## IACR News

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#### 21 August 2019

###### Diego F. Aranha, Claudio Orlandi, Akira Takahashi, Greg Zaverucha

ePrint Report
Deterministic generation of per-signature randomness has been a widely accepted solution to mitigate the catastrophic risk of randomness failure in Fiat-Shamir type signature schemes. However, recent studies have practically demonstrated that such de-randomized schemes, including EdDSA, are vulnerable to differential fault attacks, which enable fault adversaries to recover the entire secret signing key, by artificially provoking randomness reuse or corrupting computation in other ways. In order to balance concerns of both randomness failures and the threat of fault injection, some signature designs are advocating a "hedged" derivation of the per-signature randomness, by hashing the secret key, message, and a nonce. Despite the growing popularity of the hedged paradigm in practical signature schemes, to the best of our knowledge, there has been no attempt to formally analyze the fault resilience of hedged signatures in the literature.

We perform a formal security analysis of the fault resilience of signature schemes constructed via the Fiat-Shamir transform. We propose a model to characterize bit-tampering fault attacks against hedged Fiat-Shamir type signatures, and investigate their impact across different steps of the signing operation. We prove that for some types of faults, attacks are mitigated by the hedged paradigm, while attacks remain possible for others. As a concrete case study, we then apply our results to Picnic2, a recent Fiat-Shamir type signature scheme using the hedged construction.

We perform a formal security analysis of the fault resilience of signature schemes constructed via the Fiat-Shamir transform. We propose a model to characterize bit-tampering fault attacks against hedged Fiat-Shamir type signatures, and investigate their impact across different steps of the signing operation. We prove that for some types of faults, attacks are mitigated by the hedged paradigm, while attacks remain possible for others. As a concrete case study, we then apply our results to Picnic2, a recent Fiat-Shamir type signature scheme using the hedged construction.

###### Antonio Faonio, Dario Fiore, Javier Herranz, Carla Ràfols

ePrint Report
Re-randomizable RCCA-secure public key encryption (Rand-RCCA PKE) schemes reconcile
the property of re-randomizability of the ciphertexts
with the need of security against chosen-ciphertexts attacks.

In this paper we give a new construction of a Rand-RCCA PKE scheme that is perfectly re-randomizable. Our construction is structure-preserving, can be instantiated over Type-3 pairing groups, and achieves better computation and communication efficiency than the state of the art perfectly re-randomizable schemes (e.g., Prabhakaran and Rosulek, CRYPTO'07).

Next, we revive the Rand-RCCA notion showing new applications where our Rand-RCCA PKE scheme plays a fundamental part: (1) We show how to turn our scheme into a publicly-verifiable Rand-RCCA scheme; (2) We construct a malleable NIZK with a (variant of) simulation soundness that allows for re-randomizability; (3) We propose a new UC-secure Verifiable Mix-Net protocol that is secure in the common reference string model. Thanks to the structure-preserving property, all these applications are efficient. Notably, our Mix-Net protocol is the most efficient universally verifiable Mix-Net (without random oracle) where the CRS is an uniformly random string of size independent of the number of senders. The property is of the essence when such protocols are used in large scale.

In this paper we give a new construction of a Rand-RCCA PKE scheme that is perfectly re-randomizable. Our construction is structure-preserving, can be instantiated over Type-3 pairing groups, and achieves better computation and communication efficiency than the state of the art perfectly re-randomizable schemes (e.g., Prabhakaran and Rosulek, CRYPTO'07).

Next, we revive the Rand-RCCA notion showing new applications where our Rand-RCCA PKE scheme plays a fundamental part: (1) We show how to turn our scheme into a publicly-verifiable Rand-RCCA scheme; (2) We construct a malleable NIZK with a (variant of) simulation soundness that allows for re-randomizability; (3) We propose a new UC-secure Verifiable Mix-Net protocol that is secure in the common reference string model. Thanks to the structure-preserving property, all these applications are efficient. Notably, our Mix-Net protocol is the most efficient universally verifiable Mix-Net (without random oracle) where the CRS is an uniformly random string of size independent of the number of senders. The property is of the essence when such protocols are used in large scale.

###### Mohsen Jahanbani, Zeinolabedin Norouzi, Nasour Bagheri

ePrint Report
Authenticated encryption schemes provide both confidentiality and integrity services, simultaneously. Correlation power analysis (CPA) can be a thread for authenticated ciphers, like all physical implementations of any cryptographic system. In this paper, for the first time, a three-steps CPA attack against COLM, one of the winners of CAESAR, is presented to indicate its vulnerability. For this purpose, in this research paper, this authenticated encryption scheme is implemented on the FPGA of the SAKURA-G board and, by measuring and collecting 1,800 power traces, a successful CPA attack with zero value power model has been mounted on it. In addition, a protected hardware architecture for the COLM is proposed to make this design secure against first-order CPA attacks. To this end, a domain-oriented masking (DOM) scheme with two inputs/outputs share is used to protect the COLM. To verify the security of these countermeasures, we mounted a first and second-order CPA attack and a non-specified t-test on the protected COLM.

###### Ariel Gabizon, Zachary J. Williamson, Oana Ciobotaru

ePrint Report
zk-SNARK constructions that utilize an updatable universal structured reference string remove one of the main obstacles in deploying zk-SNARKs [GKMMM, Crypto 2018]. The important work of Maller et al. [MBKM, CCS 2019] presented $\mathsf{Sonic}$ - the first potentially practical zk-SNARK with fully succinct verification for general arithmetic circuits with such an SRS.
However, the version of $\mathsf{Sonic}$ enabling fully succinct verification still requires relatively high proof construction overheads. We present a universal SNARK construction with fully succinct verification, and significantly lower prover running time (roughly 7.5-20 less group exponentiations than [MBKM] in the fully succinct verifier mode depending on circuit structure).

Similarly to [MBKM],[Bootle et. al, Eurocrypt 2016] we rely on a permutation argument based on Bayer and Groth [Eurocrypt 2012]. However, we focus on ``Evaluations on a subgroup rather than coefficients of monomials''; which enables simplifying both the permutation argument and the artihmetization step.

Similarly to [MBKM],[Bootle et. al, Eurocrypt 2016] we rely on a permutation argument based on Bayer and Groth [Eurocrypt 2012]. However, we focus on ``Evaluations on a subgroup rather than coefficients of monomials''; which enables simplifying both the permutation argument and the artihmetization step.

###### Vincenzo Iovino, Ivan Visconti

ePrint Report
The Fiat-Shamir (FS) transform is a well known and widely used technique to convert any constant-round public-coin honest-verifier zero-knowledge (HVZK) proof or argument system $CIPC=(Prov,Ver)$ in a non-interactive zero-knowledge (NIZK) argument system $NIZK=(NIZK.Prove, NIZK.Verify)$.
The FS transform is secure in the random oracle (RO) model and is extremely efficient: it adds an evaluation of the
RO for every message played by $Ver$.

While a major effort has been done to attack the soundness of the transform when the RO is instantiated with a ``secure'' hash function, here we focus on a different limitation of the FS transform that exists even when there is a secure instantiation of the random oracle: the soundness of $NIZK$ holds against polynomial-time adversarial provers only. Therefore even when $CIPC$ is a proof system, $NIZK$ is only an argument system.

In this paper we propose a new transform from 3-round public-coin HVZK proof systems for several practical relations to NIZK proof systems in the RO model. Our transform outperforms the FS transform protecting the honest verifier from unbounded adversarial provers with no restriction on the number of RO queries. The protocols our transform can be applied to are the ones for proving membership to the range of a one-way group homomorphism as defined by [Maurer - Design, Codes and Cryptography 2015] except that we additionally require the function to be endowed with a trapdoor and other natural properties. For instance, we obtain new efficient instantiations of NIZK proofs for relations related to quadratic residuosity and the RSA function.

As a byproduct, with our transform we obtain essentially for free the first efficient non-interactive zap (i.e., 1-round non-interactive witness indistinguishable proof system) for several practical languages in the non-programmable RO model and in an ideal-PUF model.

Our approach to NIZK proofs can be seen as an abstraction of the celebrated work of [Feige, Lapidot and Shamir - FOCS 1990].

While a major effort has been done to attack the soundness of the transform when the RO is instantiated with a ``secure'' hash function, here we focus on a different limitation of the FS transform that exists even when there is a secure instantiation of the random oracle: the soundness of $NIZK$ holds against polynomial-time adversarial provers only. Therefore even when $CIPC$ is a proof system, $NIZK$ is only an argument system.

In this paper we propose a new transform from 3-round public-coin HVZK proof systems for several practical relations to NIZK proof systems in the RO model. Our transform outperforms the FS transform protecting the honest verifier from unbounded adversarial provers with no restriction on the number of RO queries. The protocols our transform can be applied to are the ones for proving membership to the range of a one-way group homomorphism as defined by [Maurer - Design, Codes and Cryptography 2015] except that we additionally require the function to be endowed with a trapdoor and other natural properties. For instance, we obtain new efficient instantiations of NIZK proofs for relations related to quadratic residuosity and the RSA function.

As a byproduct, with our transform we obtain essentially for free the first efficient non-interactive zap (i.e., 1-round non-interactive witness indistinguishable proof system) for several practical languages in the non-programmable RO model and in an ideal-PUF model.

Our approach to NIZK proofs can be seen as an abstraction of the celebrated work of [Feige, Lapidot and Shamir - FOCS 1990].

###### Xavier Bonnetain

ePrint Report
MiMC and GMiMC are families of MPC-friendly block ciphers and hash functions. In this note, we show that the block ciphers MiMC-$2n/n$ (or Feistel-MiMC) and univariate GMiMC are vulnerable to an attack which allows
a key recovery in $2^{n/2}$ operations. This attack, which is reminiscent of a slide attack, only relies on their weak key schedules, and is independent of the round function ($x^3$ here) and the number of rounds.

###### Simon-Philipp Merz, Romy Minko, Christophe Petit

ePrint Report
The security proofs for isogeny-based undeniable signature schemes have been based primarily on two isogeny hardness assumptions: that the One-Sided Modified SSCDH problem and the One-More SSCDH problem are hard to solve. We challenge the validity of these assumptions, showing that both the decisional and computational variants of these problems can be solved in constant time. We further demonstrate an attack, applicable to two undeniable signature schemes, one of which was proposed at PQCrypto 2014, which allows an adversary to forge signatures in $2^{4\lambda/5}$ steps on a classical computer. This is an improvement over the expected classical security of $2^{\lambda}$, where $\lambda$ is the chosen security parameter.

###### Yongha Son

ePrint Report
We examine the current parameter choice of Round5,
and rectify its consideration of the improved dual attack due to Albrecht [Albrecht-EC17]:
there is one significant optimization of Albrecht's dual attack,
which was not reflected to Round5 parameter choices.
By taking this into consideration,
some parameter choices of Round5 cannot enjoy the claimed security level.

#### 20 August 2019

###### Prasanna Ravi, Sujoy Sinha Roy, Anupam Chattopadhyay, Shivam Bhasin

ePrint Report
In this article, we demonstrate practical side-channel assisted chosen-ciphertext attacks (CCA) over multiple CCA-secure lattice-based public-key encryption schemes (PKE) and key-encapsulation mechanisms (KEM). Most lattice-based PKE/KEMs suffer from the problem of decryption failures and some of these schemes use forward error correction codes to reduce the failure probability. These error correcting codes, when used within public-key cryptographic schemes, involve computations with secret components and hence might leak sensitive side-channel information. In this work, we identify a side-channel vulnerability in constant-time error correcting codes, which help the attacker distinguish between faulty and valid codewords through the EM/power side-channel information. We exploit the vulnerability to demonstrate a practical chosen-ciphertext attacks on the CCA-secure Round5 algorithm which uses timing attack resistant error correcting code.

We further identify a generic side-channel vulnerability within the CCA transformation steps used in multiple CCA-secure lattice-based PKE/KEM schemes. Exploiting the vulnerability, we demonstrate a practical chosen-ciphertext attack which can be performed on multiple CCA-secure lattice-based PKE/KEM schemes.

We perform experimental validation of our attacks using Electromagnetic measurements observed over optimized implementations of multiple NIST candidates taken from the pqm4 library, a benchmarking framework for post quantum cryptographic implementations for the ARM Cortex-M4 microcontroller. We thus establish that (1) lattice-based schemes that use error correcting codes, no matter constant-time or not, are vulnerable to power/EM side-channel attacks and (2) the notion that CCA-secure schemes are as insecure as their CPA-secure versions unless suitably masked against side-channel attacks.

We further identify a generic side-channel vulnerability within the CCA transformation steps used in multiple CCA-secure lattice-based PKE/KEM schemes. Exploiting the vulnerability, we demonstrate a practical chosen-ciphertext attack which can be performed on multiple CCA-secure lattice-based PKE/KEM schemes.

We perform experimental validation of our attacks using Electromagnetic measurements observed over optimized implementations of multiple NIST candidates taken from the pqm4 library, a benchmarking framework for post quantum cryptographic implementations for the ARM Cortex-M4 microcontroller. We thus establish that (1) lattice-based schemes that use error correcting codes, no matter constant-time or not, are vulnerable to power/EM side-channel attacks and (2) the notion that CCA-secure schemes are as insecure as their CPA-secure versions unless suitably masked against side-channel attacks.

###### Fabian Boemer, Anamaria Costache, Rosario Cammarota, Casimir Wierzynski

ePrint Report
In previous work, Boemer et al. introduced nGraph-HE, an extension to the Intel nGraph deep learning (DL) compiler, that en- ables data scientists to deploy models with popular frameworks such as TensorFlow and PyTorch with minimal code changes. However, the class of supported models was limited to relatively shallow networks with polynomial activations. Here, we introduce nGraph-HE2, which extends nGraph-HE to enable privacy-preserving inference on standard, pre-trained models using their native activation functions and number fields (typically real numbers). The proposed framework leverages the CKKS scheme, whose support for real numbers is friendly to data science, and a client-aided model to compute activation functions.

We first present CKKS-specific optimizations, enabling a 3x-88x runtime speedup for scalar encoding, and doubling the throughput through a novel use of CKKS plaintext packing into complex numbers. Second, we optimize ciphertext-plaintext addition and multiplication, yielding 2.6x- 4.2x runtime speedup. Third, we present two graph-level optimizations: lazy rescaling and depth-aware encoding.

Together, these optimizations enable state-of-the-art throughput of 1,998 images/s on the CryptoNets network. We also present homomorphic evaluation of (to our knowledge) the largest network to date, namely, pre-trained MobileNetV2 models on the ImageNet dataset, with 60.4%/82.7% top-1/top-5 accuracy and an amortized runtime of 381 ms/image.

We first present CKKS-specific optimizations, enabling a 3x-88x runtime speedup for scalar encoding, and doubling the throughput through a novel use of CKKS plaintext packing into complex numbers. Second, we optimize ciphertext-plaintext addition and multiplication, yielding 2.6x- 4.2x runtime speedup. Third, we present two graph-level optimizations: lazy rescaling and depth-aware encoding.

Together, these optimizations enable state-of-the-art throughput of 1,998 images/s on the CryptoNets network. We also present homomorphic evaluation of (to our knowledge) the largest network to date, namely, pre-trained MobileNetV2 models on the ImageNet dataset, with 60.4%/82.7% top-1/top-5 accuracy and an amortized runtime of 381 ms/image.

#### 19 August 2019

###### M Sazadur Rahman, Adib Nahiyan, Sarah Amir, Fahim Rahman, Farimah Farahmandi, Domenic Forte, Mark Tehranipoor

ePrint Report
Logic locking has emerged as a promising solution against IP piracy and modification by untrusted entities in the integrated circuit design process. However, its security is challenged by boolean satisfiability (SAT) based attacks. Criteria that are critical to SAT attack success on obfuscated circuits includes scan architecture access to the attacker and/or that the circuit under attack is combinational. To address this issue, we propose a dynamically-obfuscated scan chain (DOSC) technique in resisting SAT attack in an obfuscated sequential design by restricting scan access only to authorized users.

###### Navid Ghaedi Bardeh

ePrint Report
In this paper, we study the results of the recently proposed exchange attack in an adaptive setting. As expected, it leads to present a better 6-round key-independent distinguisher in terms of data and computational complexities. More specifically, our 6-round adaptive distinguisher requires $2^{83}$ chosen plaintexts and $2^{83}$ adaptively chosen ciphertexts and has a computational cost of $2^{83}$ encryption.

###### Max Hoffmann, Michael Klooß, Andy Rupp

ePrint Report
Zero-knowledge arguments have become practical, and widely used,
especially in the world of Blockchain, for example in Zcash.

This work revisits zero-knowledge proofs in the discrete logarithm setting. First, we identify and carve out basic techniques (partly being used implicitly before) to optimize proofs in this setting. In particular, the linear combination of protocols is a useful tool to obtain zero-knowledge and/or reduce communication. With these techniques, we are able to devise zero-knowledge variants of the logarithmic communication arguments by Bootle et al.\ (EUROCRYPT '16) and Bünz et al. (S\&P '18) thereby introducing almost no overhead. We then construct a conceptually simple commit-and-prove argument for satisfiability of a set of quadratic equations. Unlike previous work, we are not restricted to rank 1 constraint systems (R1CS). This is, to the best of our knowledge, the first work demonstrating that general quadratic constraints, not just R1CS, are a natural relation in the dlog (or ideal linear commitment) setting. This enables new possibilities for optimisation, as, eg., any degree $n^2$ polynomial $f(X)$ can now be ``evaluated'' with at most $2n$ quadratic constraints.

Our protocols are modular. We easily construct an efficient, logarithmic size shuffle proof, which can be used in electronic voting.

Additionally, we take a closer look at quantitative security measures, eg. the efficiency of an extractor. We formalise short-circuit extraction, which allows us to give tighter bounds on the efficiency of an extractor.

This work revisits zero-knowledge proofs in the discrete logarithm setting. First, we identify and carve out basic techniques (partly being used implicitly before) to optimize proofs in this setting. In particular, the linear combination of protocols is a useful tool to obtain zero-knowledge and/or reduce communication. With these techniques, we are able to devise zero-knowledge variants of the logarithmic communication arguments by Bootle et al.\ (EUROCRYPT '16) and Bünz et al. (S\&P '18) thereby introducing almost no overhead. We then construct a conceptually simple commit-and-prove argument for satisfiability of a set of quadratic equations. Unlike previous work, we are not restricted to rank 1 constraint systems (R1CS). This is, to the best of our knowledge, the first work demonstrating that general quadratic constraints, not just R1CS, are a natural relation in the dlog (or ideal linear commitment) setting. This enables new possibilities for optimisation, as, eg., any degree $n^2$ polynomial $f(X)$ can now be ``evaluated'' with at most $2n$ quadratic constraints.

Our protocols are modular. We easily construct an efficient, logarithmic size shuffle proof, which can be used in electronic voting.

Additionally, we take a closer look at quantitative security measures, eg. the efficiency of an extractor. We formalise short-circuit extraction, which allows us to give tighter bounds on the efficiency of an extractor.

###### Ling Ren

ePrint Report
This paper gives a simple analysis of Nakamoto consensus.

#### 18 August 2019

###### Handan Kılınç Alper

ePrint Report
Ouroboros Praos is a proof of stake based blockchain protocol. One of its security
assumptions is parties are synchronized i.e., all of them knows when the protocol passes
a new state. However, it is not easy to have such a protocol in real life, especially in a
decentralized network. Therefore, we construct a new version of Ouroboros Praos by composing a new protocol called Relative Time protocol. We call the new version Ouroboros
Clepsydra. At the end of the relative time protocol, a party learns the approximate state
of the protocol based on the median of arrival times of messages sent by the other parties
and adjusts its local clock based on it. The relative time protocol does not add any new
computation to the other parties. They even do not realize that they are part of the relative time protocol. In order to prove Ouroboros Clepsydrain the Universally Composable
(UC) model, we define a general UC model to capture the notion of relative time. We
remove the synchronization assumption in Ouroboros Clepsydra and show that Ouroboros
Clepsydra is a secure proof of stake blockchain protocol in the UC model.

###### Eman Salem Alashwali, Pawel Szalachowski, Andrew Martin

ePrint Report
Experience shows that most researchers and developers tend to treat plain-domains (those that are not prefixed with “www” sub-domains, e.g. “example.com”) as synonyms for their equivalent www-domains (those that are prefixed with “www” sub-domains, e.g. “www.example.com”). In this paper, we analyse datasets of nearly two million plain-domains against their equivalent www-domains to answer the following question: Do plain-domains and their equivalent www-domains differ in TLS security configurations and certificates? If so, to what extent? Our results provide evidence of an interesting phenomenon: plain-domains and their equivalent www-domains differ in TLS security configurations and certificates in a non-trivial number of cases. Furthermore, www-domains tend to have stronger security configurations than their equivalent plain-domains. Interestingly, this phenomenon is more prevalent in the most-visited domains than in randomly-chosen domains. Further analysis of the top domains dataset shows that 53.35% of the plain-domains that show one or more weakness indicators (e.g. expired certificate) that are not shown in their equivalent www-domains perform HTTPS redirection from HTTPS plain-domains to their equivalent HTTPS www-domains. Additionally, 24.71% of these redirections contains plain-text HTTP intermediate URLs. In these cases, users see the final www-domains with strong TLS configurations and certificates, but in fact, the HTTPS request has passed through plain-domains that have less secure TLS configurations and certificates. Clearly, such a set-up introduces a weak link in the security of the overall interaction.

###### Nasrollah Pakniat

ePrint Report
Certificateless cryptography can be considered as an intermediate solution to overcome the issues in traditional public key infrastructure (PKI) and identity-based public key cryptography (ID-PKC). There exist a vast number of certificateless signature (CLS) schemes in the literature; however, most of them are not efficient enough to be utilized in limited resources environments such as Internet of things (IoT) or Healthcare Wireless Sensor Networks (HWSN). Recently, two lightweight CLS schemes have been proposed by Karati et al. and Kumar et al. to be employed in IoT and HWSNs, respectively. While both schemes are claimed to be existentially unforgeable, in this paper, we show that both these signatures can easily be forged. More specifically, it is shown that 1) in Karati et al.'s scheme, a type 1 adversary, considered in certificateless cryptography, can generate a valid partial private key corresponding to any user of its choice and as a consequence, it can forge any users' signature on any message of its choice, and 2) in Kumar et al.'s scheme, both types of adversaries which are considered in certificateless cryptography are able to forge any signer's signature on an arbitrary message.

###### Martin Albrecht, Melissa Chase, Hao Chen, Jintai Ding, Shafi Goldwasser, Sergey Gorbunov, Shai Halevi, Jeffrey Hoffstein, Kim Laine, Kristin Lauter, Satya Lokam, Daniele Micciancio, Dustin Moody, Trav

ePrint Report
Homomorphic Encryption is a breakthrough technology which can enable private cloud storage and computation solutions, and many applications have been described in the literature in the last few years. But before Homomorphic Encryption can be adopted in medical, health, and financial sectors to protect data and patient and consumer privacy, it will have to be standardized, most likely by multiple standardization bodies and government agencies. An important part of standardization is broad agreement on security levels for varying parameter sets. Although extensive research and benchmarking has been done in the research community to establish the foundations for this effort, it is hard to find all the information in one place, along with concrete parameter recommendations for applications and deployment.
This document is the first Homomorphic Encryption Standard (HES) approved by the Homomorphicencryption.org community in 2018. It captures the collective knowledge on the state of security of these schemes, specifies the schemes, and recommends a wide selection of parameters to be used for homomorphic encryption at various security levels. We describe known attacks and their estimated running times in order to make these security parameter recommendations.

###### Gaëtan Leurent, Ferdinand Sibleyras

ePrint Report
The iterated Even-Mansour construction is an elegant construction that idealizes block cipher designs such as the AES. In this work we focus on the simplest variant, the 2-round Even-Mansour construction with a single key. This is the most minimal construction that offers security beyond the birthday bound: there is a security proof up to $2^{2n/3}$ evaluations of the underlying permutations and encryption, and the best known attacks have a complexity of roughly $2^n/n$ operations.
We show that attacking this scheme with block size $n$ is related to the 3-XOR problem with element size $w = 2n$, an important algorithmic problem that has been studied since the nineties. In particular the 3-XOR problem is known to require at least $2^{w/3}$ queries, and the best known algorithms require around $2^{w/2} / w$ operations: this roughly matches the known bounds for the 2-round Even-Mansour scheme. Using this link we describe new attacks against the 2-round Even-Mansour scheme. In particular, we obtain the first algorithms where both the data and the memory complexity are significantly lower than $2^n$ .
From a practical standpoint, previous works with a data and/or memory complexity close to $2^n$ are unlikely to be more efficient than a simple brute-force search over the key. Our best algorithm requires just $\lambda n$ known plaintext/ciphertext pairs, for some constant $0 < \lambda < 1$, $2^n/\lambda n$ time, and $2^{\lambda n}$ memory. For instance, with $n = 64$ and $\lambda = 1/2$, the memory requirement is practical, and we gain a factor 32 over brute-force search. We also describe an algorithm with asymptotic complexity $O(2^n (\ln^2{n/n^2})$, improving the previous asymptotic complexity of $O(2^n/n)$, using a variant of the 3-SUM algorithm of Baran, Demaine, and Patrascu.

###### Sayandeep Saha, Debapriya Basu Roy, Arnab Bag, Sikhar Patranabis, Debdeep Mukhopadhyay

ePrint Report
Fault attacks (FA) are one of the potent practical threats
to modern cryptographic implementations. Over the years the FA tech-
niques have evolved, gradually moving towards the exploitation of device-
centric properties of the faults. In this paper, we exploit the fact that
activation and propagation of a fault through a given combinational cir-
cuit (i.e. observability of a fault) is data dependent. Next, we show that
this property of combinational circuits leads to powerful fault attacks
even for implementations having dedicated and provably secure protec-
tions against both power and fault-assisted vulnerabilities. The attacks
found in this work are applicable even if the fault injection is made at
the middle rounds of a block cipher, which are out of reach for most
of the other existing fault analysis strategies. Quite evidently, they also
work for a known plaintext scenario. Moreover, the middle round attacks
are entirely blind in the sense that no access to the ciphertexts (cor-
rect/faulty) or plaintexts are required. The adversary is only assumed
to have the power of repeating an unknown plaintext several times. Ex-
perimental validation over software implementations of PRESENT and
AES proves the efficacy of the proposed attacks.