Close to Uniform Prime Number Generation With Fewer Random Bits

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly random $a<q$ coprime to $q$, and choose $p$ of the form $a+t\cdot q$, where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H.L. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban-Davenport-Halberstam theorem. We argue that this approach has a number of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint Report 2011/48

Morphology of Fine-Particle Monolayers Deposited on Nanopatterned Substrates

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius $r_0$ is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, $a$, and cell-cell separation, $b$. The model shows a surprisingly rich behavior in the space of the two dimensionless parameters $\alpha=a/2r_0$ and $\beta=b/2r_0$. Extensive Monte Carlo simulations for system sizes of $500\times500$ square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.Comment: 11 pages, 10 figures, 3 table

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

Nearby Optical Galaxies: Selection of the Sample and Identification of Groups

In this paper we describe the Nearby Optical Galaxy (NOG) sample, which is a complete, distance-limited ($cz\leq$6000 km/s) and magnitude-limited (B$\leq$14) sample of $\sim$7000 optical galaxies. The sample covers 2/3 (8.27 sr) of the sky ($|b|>20^{\circ}$) and appears to have a good completeness in redshift (98%). We select the sample on the basis of homogenized corrected total blue magnitudes in order to minimize systematic effects in galaxy sampling. We identify the groups in this sample by means of both the hierarchical and the percolation {\it friends of friends} methods. The resulting catalogs of loose groups appear to be similar and are among the largest catalogs of groups presently available. Most of the NOG galaxies ($\sim$60%) are found to be members of galaxy pairs ($\sim$580 pairs for a total of $\sim$15% of objects) or groups with at least three members ($\sim$500 groups for a total of $\sim$45% of objects). About 40% of galaxies are left ungrouped (field galaxies). We illustrate the main features of the NOG galaxy distribution. Compared to previous optical and IRAS galaxy samples, the NOG provides a denser sampling of the galaxy distribution in the nearby universe. Given its large sky coverage, the identification of groups, and its high-density sampling, the NOG is suited for the analysis of the galaxy density field of the nearby universe, especially on small scales.Comment: 47 pages including 6 figures. Accepted for publication in Ap

Secure Split Test for Preventing IC Piracy by Un-Trusted Foundry and Assembly

In the era of globalization, integrated circuit design and manufacturing is spread across different continents. This has posed several hardware intrinsic security issues. The issues are related to overproduction of chips without knowledge of designer or OEM, insertion of hardware Trojans at design and fabrication phase, faulty chips getting into markets from test centers, etc. In this thesis work, we have addressed the problem of counterfeit IC‟s getting into the market through test centers. The problem of counterfeit IC has different dimensions. Each problem related to counterfeiting has different solutions. Overbuilding of chips at overseas foundry can be addressed using passive or active metering. The solution to avoid faulty chips getting into open markets from overseas test centers is secure split test (SST). The further improvement to SST is also proposed by other researchers and is known as Connecticut Secure Split Test (CSST). In this work, we focus on improvements to CSST techniques in terms of security, test time and area. In this direction, we have designed all the required sub-blocks required for CSST architecture, namely, RSA, TRNG, Scrambler block, study of benchmark circuits like S38417, adding scan chains to benchmarks is done. Further, as a security measure, we add, XOR gate at the output of the scan chains to obfuscate the signal coming out of the scan chains. Further, we have improved the security of the design by using the PUF circuit instead of TRNG and avoid the use of the memory circuits. This use of PUF not only eliminates the use of memory circuits, but also it provides the way for functional testing also. We have carried out the hamming distance analysis for introduced security measure and results show that security design is reasonably good.Further, as a future work we can focus on: • Developing the circuit which is secuered for the whole semiconductor supply chain with reasonable hamming distance and less area overhead

DoWitcher: Effective Worm Detection and Containment in the Internet Core

Enterprise networks are increasingly offloading the responsibility for worm detection and containment to the carrier networks. However, current approaches to the zero-day worm detection problem such as those based on content similarity of packet payloads are not scalable to the carrier link speeds (OC-48 and up-wards). In this paper, we introduce a new system, namely DoWitcher, which in contrast to previous approaches is scalable as well as able to detect the stealthiest worms that employ low-propagation rates or polymorphisms to evade detection. DoWitcher uses an incremental approach toward worm detection: First, it examines the layer-4 traffic features to discern the presence of a worm anomaly; Next, it determines a flow-filter mask that can be applied to isolate the suspect worm flows and; Finally, it enables full-packet capture of only those flows that match the mask, which are then processed by a longest common subsequence algorithm to extract the worm content signature. Via a proof-of-concept implementation on a commercially available network analyzer processing raw packets from an OC-48 link, we demonstrate the capability of DoWitcher to detect low-rate worms and extract signatures for even the polymorphic worm

Testing probability distributions underlying aggregated data

In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution $D$ over $[n]$. More precisely, we define both the dual and cumulative dual access models, in which the algorithm $A$ can both sample from $D$ and respectively, for any $i\in[n]$, - query the probability mass $D(i)$ (query access); or - get the total mass of $\{1,\dots,i\}$, i.e. $\sum_{j=1}^i D(j)$ (cumulative access) These two models, by generalizing the previously studied sampling and query oracle models, allow us to bypass the strong lower bounds established for a number of problems in these settings, while capturing several interesting aspects of these problems -- and providing new insight on the limitations of the models. Finally, we show that while the testing algorithms can be in most cases strictly more efficient, some tasks remain hard even with this additional power

From Car Parking to Protein Adsorption: An Overview of Sequential Adsorption Processes

The adsorption or adhesion of large particles (proteins, colloids, cells, >...) at the liquid-solid interface plays an important role in many diverse applications. Despite the apparent complexity of the process, two features are particularly important: 1) the adsorption is often irreversible on experimental time scales and 2) the adsorption rate is limited by geometric blockage from previously adsorbed particles. A coarse-grained description that encompasses these two properties is provided by sequential adsorption models whose simplest example is the random sequential adsorption (RSA) process. In this article, we review the theoretical formalism and tools that allow the systematic study of kinetic and structural aspects of these sequential adsorption models. We also show how the reference RSA model may be generalized to account for a variety of experimental features including particle anisotropy, polydispersity, bulk diffusive transport, gravitational effects, surface-induced conformational and orientational change, desorption, and multilayer formation. In all cases, the significant theoretical results are presented and their accuracy (compared to computer simulation) and applicability (compared to experiment) are discussed.Comment: 51 pages, 18 Figures, to appear in a special volume entitled "Adhesion of Submicron Particles on Solid Surfaces" of Colloids and Surfaces A, guest-edited by V. Privman.to appear in a special volume entitle