, full key recovery exploiting all leakage requires a clever combining strategy. We introduce the use of cluster graph inference (an established tool from probabilistic graphical model theory) to enhance both unprofiled or profiled differential power analysis, enabling us to handle
      the increase of S-Boxes with their intertwined leakage.
      We evaluate the strength of our attack both in the Hamming weight model and against two implementations running on an STM32F303 ARM Cortex-M4 hosted on a ChipWhisperer target board, showing that our attack reduces the number of traces required to attack SKINNY by a factor of around 2.75.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.460-492
  • Revisiting the Computation Analysis against Internal Encodings in
           White-Box Implementations

    • Authors: Yufeng Tang, Zheng Gong, Bin Li, Liangju Zhao
      Pages: 493 - 522
      Abstract: White-box implementations aim to prevent the key extraction of the cryptographic algorithm even if the attacker has full access to the execution environment. To obfuscate the round functions, Chow et al. proposed a pivotal principle of white-box implementations to convert the round functions as look-up tables which are encoded by random internal encodings. These encodings consist of a linear mapping and a non-linear nibble permutation. At CHES 2016, Bos et al. introduced differential computation analysis (DCA) to extract the secret key from the runtime information, such as accessed memory and registers. Following this attack, many computation analysis methods were proposed to break the white-box implementations by leveraging some properties of the linear internal encodings, such as Hamming weight and imbalance. Therefore, it becomes an alternative choice to use a non-linear byte encoding to thwart DCA. At CHES 2021, Carlet et al. proposed a structural attack and revealed the weakness of the non-linear byte encodings which are combined with a non-invertible linear mapping. However, such a structural attack requires the details of the implementation, which relies on extra reverse engineering efforts in practice. To the best of our knowledge, it still lacks a thorough investigation of whether the non-linear byte encodings can resist the computation analyses.
      In this paper, we revisit the proposed computation analyses by investigating their capabilities against internal encodings with different algebraic degrees. Particularly, the algebraic degree of encodings is leveraged to explain the key leakage on the non-linear encodings. Based on this observation, we propose a new algebraic degree computation analysis (ADCA), which targets the mappings from the inputs to each sample of the computation traces. Different from the previous computation analyses, ADCA is a higher-degree attack that can distinguish the correct key by matching the algebraic degrees of the mappings. The experimental results prove that ADCA can break the internal encodings from degree 1 to 6 with the lowest time complexity. nstead of running different computation analyses separately, ADCA can be used as a generic tool to attack the white-box implementations.
      PubDate: 2023-08-31
      DOI: 10.46586/tches.v2023.i4.493-522
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