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Über dieses Buch

This book constitutes the proceedings of the 15th International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2013, held in Santa Barbara, CA, USA, in August 2013. The 27 papers presented were carefully reviewed and selected from 132 submissions. The papers are organized in the following topical sections: side-channel attacks; physical unclonable function; lightweight cryptography; hardware implementations and fault attacks; efficient and secure implementations; elliptic curve cryptography; masking; side-channel attacks and countermeasures.



Side-Channel Attacks

On the Simplicity of Converting Leakages from Multivariate to Univariate

(Case Study of a Glitch-Resistant Masking Scheme)
Several masking schemes to protect cryptographic implementations against side-channel attacks have been proposed. A few considered the glitches, and provided security proofs in presence of such inherent phenomena happening in logic circuits. One which is based on multi-party computation protocols and utilizes Shamir’s secret sharing scheme was presented at CHES 2011. It aims at providing security for hardware implementations – mainly of AES – against those sophisticated side-channel attacks that also take glitches into account. One part of this article deals with the practical issues and relevance of the aforementioned masking scheme. Following the recommendations given in the extended version of the mentioned article, we first provide a guideline on how to implement the scheme for the simplest settings. Constructing an exemplary design of the scheme, we provide practical side-channel evaluations based on a Virtex-5 FPGA. Our results demonstrate that the implemented scheme is indeed secure against univariate power analysis attacks given a basic measurement setup. In the second part of this paper we show how using very simple changes in the measurement setup opens the possibility to exploit multivariate leakages while still performing a univariate attack. Using these techniques the scheme under evaluation can be defeated using only a moderate number of measurements. This is applicable not only to the scheme showcased here, but also to most other known masking schemes where the shares of sensitive values are processed in adjacent clock cycles.
Amir Moradi, Oliver Mischke

Success through Confidence: Evaluating the Effectiveness of a Side-Channel Attack

Side-channel attacks usually apply a divide-and-conquer strategy, separately recovering different parts of the secret. Their efficiency in practice relies on the adversary ability to precisely assess the success or unsuccess of each of these recoveries. This makes the study of the attack success rate a central problem in side channel analysis. In this paper we tackle this issue in two different settings for the most popular attack, namely the Correlation Power Analysis (CPA). In the first setting, we assume that the targeted subkey is known and we compare the state of the art formulae expressing the success rate as a function of the leakage noise and the algebraic properties of the cryptographic primitive. We also make the link between these formulae and the recent work of Fei et al. at CHES 2012. In the second setting, the subkey is no longer assumed to be known and we introduce the notion of confidence level in an attack result, allowing for the study of different heuristics. Through experiments, we show that the rank evolution of a subkey hypothesis can be exploited to compute a better confidence than considering only the final result.
Adrian Thillard, Emmanuel Prouff, Thomas Roche

Profiling DPA: Efficacy and Efficiency Trade-Offs

Linear regression-based methods have been proposed as efficient means of characterising device leakage in the training phases of profiled side-channel attacks. Empirical comparisons between these and the ‘classical’ approach to template building have confirmed the reduction in profiling complexity to achieve the same attack-phase success, but have focused on a narrow range of leakage scenarios which are especially favourable to simple (i.e. efficiently estimated) model specifications. In this contribution we evaluate—from a theoretic perspective as much as possible—the performance of linear regression-based templating in a variety of realistic leakage scenarios as the complexity of the model specification varies. We are particularly interested in complexity trade-offs between the number of training samples needed for profiling and the number of attack samples needed for successful DPA: over-simplified models will be cheaper to estimate but DPA using such a degraded model will require more data to recover the key. However, they can still offer substantial improvements over non-profiling strategies relying on the Hamming weight power model, and so represent a meaningful middle-ground between ‘no’ prior information and ‘full’ prior information.
Carolyn Whitnall, Elisabeth Oswald

Non-invasive Spoofing Attacks for Anti-lock Braking Systems

This work exposes a largely unexplored vector of physical-layer attacks with demonstrated consequences in automobiles. By modifying the physical environment around analog sensors such as Antilock Braking Systems (ABS), we exploit weaknesses in wheel speed sensors so that a malicious attacker can inject arbitrary measurements to the ABS computer which in turn can cause life-threatening situations. In this paper, we describe the development of a prototype ABS spoofer to enable such attacks and the potential consequences of remaining vulnerable to these attacks. The class of sensors sensitive to these attacks depends on the physics of the sensors themselves. ABS relies on magnetic–based wheel speed sensors which are exposed to an external attacker from underneath the body of a vehicle. By placing a thin electromagnetic actuator near the ABS wheel speed sensors, we demonstrate one way in which an attacker can inject magnetic fields to both cancel the true measured signal and inject a malicious signal, thus spoofing the measured wheel speeds. The mounted attack is of a non-invasive nature, requiring no tampering with ABS hardware and making it harder for failure and/or intrusion detection mechanisms to detect the existence of such an attack. This development explores two types of attacks: a disruptive, naive attack aimed to corrupt the measured wheel speed by overwhelming the original signal and a more advanced spoofing attack, designed to inject a counter-signal such that the braking system mistakenly reports a specific velocity. We evaluate the proposed ABS spoofer module using industrial ABS sensors and wheel speed decoders, concluding by outlining the implementation and lifetime considerations of an ABS spoofer with real hardware.
Yasser Shoukry, Paul Martin, Paulo Tabuada, Mani Srivastava

Physical Unclonable Function

An Accurate Probabilistic Reliability Model for Silicon PUFs

The power of an accurate model for describing a physical process or designing a physical system is beyond doubt. The currently used reliability model for physically unclonable functions (PUFs) assumes an equally likely error for every evaluation of every PUF response bit. This limits an accurate description since experiments show that certain responses are more error-prone than others, but this fixed error rate model only captures average case behavior. We introduce a new PUF reliability model taking this observed heterogeneous nature of PUF cells into account. An extensive experimental validation demonstrates the new predicted distributions describe the empirically observed data statistics almost perfectly, even considering sensitivity to operational temperature. This allows studying PUF reliability behavior in full detail, including average and worst case probabilities, and is an invaluable tool for designing more efficient and better adapted PUFs and PUF-based systems.
Roel Maes

A High Reliability PUF Using Hot Carrier Injection Based Response Reinforcement

Achieving high reliability across environmental variations and over aging in physical unclonable functions (PUFs) remains a challenge for PUF designers. The conventional method to improve PUF reliability is to use powerful error correction codes (ECC) to correct the errors in the raw response from the PUF core. Unfortunately, these ECC blocks generally have high VLSI overheads, which scale up quickly with the error correction capability. Alternately, researchers have proposed techniques to increase the reliability of the PUF core, and thus significantly reduce the required strength (and complexity) of the ECC. One method of increasing the reliability of the PUF core is to use normally detrimental IC aging effects to reinforce the desired (or “golden”) response of the PUF by altering the PUF circuit characteristics permanently and hence making the PUF more reliable. In this work, we present a PUF response reinforcement technique based on hot carrier injection (HCI) which can reinforce the PUF golden response in short stress times (i.e., tens of seconds), without impacting the surrounding circuits, and that has high permanence (i.e., does not degrade significantly over aging). We present a self-contained HCI-reinforcement-enabled PUF circuit based on sense amplifiers (SA) which autonomously self-reinforces with minimal external intervention. We have fabricated a custom ASIC testchip in 65nm bulk CMOS with the proposed PUF design. Measured results show high reliability across environmental variations and accelerated aging, as well as good uniqueness and randomness. For example, 1600 SA elements, after being HCI stressed for 125s, show 100% reliability (zero errors) across ±20% voltage variations a temperature range of -20°C to 85°C.
Mudit Bhargava, Ken Mai

On the Effectiveness of the Remanence Decay Side-Channel to Clone Memory-Based PUFs

We present a side-channel attack based on remanence decay in volatile memory and show how it can be exploited effectively to launch a non-invasive cloning attack against SRAM PUFs — an important class of PUFs typically proposed as lightweight security primitive with low overhead by using the existing memory of the underlying device. We validate our approach against two SRAM PUF implementations in 65 nm CMOS ASICs. We discuss countermeasures against our attack and propose the constructive use of remanence decay to improve the cloning-resistance of SRAM PUFs.
Moreover, as a further contribution of independent interest, we show how to use our evaluation results to significantly improve the performance of the recently proposed TARDIS scheme, which is based on remanence decay in SRAM and used as a time-keeping mechanism for low-power clock-less devices.
Yossef Oren, Ahmad-Reza Sadeghi, Christian Wachsmann

Lightweight Cryptography

Pushing the Limits of SHA-3 Hardware Implementations to Fit on RFID

There exists a broad range of RFID protocols in literature that propose hash functions as cryptographic primitives. Since keccak has been selected as the winner of the NIST SHA-3 competition in 2012, there is the question of how far we can push the limits of keccak to fulfill the stringent requirements of passive low-cost RFID. In this paper, we address this question by presenting a hardware implementation of keccak that aims for lowest power and lowest area. Our smallest (full-state) design requires only 2 927 GEs (for designs with external memory available) and 5 522 GEs (total size including memory). It has a power consumption of 12.5 μW at 1 MHz on a low leakage 130 nm CMOS process technology. As a result, we provide a design that needs 40% less resources than related work. Our design is even smaller than the smallest SHA-1 and SHA-2 implementations.
Peter Pessl, Michael Hutter

Fides: Lightweight Authenticated Cipher with Side-Channel Resistance for Constrained Hardware

In this paper, we present a novel lightweight authenticated cipher optimized for hardware implementations called Fides. It is an online nonce-based authenticated encryption scheme with authenticated data whose area requirements are as low as 793 GE and 1001 GE for 80-bit and 96-bit security, respectively. This is at least two times smaller than its closest competitors Hummingbird-2 and Grain-128a. While being extremely compact, Fides is both throughput and latency efficient, even in its most serial implementations. This is attained by our novel sponge-like design approach. Moreover, cryptographically optimal 5-bit and 6-bit S-boxes are used as basic nonlinear components while paying a special attention on the simplicity of providing first order side-channel resistance with threshold implementation.
Begül Bilgin, Andrey Bogdanov, Miroslav Knežević, Florian Mendel, Qingju Wang

Hardware Implementations and Fault Attacks

On Measurable Side-Channel Leaks Inside ASIC Design Primitives

Leaks inside semi-custom ASIC (Application Specific Integrated Circuit) design primitives are rigorously investigated. The study is conducted by measuring a dedicated TEG (Test Element Group) chip with a small magnetic-field probe on the chip surface. Measurement targets are standard cells and a memory macro cell. Leaks inside the primitives are focused as many of conventional countermeasures place measurability boundaries on these primitives. Firstly, it is shown that current-path leak: a leak based on input-dependent active current path within a standard cell [1] is measurable. Major gate-level countermeasures (RSL, MDPL, and WDDL) become vulnerable if the current-path leak is considered. Secondly, it is shown that internal-gate leak: a leak based on non-linear sub-circuit within a XOR cell is measurable. It can be exploited to bias the distribution of the random mask. Thirdly, it is shown that geometric leak: a leak based on geometric layout of the memory matrix structure is measurable. It is a leak correlated to integer representation of the memory address. We also show that a ROM-based countermeasure (Dual-rail RSL memory [10]) becomes vulnerable with the geometric leak. A general transistor-level design method to counteract the current-path and internal-gate leaks is also shown.
Takeshi Sugawara, Daisuke Suzuki, Minoru Saeki, Mitsuru Shiozaki, Takeshi Fujino

A Very High Speed True Random Number Generator with Entropy Assessment

The proposed true random number generator (TRNG) exploits the jitter of events propagating in a self-timed ring (STR) to generate random bit sequences at a very high bit rate. It takes advantage of a special feature of STRs that allows the time elapsed between successive events to be set as short as needed, even in the order of picoseconds. If the time interval between the events is set in concordance with the clock jitter magnitude, a simple entropy extraction scheme can be applied to generate random numbers. The proposed STR-based TRNG (STRNG) follows AIS31 recommendations: by using the proposed stochastic model, designers can compute a lower entropy bound as a function of the STR characteristics (number of stages, oscillation period and jitter magnitude). Using the resulting entropy assessment, they can then set the compression rate in the arithmetic post-processing block to reach the required security level determined by the entropy per output bit. Implementation of the generator in two FPGA families confirmed its feasibility in digital technologies and also confirmed it can provide high quality random bit sequences that pass the statistical tests required by AIS31 at rates as high as 200 Mbit/s.
Abdelkarim Cherkaoui, Viktor Fischer, Laurent Fesquet, Alain Aubert

Stealthy Dopant-Level Hardware Trojans

In recent years, hardware Trojans have drawn the attention of governments and industry as well as the scientific community. One of the main concerns is that integrated circuits, e.g., for military or critical-infrastructure applications, could be maliciously manipulated during the manufacturing process, which often takes place abroad. However, since there have been no reported hardware Trojans in practice yet, little is known about how such a Trojan would look like, and how difficult it would be in practice to implement one.
In this paper we propose an extremely stealthy approach for implementing hardware Trojans below the gate level, and we evaluate their impact on the security of the target device. Instead of adding additional circuitry to the target design, we insert our hardware Trojans by changing the dopant polarity of existing transistors. Since the modified circuit appears legitimate on all wiring layers (including all metal and polysilicon), our family of Trojans is resistant to most detection techniques, including fine-grain optical inspection and checking against “golden chips”. We demonstrate the effectiveness of our approach by inserting Trojans into two designs — a digital post-processing derived from Intel’s cryptographically secure RNG design used in the Ivy Bridge processors and a side-channel resistant SBox implementation — and by exploring their detectability and their effects on security.
Georg T. Becker, Francesco Regazzoni, Christof Paar, Wayne P. Burleson

A Differential Fault Attack on MICKEY 2.0

In this paper we present a differential fault attack on the stream cipher MICKEY 2.0 which is in eStream’s hardware portfolio. While fault attacks have already been reported against the other two eStream hardware candidates Trivium and Grain, no such analysis is known for MICKEY. Using the standard assumptions for fault attacks, we show that if the adversary can induce random single bit faults in the internal state of the cipher, then by injecting around 216.7 faults and performing 232.5 computations on an average, it is possible to recover the entire internal state of MICKEY at the beginning of the key-stream generation phase. We further consider the scenario where the fault may affect at most three neighbouring bits and in that case we require around 218.4 faults on an average.
Subhadeep Banik, Subhamoy Maitra

Efficient and Secure Implementations

Improving Modular Inversion in RNS Using the Plus-Minus Method

The paper describes a new RNS modular inversion algorithm based on the extended Euclidean algorithm and the plus-minus trick. In our algorithm, comparisons over large RNS values are replaced by cheap computations modulo 4. Comparisons to an RNS version based on Fermat’s little theorem were carried out. The number of elementary modular operations is significantly reduced: a factor 12 to 26 for multiplications and 6 to 21 for additions. Virtex 5 FPGAs implementations show that for a similar area, our plus-minus RNS modular inversion is 6 to 10 times faster.
Karim Bigou, Arnaud Tisserand

McBits: Fast Constant-Time Code-Based Cryptography

This paper presents extremely fast algorithms for code-based public-key cryptography, including full protection against timing attacks. For example, at a 2128 security level, this paper achieves a reciprocal decryption throughput of just 60493 cycles (plus cipher cost etc.) on a single Ivy Bridge core. These algorithms rely on an additive FFT for fast root computation, a transposed additive FFT for fast syndrome computation, and a sorting network to avoid cache-timing attacks.
Daniel J. Bernstein, Tung Chou, Peter Schwabe

Smaller Keys for Code-Based Cryptography: QC-MDPC McEliece Implementations on Embedded Devices

In the last years code-based cryptosystems were established as promising alternatives for asymmetric cryptography since they base their security on well-known NP-hard problems and still show decent performance on a wide range of computing platforms. The main drawback of code-based schemes, including the popular proposals by McEliece and Niederreiter, are the large keys whose size is inherently determined by the underlying code. In a very recent approach, Misoczki et al. proposed to use quasi-cyclic MDPC (QC-MDPC) codes that allow for a very compact key representation. In this work, we investigate novel implementations of the McEliece scheme using such QC-MDPC codes tailored for embedded devices, namely a Xilinx Virtex-6 FPGA and an 8-bit AVR microcontroller. In particular, we evaluate and improve different approaches to decode QC-MDPC codes. Besides competitive performance for encryption and decryption on the FPGA, we achieved a very compact implementation on the microcontroller using only 4,800 and 9,600 bits for the public and secret key at 80 bits of equivalent symmetric security.
Stefan Heyse, Ingo von Maurich, Tim Güneysu

Sleuth: Automated Verification of Software Power Analysis Countermeasures

Security analysis is a crucial concern in the design of hardware and software systems, yet there is a distinct lack of automated methodologies. In this paper, we remedy this situation for the verification of software countermeasure implementations. In this context, verifying the security of a protected implementation against side-channel attacks corresponds to assessing whether any particular leakage in any particular computational phase is statistically dependent on the secret data and statistically independent of any random information used to protect the implementation. We present a novel methodology to reduce this verification problem into a set of Boolean satisfiability problems, which can be efficiently solved by leveraging recent advances in SAT solving. To show the effectiveness of our methodology, we have implemented an automatic verification tool, named Sleuth, as an advanced analysis pass in the back-end of the LLVM compiler. Our results show that one can automatically detect several examples of classic pitfalls in the implementation of countermeasures with reasonable runtimes.
Ali Galip Bayrak, Francesco Regazzoni, David Novo, Paolo Ienne

Elliptic Curve Cryptography

Lambda Coordinates for Binary Elliptic Curves

In this work we present the λ-coordinates, a new system for representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and timing results of our software implementation over the field \(\mathbb{F}_{2^{254}}\). As a result, we improve speed records for protected/unprotected single/multi-core software implementations of random-point elliptic curve scalar multiplication at the 128-bit security level. When implemented on a Sandy Bridge 3.4GHz Intel Xeon processor, our software is able to compute a single/multi-core unprotected scalar multiplication in 72,300 and 47,900 clock cycles, respectively; and a protected single-core scalar multiplication in 114,800 cycles. These numbers improve by around 2% on the newer Core i7 2.8GHz Ivy Bridge platform.
Thomaz Oliveira, Julio López, Diego F. Aranha, Francisco Rodríguez-Henríquez

High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition

This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography, motivated by the fact that they allow for an 8-dimensional scalar decomposition when using a combination of the GLV/GLS algorithms. Besides lowering the number of doublings required in a scalar multiplication, this approach has the advantage of performing arithmetic operations in a 64-bit ground field, making it an attractive candidate for embedded devices. We found cryptographically secure genus 2 curves which, although susceptible to index calculus attacks, aim for the standardized 112-bit security level. Our implementation results on both high-end architectures (Ivy Bridge) and low-end ARM platforms (Cortex-A8) highlight the practical benefits of this approach.
Joppe W. Bos, Craig Costello, Huseyin Hisil, Kristin Lauter

On the Implementation of Unified Arithmetic on Binary Huff Curves

Unified formula for computing elliptic curve point addition and doubling are considered to be resistant against simple power-analysis attack. A new elliptic curve formula known as unified binary Huff curve in this regard has appeared into the literature in 2011. This paper is devoted to analyzing the applicability of this elliptic curve in practice. Our paper has two contributions. We provide an efficient implementation of the unified Huff formula in projective coordinates on FPGA. Secondly, we point out its side-channel vulnerability and show the results of an actual attack. It is claimed that the formula is unified and there will be no power consumption difference when computing point addition and point doubling operations, observable with simple power analysis (SPA). In this paper, we contradict their claim showing actual SPA results on a FPGA platform and propose a modified arithmetic and its suitable implementation technique to overcome the vulnerability.
Santosh Ghosh, Amit Kumar, Amitabh Das, Ingrid Verbauwhede

Inverting the Final Exponentiation of Tate Pairings on Ordinary Elliptic Curves Using Faults

The calculation of the Tate pairing on ordinary curves involves two major steps: the Miller Loop (ML) followed by the Final Exponentiation (FE). The first step for achieving a full pairing inversion would be to invert this FE, which in itself is a mathematically difficult problem. To our best knowledge, most fault attack schemes proposed against pairing algorithms have mainly focussed on the ML. They solved, if at all, the inversion of the FE in some special ‘easy’ cases or even showed that the complexity of the FE is an intrinsic countermeasure against a successful full fault attack on the Tate pairing. In this paper, we present a fault attack on the FE whereby the inversion of the final exponentiation becomes feasible using 3 independent faults.
Ronan Lashermes, Jacques Fournier, Louis Goubin


Block Ciphers That Are Easier to Mask: How Far Can We Go?

The design and analysis of lightweight block ciphers has been a very active research area over the last couple of years, with many innovative proposals trying to optimize different performance figures. However, since these block ciphers are dedicated to low-cost embedded devices, their implementation is also a typical target for side-channel adversaries. As preventing such attacks with countermeasures usually implies significant performance overheads, a natural open problem is to propose new algorithms for which physical security is considered as an optimization criteria, hence allowing better performances again. We tackle this problem by studying how much we can tweak standard block ciphers such as the AES Rijndael in order to allow efficient masking (that is one of the most frequently considered solutions to improve security against side-channel attacks). For this purpose, we first investigate alternative S-boxes and round structures. We show that both approaches can be used separately in order to limit the total number of non-linear operations in the block cipher, hence allowing more efficient masking. We then combine these ideas into a concrete instance of block cipher called Zorro. We further provide a detailed security analysis of this new cipher taking its design specificities into account, leading us to exploit innovative techniques borrowed from hash function cryptanalysis (that are sometimes of independent interest). Eventually, we conclude the paper by evaluating the efficiency of masked Zorro implementations in an 8-bit microcontroller, and exhibit their interesting performance figures.
B. Gérard, Vincent Grosso, M. Naya-Plasencia, François-Xavier Standaert

Masking vs. Multiparty Computation: How Large Is the Gap for AES?

In this paper, we evaluate the performances of state-of-the-art higher-order masking schemes for the AES. Doing so, we pay a particular attention to the comparison between specialized solutions introduced exclusively as countermeasures against side-channel analysis, and a recent proposal by Roche and Prouff exploiting MultiParty Computation (MPC) techniques. We show that the additional security features this latter scheme provides (e.g. its glitch-freeness) comes at the cost of large performance overheads. We then study how exploiting standard optimization techniques from the MPC literature can be used to reduce this gap. In particular, we show that “packed secret sharing” based on a modified multiplication algorithm can speed up MPC-based masking when the order of the masking scheme increases. Eventually, we discuss the randomness requirements of masked implementations. For this purpose, we first show with information theoretic arguments that the security guarantees of masking are only preserved if this randomness is uniform, and analyze the consequences of a deviation from this requirement. We then conclude the paper by including the cost of randomness generation in our performance evaluations. These results should help actual designers to choose a masking scheme based on security and performance constraints.
Vincent Grosso, François-Xavier Standaert, Sebastian Faust

Analysis and Improvement of the Generic Higher-Order Masking Scheme of FSE 2012

Masking is a well-known technique used to prevent block cipher implementations from side-channel attacks. Higher-order side channel attacks (e.g. higher-order DPA attack) on widely used block cipher like AES have motivated the design of efficient higher-order masking schemes. Indeed, it is known that as the masking order increases, the difficulty of side-channel attack increases exponentially. However, the main problem in higher-order masking is to design an efficient and secure technique for S-box computations in block cipher implementations. At FSE 2012, Carlet et al. proposed a generic masking scheme that can be applied to any S-box at any order. This is the first generic scheme for efficient software implementations. Analysis of the running time, or masking complexity, of this scheme is related to a variant of the well-known problem of efficient exponentiation (addition chain), and evaluation of polynomials.
In this paper we investigate optimal methods for exponentiation in \(\mathbb{F}_{2^{n}}\) by studying a variant of addition chain, which we call cyclotomic-class addition chain, or CC-addition chain. Among several interesting properties, we prove lower bounds on min-length CC-addition chains. We define the notion of \(\mathbb{F}_{2^n}\)-polynomial chain, and use it to count the number of non-linear multiplications required while evaluating polynomials over \(\mathbb{F}_{2^{n}}\). We also give a lower bound on the length of such a chain for any polynomial. As a consequence, we show that a lower bound for the masking complexity of DES S-boxes is three, and that of PRESENT S-box is two. We disprove a claim previously made by Carlet et al. regarding min-length CC-addition chains. Finally, we give a polynomial evaluation method, which results into an improved masking scheme (compared to the technique of Carlet et al.) for DES S-boxes. As an illustration we apply this method to several other S-boxes and show significant improvement for them.
Arnab Roy, Srinivas Vivek

Side-Channel Attacks and Countermeasures

Using Bleichenbacher”s Solution to the Hidden Number Problem to Attack Nonce Leaks in 384-Bit ECDSA

In this paper we describe an attack against nonce leaks in 384-bit ECDSA using an FFT-based attack due to Bleichenbacher. The signatures were computed by a modern smart card. We extracted the low-order bits of each nonce using a template-based power analysis attack against the modular inversion of the nonce. We also developed a BKZ-based method for the range reduction phase of the attack, as it was impractical to collect enough signatures for the collision searches originally used by Bleichenbacher. We confirmed our attack by extracting the entire signing key using a 5-bit nonce leak from 4000 signatures.
Elke De Mulder, Michael Hutter, Mark E. Marson, Peter Pearson

A New Model for Error-Tolerant Side-Channel Cube Attacks

Side-channel cube attacks are a class of leakage attacks on block ciphers in which the attacker is assumed to have access to some leaked information on the internal state of the cipher as well as the plaintext/ciphertext pairs. The known Dinur-Shamir model and its variants require error-free data for at least part of the measurements. In this paper, we consider a new and more realistic model which can deal with the case when all the leaked bits are noisy. In this model, the key recovery problem is converted to the problem of decoding a binary linear code over a binary symmetric channel with the crossover probability which is determined by the measurement quality and the cube size. We use the maximum likelihood decoding method to recover the key. As a case study, we demonstrate efficient key recovery attacks on PRESENT. We show that the full 80-bit key can be restored with 210.2 measurements with an error probability of 19.4% for each measurement.
Zhenqi Li, Bin Zhang, Junfeng Fan, Ingrid Verbauwhede

Leakage-Resilient Symmetric Encryption via Re-keying

In the paper, we study whether it is possible to construct an efficient leakage-resilient symmetric scheme using the AES block cipher. We aim at bridging the gap between the theoretical leakage-resilient symmetric primitives used to build encryption schemes and the practical schemes that do not have any security proof against side-channel adversaries. Our goal is to construct an as efficient as possible leakage-resilient encryption scheme, but we do not want to change the cryptographic schemes already implemented. The basic idea consists in adding a leakage-resilient re-keying scheme on top of the encryption scheme and has been already suggested by Kocher to thwart differential power analysis techniques. Indeed, in such analysis, the adversary queries the encryption box and from the knowledge of the plaintext/ciphertext, she can perform a divide-and-conquer key recovery attack. The method consisting in changing the key for each or after a small number of encryption with the same key is known as re-keying. It prevents DPA adversaries but not SPA attacks which uses one single leakage trace. Here, we prove that using a leakage-resilient re-keying scheme on top of a secure encryption scheme in the standard model, leads to a leakage-resilient encryption scheme. The main advantage of the AES block cipher is that its implementations are generally heuristically-secure against SPA adversaries. This assumption is used in many concrete instantiations of leakage-resilient symmetric primitives. Consequently, if we use it and change the key for each new message block, the adversary will not be able to recover any key if the re-keying scheme is leakage-resilient. There is mainly two different techniques for re-keying scheme, either parallel or sequential, but if we want to avoid the adversary having access to many inputs/outputs, only the sequential method is possible. However, the main drawback of the latter technique is that in case of de-synchronization, many useless computations are required. In our re-keying scheme, we use ideas from the skip-list data structure to efficiently recover a specific key.
Michel Abdalla, Sonia Belaïd, Pierre-Alain Fouque


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