Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Cryptanalysis of The Lifted Unbalanced Oil Vinegar Signature Scheme

In 2017, Ward Beullens \textit{et al.} submitted Lifted Unbalanced Oil and Vinegar (LUOV)\cite{beullens2017field}, a signature scheme based on the famous multivariate public key cryptosystem (MPKC) called Unbalanced Oil and Vinegar (UOV), to NIST for the competition for post-quantum public key scheme standardization. The defining feature of LUOV is that, though the public key $\mathcal{P}$ works in the extension field of degree $r$ of $\mathbb{F}_2$, the coefficients of $\mathcal{P}$ come from $\mathbb{F}_2$. This is done to significantly reduce the size of $\mathcal{P}$. The LUOV scheme is now in the second round of the NIST PQC standardization process. In this paper we introduce a new attack on LUOV. It exploits the lifted structure of LUOV to reduce direct attacks on it to those over a subfield. We show that this reduces the complexity below the targeted security for the NIST post-quantum standardization competition

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

Many Labs 5:Testing pre-data collection peer review as an intervention to increase replicability

Replication studies in psychological science sometimes fail to reproduce prior findings. If these studies use methods that are unfaithful to the original study or ineffective in eliciting the phenomenon of interest, then a failure to replicate may be a failure of the protocol rather than a challenge to the original finding. Formal pre-data-collection peer review by experts may address shortcomings and increase replicability rates. We selected 10 replication studies from the Reproducibility Project: Psychology (RP:P; Open Science Collaboration, 2015) for which the original authors had expressed concerns about the replication designs before data collection; only one of these studies had yielded a statistically significant effect (p < .05). Commenters suggested that lack of adherence to expert review and low-powered tests were the reasons that most of these RP:P studies failed to replicate the original effects. We revised the replication protocols and received formal peer review prior to conducting new replication studies. We administered the RP:P and revised protocols in multiple laboratories (median number of laboratories per original study = 6.5, range = 3?9; median total sample = 1,279.5, range = 276?3,512) for high-powered tests of each original finding with both protocols. Overall, following the preregistered analysis plan, we found that the revised protocols produced effect sizes similar to those of the RP:P protocols (?r = .002 or .014, depending on analytic approach). The median effect size for the revised protocols (r = .05) was similar to that of the RP:P protocols (r = .04) and the original RP:P replications (r = .11), and smaller than that of the original studies (r = .37). Analysis of the cumulative evidence across the original studies and the corresponding three replication attempts provided very precise estimates of the 10 tested effects and indicated that their effect sizes (median r = .07, range = .00?.15) were 78% smaller, on average, than the original effect sizes (median r = .37, range = .19?.50)

Determination of ion incidence angles in plasma immersion ion implantation by means of a hollow multi-aperture target

In plasma immersion ion implantation, ions are accelerated from a spherical cathode sheath edge which surrounds the target. On a non-spherical target, a distribution of angles of ion incidence can be expected. In order to determine the angles of ion incidence, a hollow cylindrical target with an upper cover plate with small drill holes was used. Ions enter the target through these apertures and impinge onto the inner bottom which is covered with cellulose. The organic material is blackened as a consequence of ion bombardment. The position of the black spots is determined by the position of the aperture with respect to the cellulose bottom and by the angle under which the ions enter the aperture, i.e. the angle of ion incidence on the plate. By measuring the position of the spots, the angles of incidence can be calculated. The obtained data show that in the center of the cylindrical target the ions impinge at right angles, whereas in the outer parts smaller angles of incidence are found. The distribution of angles is a function of the process parameters such as pulse length and pulse voltage