Linear Hashing Research Articles

Lower Bound on Number of Compression Calls of a Collision-Resistance Preserving Hash

The collision-resistant hash function is an early cryptographic primitive that finds extensive use in various applications. Remarkably, the Merkle-Damgård and Merkle tree hash structures possess the collision-resistance preserving property, meaning the hash function remains collision-resistant when the underlying compression function is collision-resistant. This raises the intriguing question of whether reducing the number of underlying compression function calls with the collision-resistance preserving property is possible. In pursuit of addressing these inquiries, we prove that for an ℓ n -to- s n -bit collision-resistance preserving hash function designed using r t n -to- n -bit compression function calls, we must have r ≥ ⌈ ( ℓ − s ) / ( t − 1 ) ⌉ . Throughout the paper, all operations other than the compression function are assumed to be linear (which we call linear hash mode).

Performance of Linear and Spiral Hashing Algorithms

Linear Hashing is an important algorithm for many key-value stores in main memory. Spiral Storage was invented to overcome the poor fringe behavior of Linear Hashing, but after an influential study by Larson, it seems to have been discarded. Since almost 50 years have passed, we repeat Larson’s comparison with the in-memory implementation of both to see whether his verdict still stands. Our study shows that Spiral Storage has slightly better lookup performance but slightly poorer insert performance. However, Spiral Hashing has more predictable performance for inserts and, in particular, better fringe behavior.

Linear Hashing with $\ell_\infty$ guarantees and two-sided Kakeya bounds

We show that a randomly chosen linear map over a finite field gives a good hash function in the $\ell_\infty$ sense. More concretely, consider a set $S \subset \mathbb{F}_q^n$ and a randomly chosen linear map $L : \mathbb{F}_q^n \to \mathbb{F}_q^t$ with $q^t$ taken to be sufficiently smaller than $ |S|$. Let $U_S$ denote a random variable distributed uniformly on $S$. Our main theorem shows that, with high probability over the choice of $L$, the random variable $L(U_S)$ is close to uniform in the $\ell_\infty$ norm. In other words, {\em every} element in the range $\mathbb{F}_q^t$ has about the same number of elements in $S$ mapped to it. This complements the widely-used Leftover Hash Lemma (LHL) which proves the analog statement under the statistical, or $\ell_1$, distance (for a richer class of functions) as well as prior work on the expected largest 'bucket size' in linear hash functions [ADMPT99]. By known bounds from the load balancing literature [RS98], our results are tight and show that linear functions hash as well as trully random function up to a constant factor in the entropy loss. Our proof leverages a connection between linear hashing and the finite field Kakeya problem and extends some of the tools developed in this area, in particular the polynomial method.

A new lattice-based partially blind signature with more complete proof

Partially blind signatures are introduced on the basis of blind signatures, which not only retain the advantages of blind signatures, but also solve the contradiction between anonymity and controllability in blind signatures. With the development of quantum computing technology, it becomes more urgent to construct secure partially blind signature schemes in quantum environments. In this paper, we present a new partially blind signature scheme and prove the security under the Ring-SIS assumption in the random oracle model. To avoid the restart problem of signature schemes caused by rejection sampling, a large number of random numbers are sampled in advance, so that they only need to be re-selected at the current stage without terminating the whole signature process when the conditions are not met. In addition, the hash tree technology is used to reduce communication costs and improve interactive performance. In order to avoid the errors in the security proof of the previous scheme, our proof builds upon and extends the modular framework for blind signatures of Hauck et al. and the correctness, partial blindness, and one-more unforgeability of the scheme are proved in detail according to the properties of the linear hash function.

Linear hashing in the Boolean cube with clusters of limited size

Показано, что для произвольного подмножества $n$-мерного булева куба из $M$ элементов существует линейная хеш-функция, кластеры которой состоят не более чем из $a$ элементов, и ранг которой не превосходит ${2\log_2 M-2\log_2 a+\mathcal O(1)}$.

Enabling secure lightweight mobile Narrowband Internet of Things (NB-IoT) applications using blockchain

Narrowband Internet of Things (NB-IoT) is a low bandwidth 3GPP communication standard transmitting small quantities of data over long distances at random intervals. However, as NB-IoT cannot support seamless handover between base stations, its applications are limited to stationary devices, which may result in the potential risk of fake base station connections in an attempt to maintain connectivity across cells. Considering characteristics such as low power consumption and high connection density, researchers envision using NB-IoT in mobile applications such as public-bike sharing, pet tracking etc. Connecting NB-IoT devices using decentralised architecture such as blockchain ensures seamless communication in mobile applications and eliminates bottlenecks due to multiple data requests observed in centralised networks. In this paper, we develop a hybrid blockchain framework facilitating mutual authentication between base stations to enhance user privacy and prevent fake base station connections and certificate transfers. Zero-knowledge proof used as the consensus algorithm enhances user privacy and message confidentiality. IoT devices are designed to store the hashes of their approved transactions as a linear hash chain instead of the complete merkle tree to minimise hash verification complexity. Additionally, base station memory is partitioned dynamically to enhance scalability and memory utilisation efficiency. We prototype our framework on Remix IDE in Ethereum and implement it on Raspberry Pi 4. The security of the proposed framework is formally verified using Scyther. Further, we show that our approach achieves 80.50% lower computational power, 74.73% lower execution time and 50% lower memory, respectively, in comparison with existing schemes making our proposed scheme lightweight.

Load Thresholds for Cuckoo Hashing with Overlapping Blocks

We consider a natural variation of cuckoo hashing proposed by Lehman and Panigrahy (2009). Each of cn objects is assigned k = 2 intervals of size ℓ in a linear hash table of size n and both starting points are chosen independently and uniformly at random. Each object must be placed into a table cell within its intervals, but each cell can only hold one object. Experiments suggested that this scheme outperforms the variant with blocks in which intervals are aligned at multiples of ℓ. In particular, the load threshold is higher, i.e., the load c that can be achieved with high probability. For instance, Lehman and Panigrahy (2009) empirically observed the threshold for ℓ = 2 to be around 96.5% as compared to roughly 89.7% using blocks. They pinned down the asymptotics of the thresholds for large ℓ, but the precise values resisted rigorous analysis. We establish a method to determine these load thresholds for all ℓ ≥ 2, and, in fact, for general k ≥ 2. For instance, for k = ℓ = 2, we get ≈ 96.4995%. We employ a theorem due to Leconte, Lelarge, and Massoulié (2013), which adapts methods from statistical physics to the world of hypergraph orientability. In effect, the orientability thresholds for our graph families are determined by belief propagation equations for certain graph limits. As a side note, we provide experimental evidence suggesting that placements can be constructed in linear time using an adapted version of an algorithm by Khosla (2013).

Cryptographic Algorithm for Enhancing Data Security in Wireless IoT Sensor Networks

Wireless IoT Sensor Network can handle audio, video, text, etc., through the interconnection of ubiquitous devices. The entertainment and application-centric network relies on its autonomous nodes for handling large streams of multimedia data. Security breaches and threats due to insider attacks reduce the data handling and distribution capacity of the nodes. For addressing the insider attacks problem, Session-Critical Distributed Authentication Method (SCDAM) is proposed. The proposed method relies on short-lived concealed authentication based on an improved elliptic curve cryptography (ECC) algorithm. In this authentication, the session time and the interrupts are accounted for, providing end-to-end authentication. The session keys are distributed before and after each interrupt from which the shared data is authenticated. This authentication process uses a linear hash process, ensuring non-repetition of keys in the consecutive sessions. This proposed authentication method is capable of providing improved sessions, less data distribution loss, and complexity.

Design of College English Online Teaching Platform Based on Dual-Server PEKS Framework

To improve the English learning efficiency of college students and improve the performance of network teaching, the research on the college English network teaching platform is carried out under the dual-server PEKS framework. After systematic testing and debugging, deployment and implementation, course migration, personnel training, and other links, the system has successfully completed deployment and implementation, which strongly support the research on the college English network teaching platform. The proposed dual-server PEKS search framework makes the teaching platform more secure by designing a linear homomorphic smooth projection HASH function and solves the security loopholes of traditional PEKS. Relevant research groups have conducted questionnaire surveys and information feedback on some teachers and students and generally have a good evaluation of the online teaching platform, indicating that the system has better realized the predetermined functions and effectively supported the research on the college English online teaching platform.

Fingerprint-Based Data Deduplication Using a Mathematical Bounded Linear Hash Function

Due to the quick increase in digital data, especially in mobile usage and social media, data deduplication has become a vital and cost-effective approach for removing redundant data segments, reducing the pressure imposed by enormous volumes of data that must be kept. As part of the data deduplication process, fingerprints are employed to represent and identify identical data blocks. However, when the amount of data increases, the number of fingerprints grows as well, and due to the restricted memory size, the speed of data deduplication suffers dramatically. Various deduplication solutions show a bottleneck in the form of matching lookups and chunk fingerprint calculations, for which we pay in the form of storage and processors needed for storing hashes. Utilizing a fast hash algorithm to improve the fingerprint lookup performance is an appealing challenge. Thus, this study is focused on enhancing the deduplication system by suggesting a novel and effective mathematical bounded linear hashing algorithm that decreases the hashing time by more than two times compared to MD5 and SHA-1 and reduces the size of the hash index table by 50%. Due to the enormous number of chunk hash values, looking up and comparing hash values takes longer for large datasets; this work offers a hierarchal fingerprint lookup strategy to minimize the hash judgement comparison time by up to 78%. Our suggested system reduces the high latency imposed by deduplication procedures, primarily the hashing and matching phases. The symmetry of our work is based on the balance between the proposed hashing algorithm performance and its reflection on the system efficiency, as well as evaluating the approximate symmetries of the hashing and lookup phases compared to the other deduplication systems.

Optimization of neutron tracking algorithms for GPU-based continuous energy Monte Carlo calculation

The implementation and optimization strategies of the neutron tracking algorithms in the GPU-based continuous-energy Monte Carlo (MC) code PRAGMA are presented. The strategies consist of 1) a mixed precision technique, 2) an event-based tracking algorithm, 3) the history-based tracking algorithm improved for GPUs by imposing transition limits, 4) the region partitioning and energy sort schemes to vectorize macroscopic cross section calculations, 5) the unionized grid method improved by a linear hashing scheme, and 6) the GPU-specific implementation techniques such as the use of built-in vector types and an array-based race-free bank algorithm utilizing GPU atomic addition. The developed algorithms and strategies are examined for pin cell and full-core problems consisting of fresh and depleted fuels. PRAGMA turned out to be especially efficient in depleted fuel calculation; PRAGMA effectively overcame the performance drop in the depleted fuel calculation by vectorized cross section calculation. In the full-core calculations PRAGMA also rendered outstanding performance; calculations employing 11.5 billion histories and 20 consumer-grade GPUs could be finished within 15 min for a 3D APR1400 fresh core problem, and within half an hour for a mock-up depleted core problem.

Cluster-wise unsupervised hashing for cross-modal similarity search

Cross-modal hashing similarity retrieval plays dual roles across various applications including search engines and autopilot systems. More generally, these methods also known to reduce the computation and memory storage in a training scheme. The key limitation of current methods are that: (i) they relax the discrete constrains to solve the optimization problem which may defeat the model purpose, (ii) projecting heterogenous data into a latent space may encourage to loss the diverse representations in such data, (iii) transforming real-valued data point to the binary codes always resulting in a loss of information and producing the suboptimal continuous latent space. In this paper, we propose a novel framework to project the original data points from different modalities into its own low-dimensional latent space and finds the cluster centroid points in its a low-dimensional space, using Cluster-wise Unsupervised Hashing (CUH). In particular, the proposed clustering scheme aims to jointly learns the compact hash codes and the corresponding linear hash functions. A discrete optimization framework is developed to learn the unified binary codes across modalities under of the guidance cluster-wise code-prototypes. Extensive experiments over multiple datasets demonstrate the effectiveness of our proposed model in comparison with the state-of-the-art in unsupervised cross-modal hashing tasks.

Dash

Byte-addressable persistent memory (PM) brings hash tables the potential of low latency, cheap persistence and instant recovery. The recent advent of Intel Optane DC Persistent Memory Modules (DCPMM) further accelerates this trend. Many new hash table designs have been proposed, but most of them were based on emulation and perform sub-optimally on real PM. They were also piece-wise and partial solutions that side-step many important properties, in particular good scalability, high load factor and instant recovery. We present Dash, a holistic approach to building dynamic and scalable hash tables on real PM hardware with all the aforementioned properties. Based on Dash, we adapted two popular dynamic hashing schemes (extendible hashing and linear hashing). On a 24-core machine with Intel Optane DCPMM, we show that compared to state-of-the-art, Dash-enabled hash tables can achieve up to ∼3.9× higher performance with up to over 90% load factor and an instant recovery time of 57ms regardless of data size.

SAL-Hashing: A Self-Adaptive Linear Hashing Index for SSDs

Flash memory based solid state drives (SSDs) have emerged as a new alternative to replace magnetic disks due to their high performance and low power consumption. However, random writes on SSDs are much slower than SSD reads. Therefore, traditional index structures, which are designed based on the symmetrical I/O property of magnetic disks, cannot completely exert the high performance of SSDs. In this paper, we propose an SSD-optimized linear hashing index called Self-Adaptive Linear Hashing ( SAL-hashing ) to reduce small random-writes to SSDs that are caused by index operations. The contributions of our work are manifold. First, we propose to organize the buckets of a linear hashing index into groups and sets to facilitate coarse-grained writes and adaptivity to access patterns. A group consisting of a fixed number of buckets is proposed to transform small random writes to buckets into coarse-grained writes and in turn improve write performance of the index. A set consists of a number of groups, and we propose to employ different split strategies for each set. With this mechanism, SAL-hashing is able to adapt to the changes of access patterns. Second, we attach a log region to each set, and amortize the cost of reads and writes by committing updates to the log region in batch. Third, in order to reduce search cost, each log region is equipped with Bloom filters to index update logs. We devise a cost-based online algorithm to adaptively merge the log region with the corresponding set when the set becomes search-intensive. Fourth, we propose a new technique called virtual split to optimize the search performance of SAL-hashing . Finally, we propose a new scheme for the management of the log buffer. We conduct extensive experiments on real SSDs. The results suggest that our proposal is self-adaptive according to the change of access patterns, and outperforms several competitors under various workloads.

Unsupervised hashing based on the recovery of subspace structures

Unsupervised semantic hashing should in principle keep the semantics among samples consistent with the intrinsic geometric structures of the dataset. In this paper, we propose a novel multiple stage unsupervised hashing method, named “Unsupervised Hashing based on the Recovery of Subspace Structures” (RSSH) for image retrieval. Specifically, we firstly adapt the Low-rank Representation (LRR) model into a new variant which treats the real-world data as samples drawn from a union of several low-rank subspaces. Then, the pairwise similarities are represented in a space-and-time saving manner based on the learned low-rank correlation matrix of the modified LRR. Next, the challenging discrete graph hashing is employed for binary hashing codes. Notably, we convert the original graph hashing model into an optimization-friendly formalization, which is addressed with efficient closed-form solutions for its subproblems. Finally, the devised linear hash functions are fast achieved for out-of-samples. Retrieval experiments on four image datasets testify the superiority of RSSH to several state-of-the-art hashing models. Besides, it’s worth mentioning that RSSH, a shallow model, significantly outperforms two recently proposed unsupervised deep hashing methods, which further confirms its effectiveness.

Model Optimization Boosting Framework for Linear Model Hash Learning.

Efficient hashing techniques have attracted extensive research interests in both storage and retrieval of highdimensional data, such as images and videos. In existing hashing methods, a linear model is commonly utilized owing to its efficiency. To obtain better accuracy, linear-based hashing methods focus on designing a generalized linear objective function with different constraints or penalty terms that consider the inherent characteristics and neighborhood information of samples. Differing from existing hashing methods, in this study, we propose a self-improvement framework called Model Boost (MoBoost) to improve model parameter optimization for linear-based hashing methods without adding new constraints or penalty terms. In the proposed MoBoost, for a linear-based hashing method, we first repeatedly execute the hashing method to obtain several hash codes to training samples. Then, utilizing two novel fusion strategies, these codes are fused into a single set. We also propose two new criteria to evaluate the goodness of hash bits during the fusion process. Based on the fused set of hash codes, we learn new parameters for the linear hash function that can significantly improve the accuracy. In general, the proposed MoBoost can be adopted by existing linear-based hashing methods, achieving more precise and stable performance compared to the original methods, and adopting the proposed MoBoost will incur negligible time and space costs. To evaluate the proposed MoBoost, we performed extensive experiments on four benchmark datasets, and the results demonstrate superior performance.

Linear Hashing Is Awesome

We consider the hash function $h(x) = ((ax+b)mod p)mod n$ where $a,b$ are chosen uniformly at random from $\{0,1,\ldots,p-1\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $...

Binary Linear Hash Certificateless Congruential Signcryption for Secured Message Communication in Mobile Network

Binary Linear Hash Certificateless Congruential Signcryption for Secured Message Communication in Mobile Network

О ПОСТРОЕНИИ (n, k)-СХЕМЫ ВИЗУАЛЬНОЙ КРИПТОГРАФИИ С ПРИМЕНЕНИЕМ КЛАССА ЛИНЕЙНЫХ ХЭШ-ФУНКЦИЙ НАД БИНАРНЫМ ПОЛЕМ

О ПОСТРОЕНИИ (n, k)-СХЕМЫ ВИЗУАЛЬНОЙ КРИПТОГРАФИИ С ПРИМЕНЕНИЕМ КЛАССА ЛИНЕЙНЫХ ХЭШ-ФУНКЦИЙ НАД БИНАРНЫМ ПОЛЕМ

Research on Time Series Query Method Based on Linear Hash Index

With the continuous development of China's information technology, many data will also be produced. In these data, time series data is an important data type. In this paper, we propose a new query processing method for time series, in order to reduce the index creation time and improve query efficiency. Experimental results show that the linear hash index in this method is reduced in the time of creation. In the query phase, the method of combining the K nearest neighbor and the lower bound distance is used to filter out the redundant results.