Characterization of Cultivatable Arsenic Resistant Bacteria from Black Mountain Open Space Park

Arsenic is a ubiquitous naturally occurring element. This metalloid is highly toxic and its dispersal in the environment represents an increasing threat to the organisms living in it. Arsenic-resistant bacteria have developed strategies to resist to the stress of this metal. Arsenic-rich soils were detected in San Diego County at the Black Mountain Open Space Park. This study focuses on the characterization of the cultivable bacteria presenting As resistance properties at this site. It is hypothesized that extreme exposure to an arsenic-rich environment has contributed to the evolution of species that possess favorable traits towards As resistance. Our findings show evolutionary diversity among the isolated species. Some species presented the ability to employ As as a source of energy. Screening for As resistance gene arsC was performed and phylogenetic comparison of the 16S rRNA tree with the arsC gene tree will allow to determine HGT occurrence within the microbial community

Safe-Error Analysis of Post-Quantum Cryptography Mechanisms

International audienceThe NIST selection process for standardizing Post-Quantum Cryptography Mechanisms is currently running. Many papers already studied their theoretical security, but the resistance in deployed device has not been much investigated so far. In particular, fault attack is a serious threat for algorithms implemented in embedded devices. One particularly powerful technique is to used safe-error attacks. Such attacks exploit the fact that a specific fault may or may not lead to a faulty output depending on a secret value. In this paper, we investigate the resistance of various Post-Quantum candidates algorithms against such attacks

Biscuit: New MPCitH Signature Scheme from Structured Multivariate Polynomials

This paper describes Biscuit, a new multivariate-based signature scheme derived using the MPCitH approach. The security of Biscuit is related to the problem of solving a set of quadratic structured systems of algebraic equations. These equations are highly compact and can be evaluated using very few multiplications. The core of Biscuit is a rather simple MPC protocol which consists of the parallel execution of a few secure multiplications using standard optimized multiplicative triples. This paper also includes several improvements with respect to Biscuit submission to the last NIST PQC standardization process for additional signature schemes. Notably, we introduce a new hypercube variant of Biscuit, refine the security analysis with recent third-party attacks, and present a new avx2 implementation of Biscuit

Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach

International audienceThe Polynomial System Solving (PoSSo) problem is a fundamental NP-Hard problem in computer algebra. Among others, PoSSo have applications in area such as coding theory and cryptology. Typically, the security of multivariate public-key schemes (MPKC) such as the UOV cryptosystem of Kipnis, Shamir and Patarin is directly related to the hardness of PoSSo over finite fields. The goal of this paper is to further understand the influence of finite fields on the hardness of PoSSo. To this end, we consider the so-called hybrid approach. This is a polynomial system solving method dedicated to finite fields proposed by Bettale, Faugère and Perret (Journal of Mathematical Cryptography, 2009). The idea is to combine exhaustive search with Gröbner bases. The efficiency of the hybrid approach is related to the choice of a trade-off between the two meth- ods. We propose here an improved complexity analysis dedicated to quadratic systems. Whilst the principle of the hybrid approach is simple, its careful analysis leads to rather surprising and somehow unexpected results. We prove that the optimal trade-off (i.e. num- ber of variables to be fixed) allowing to minimize the complexity is achieved by fixing a number of variables proportional to the number of variables of the system considered, denoted n. Under some nat- ural algebraic assumption, we show that the asymptotic complexity of the hybrid approach is 2^{n(3.31−3.62 log_2(q))} , where q is the size of the field (under the condition in particular that log(q) 2). We have been able to quantify the gain provided by the hybrid approach compared to a direct Gröbner basis method. For quadratic systems, we show (assuming a natural algebraic as- sumption) that this gain is exponential in the number of variables. Asymptotically, the gain is 2^{1.49 n} when both n and q grow to infinity and log(q) << n

Differential Power Analysis of HMAC SHA-2 in the Hamming Weight Model

International audienceAs any algorithm manipulating secret data, HMAC is potentially vulnerable to side channel attacks. In 2007, McEvoy et al. proposed a differential power analysis attack against HMAC instantiated with hash functions from the SHA-2 family. Their attack works in the Hamming distance leakage model and makes strong assumptions on the target implementation. In this paper, we present an attack on HMAC SHA-2 in the Hamming weight leakage model, which advantageously can be used when no information is available on the targeted implementation. Furthermore, our attack can be adapted to the Hamming distance model with weaker assumptions on the implementation. We show the feasibility of our attack on simulations, and we study its overall cost and success rate. We also provide an evaluation of the performance overhead induced by the countermeasures necessary to avoid the attack

On the Complexity of Solving Quadratic Boolean Systems

A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in $4\log_2 n\,2^n$ operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step. Under precise algebraic assumptions on the input system, we show that the deterministic variant of our algorithm has complexity bounded by $O(2^{0.841n})$ when $m=n$, while a probabilistic variant of the Las Vegas type has expected complexity $O(2^{0.792n})$. Experiments on random systems show that the algebraic assumptions are satisfied with probability very close to~1. We also give a rough estimate for the actual threshold between our method and exhaustive search, which is as low as~200, and thus very relevant for cryptographic applications.Comment: 25 page

Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

Two-Face: New Public Key Multivariate Schemes

We present here new multivariate schemes that can be seen as HFE generalization having a property called `Two-Face\u27. Particularly, we present five such families of algorithms named `Dob\u27, `Simple Pat\u27, `General Pat\u27, `Mac\u27, and `Super Two-Face\u27. These families have connections between them, some of them are refinements or generalizations of others. Notably, some of these schemes can be used for public key encryption, and some for public key signature. We introduce also new multivariate quadratic permutations that may have interest beyond cryptography

A Polynomial-Time Key-Recovery Attack on MQQ Cryptosystems

International audienceWe investigate the security of the family of MQQ public key cryptosystems using multivariate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular, the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature scheme MQQ-SIG and the encryption scheme MQQ-ENC, although using different types of MQQs, share a common algebraic structure that introduces a weakness in both schemes. We use this weakness to mount a successful polynomial time key-recovery attack. Our key-recovery attack finds an equivalent key using the idea of so-called {\it good keys} that reveals the structure gradually. In the process we need to solve a MinRank problem that, because of the structure, can be solved in polynomial-time assuming some mild algebraic assumptions. We highlight that our theoretical results work in characteristic $2$ which is known to be the most difficult case to address in theory for MinRank attacks. Also, we emphasize that our attack works without any restriction on the number of polynomials removed from the public-key, that is, using the minus modifier. This was not the case for previous MinRank like-attacks against \MQ\ schemes. From a practical point of view, we are able to break an MQQ-SIG instance of $80$ bits security in less than $2$ days, and one of the more conservative MQQ-ENC instances of $128$ bits security in little bit over $9$ days. Altogether, our attack shows that it is very hard to design a secure public key scheme based on an easily invertible MQQ structure