Class Of Hash Functions Research Articles

Smart Concept Map Generation for Learning Using Class of Hash Functions

Concept Maps have recently been used by several researchers to construct web-based learning systems. This is due to their flexibility in organizing knowledge. However, for an effective use of Concept Maps in web-based learning, automated construction is necessary. This study first gives brief details about the use of Concept Maps in electronic and mobile learning environments. Direct Hashing and Pruning algorithm is then used for automated generation of Concept Maps. The generated Concept Maps, however, depend on the nature of the hash function. The uses of three different types of hash functions are investigated and results compared. A prototype of the learning system is developed using an Android emulator. Finally, the proposed methodology is compared with other pioneering learning systems developed by the researchers using Concept Maps.

Multiple Object Identification Coding

In the case of ordinary identification coding, a code is devised to identify a single object among $N$ objects. But, in this paper, we consider a coding problem to identify $K$ objects at once among $N$ objects in the both cases that $K$ objects are ranked or not ranked. By combining Moulin–Koetter scheme with the $\varepsilon $ -almost strongly universal class of hash functions used in Kurosawa–Yoshida scheme, an efficient and explicit coding scheme is proposed for $K$ -multiple-object identification ( $K$ -MOID) coding. Furthermore, it is shown that the $K$ -MOID capacity $ C_{\text {$K$-MOID}}$ , which is the maximum achievable coding rate in the $K$ -MOID coding, is equal to the ordinary channel capacity, and the proposed scheme can attain $ C_{\text {$K$-MOID}}$ .

Fast randomized approximate string matching with succinct hash data structures

BackgroundThe high throughput of modern NGS sequencers coupled with the huge sizes of genomes currently analysed, poses always higher algorithmic challenges to align short reads quickly and accurately against a reference sequence. A crucial, additional, requirement is that the data structures used should be light. The available modern solutions usually are a compromise between the mentioned constraints: in particular, indexes based on the Burrows-Wheeler transform offer reduced memory requirements at the price of lower sensitivity, while hash-based text indexes guarantee high sensitivity at the price of significant memory consumption.MethodsIn this work we describe a technique that permits to attain the advantages granted by both classes of indexes. This is achieved using Hamming-aware hash functions--hash functions designed to search the entire Hamming sphere in reduced time--which are also homomorphisms on de Bruijn graphs. We show that, using this particular class of hash functions, the corresponding hash index can be represented in linear space introducing only a logarithmic slowdown (in the query length) for the lookup operation. We point out that our data structure reaches its goals without compressing its input: another positive feature, as in biological applications data is often very close to be un-compressible.ResultsThe new data structure introduced in this work is called dB-hash and we show how its implementation--BW-ERNE--maintains the high sensitivity and speed of its (hash-based) predecessor ERNE, while drastically reducing space consumption. Extensive comparison experiments conducted with several popular alignment tools on both simulated and real NGS data, show, finally, that BW-ERNE is able to attain both the positive features of succinct data structures (that is, small space) and hash indexes (that is, sensitivity).ConclusionsIn applications where space and speed are both a concern, standard methods often sacrifice accuracy to obtain competitive throughputs and memory footprints. In this work we show that, combining hashing and succinct indexing techniques, we can attain good performances and accuracy with a memory footprint comparable to that of the most popular compressed indexes.

Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

In this paper, we introduce the concept of dual universality of hash functions and present its applications to quantum cryptography. We begin by establishing the one-to-one correspondence between a linear function family {\cal F} and a code family {\cal C}, and thereby defining \varepsilon-almost dual universal_2 hash functions, as a generalization of the conventional universal_2 hash functions. Then we show that this generalized (and thus broader) class of hash functions is in fact sufficient for the security of quantum cryptography. This result can be explained in two different formalisms. First, by noting its relation to the \delta-biased family introduced by Dodis and Smith, we demonstrate that Renner's two-universal hashing lemma is generalized to our class of hash functions. Next, we prove that the proof technique by Shor and Preskill can be applied to quantum key distribution (QKD) systems that use our generalized class of hash functions for privacy amplification. While Shor-Preskill formalism requires an implementer of a QKD system to explicitly construct a linear code of the Calderbank-Shor-Steane type, this result removes the existing difficulty of the construction a linear code of CSS code by replacing it by the combination of an ordinary classical error correcting code and our proposed hash function. We also show that a similar result applies to the quantum wire-tap channel. Finally we compare our results in the two formalisms and show that, in typical QKD scenarios, the Shor-Preskill--type argument gives better security bounds in terms of the trace distance and Holevo information, than the method based on the \delta-biased family.

Pseudorandom numbers and hash functions from iterations of multivariate polynomials

Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather stronger bounds on the discrepancy for pseudorandom vectors generated by these iterations. Here we add new arguments to our original approach and also extend some of our recent constructions and results to more general orbits of polynomial iterations which may involve distinct polynomials as well. Using this construction we design a new class of hash functions from iterations of polynomials and use our estimates to motivate their “mixing” properties.

MRD Hashing

We propose two new classes of hash functions which are motivated by Maximum Rank Distance (MRD) codes. We analise the security of these schemes. The system setup phase is computationally expensive for general field extensions. To overcome this limitation we derive an algebraic solution which avoids computations in special extension fields in the intended operational range of the hash functions.

Hybrid authentication based on noisy channels

We consider a cryptographic scenario where some center broadcasts a random binary string to Alice, Bob and Eve over binary symmetric channels with bit error probabilities ?A, ?B and ?E respectively. Alice and Bob share no secret key initially, and their goal is to generate, after public discussion, a common information-theoretically secure key facing an active eavesdropper Eve. Under the condition ?A<?E and ?B<?E, code authentication (CA) can be used as part of a public discussion protocol to solve this problem. This authentication exploits parts of substrings received by Alice and Bob from the broadcasting center as authenticators to messages transmitted in a public discussion. Unfortunately, it happens to be ineffective because it produces a key of small length. We propose a hybrid authentication (HA) that combines both keyless code authentication and key authentication based on an almost strong universal class of hash functions. We prove a theorem that allows estimation of the performance evaluation of hybrid authentication. The selection algorithm for the main HA parameters, given security and reliability thresholds, is presented in detail.

Practical Considerations of Parallel Simulations and Architecture Independent Parallel Algorithm Design

We examine combinatorial properties of a class of hash functions and its application to the simulations of classical models of parallel computation on other models, such as theBSPand theS*PRAM, optimally in communication to within additive lower order terms. The BSP model can serve as a programming paradigm as well; we also examine the implications of architecture independent parallel algorithm design in the context of the BSP model and show how it can lead to portable and scalable implementations of algorithms that can work on a multiplicity of hardware platforms with only recompilation of the source program code. Toward this end, dense Cholesky factorization algorithms are presented and their performance on three parallel hardware platforms, an SGI Power Challenge, IBM SP2, and Cray T3D, is examined and analyzed.

Combinatorial techniques for universal hashing

The idea of a universal class of hash functions is due to Carter and Wegman. The goal is to define a collection of hash functions in such a way that a random choice of a function in the class yields a low probability that any two distinct inputs will collide. In this paper, we present some characterizations of universal classes of hash functions in terms of combinatorial designs such as resolvable balanced incomplete block designs and orthogonal arrays. The two classes of hash functions that we study are called optimally universal and strongly universal. We show that optimally universal classes of hash functions are equivalent to resolvable balanced incomplete block designs and strongly universal classes are equivalent to orthogonal arrays. Consequently, known classes of combinatorial designs yield new, small, and efficient classes of universal hash functions.