scholarly journals The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1108
Author(s):  
Jheyne N. Ortiz ◽  
Robson R. de Araujo ◽  
Diego F. Aranha ◽  
Sueli I. R. Costa ◽  
Ricardo Dahab
Keyword(s):  
Public Key Cryptography ◽  
Number Fields ◽  
Canonical Embedding ◽  
Worst Case ◽  
Average Case ◽  
Twist Factor ◽  
Algebraic Lattices ◽  
Cyclotomic Number Fields ◽  
Lattice Based Cryptography ◽  
Respective Number

Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring instantiations enlarges the scope of possible applications and favors the diversification of security assumptions. In this work, we extend the Ring-LWE problem in lattice-based cryptography to include algebraic lattices, realized through twisted embeddings. We define the class of problems Twisted Ring-LWE, which replaces the canonical embedding by an extended form. By doing so, we allow the Ring-LWE problem to be used over maximal real subfields of cyclotomic number fields. We prove that Twisted Ring-LWE is secure by providing a security reduction from Ring-LWE to Twisted Ring-LWE in both search and decision forms. It is also shown that the twist factor does not affect the asymptotic approximation factors in the worst-case to average-case reductions. Thus, Twisted Ring-LWE maintains the consolidated hardness guarantee of Ring-LWE and increases the existing scope of algebraic lattices that can be considered for cryptographic applications. Additionally, we expand on the results of Ducas and Durmus (Public-Key Cryptography, 2012) on spherical Gaussian distributions to the proposed class of lattices under certain restrictions. As a result, sampling from a spherical Gaussian distribution can be done directly in the respective number field while maintaining its format and standard deviation when seen in Zn via twisted embeddings.

Post-Quantum Lattice-Based Cryptography

2021 ◽  
pp. 102-123
Author(s):  
Aarti Dadheech
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Cryptography ◽  
Future Internet ◽  
Worst Case ◽  
Quantum Lattice ◽  
Average Case ◽  
Cryptographic Algorithms ◽  
The Future ◽  
Lattice Based Cryptography

Quantum cryptography is a branch of cryptography that is a mixture of quantum mechanics and classical cryptography. The study of quantum cryptography is to design cryptographic algorithms and protocols that are against quantum computing attacks. In this chapter, the authors focus on analyzing characteristics of the quantum-proof cryptosystem and its applications in the future internet. Lattice-based cryptography provides a much stronger belief of security, in that the average-case of certain problems is equivalent to the worst-case of those problems. With the increase in cryptanalytic attacks conventional cryptographic schemes will soon become obsolete. As the reality of quantum computing approaches, these cryptosystems will need to be replaced with efficient quantum-resistant cryptosystems. We need an alternate security mechanism which is as hard as the existing number theoretic approaches. In this chapter, the authors discuss the security dimension of lattice-based cryptography whose strength lies in the hardness of lattice problems and also study its application areas.

Design and Implementation of a Lattice-Based Public-Key Encryption Scheme

2018 ◽  
Vol 27 (13) ◽  
pp. 1850201 ◽  
Author(s):  
Hui Lin ◽  
Dongsheng Liu ◽  
Cong Zhang ◽  
Yahui Dong
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Linear Feedback ◽  
Circuit Realization ◽  
Worst Case ◽  
The Public ◽  
Current State ◽  
Hardware Implementations ◽  
Simple Implementation ◽  
Lattice Based Cryptography

Due to its advantage of quantum resistance and the provable security under some worst-case hardness assumptions, lattice-based cryptography is being increasingly researched. This paper tries to explore and present a novel lattice-based public key cryptography and its implementation of circuits. In this paper, the LWE (learning with error) cryptography is designed for circuit realization in a practical way. A strategy is proposed to dramatically reduce the stored public key size from [Formula: see text] to [Formula: see text], with only several additional linear feedback shift registers. The circuit design is implemented on Xilinx Spartan-3A FPGA and performs very well with limited resources. Only 125 slices and 8 BRAMs are occupied, and there are no complex operation devices such as multipliers or dividers, all the involved arithmetic operations are additions. This design is smaller than most hardware implementations of LWE or Ring-LWE cryptography in current state, while having an acceptable frequency at 111 MHz. Therefore, LWE cryptography can be practically realized, and its advantages of quantum resistance and simple implementation make the public key cryptography promising for some applications in devices such as smart cards.

Fuzzy Certificateless Identity-Based Encryption Protocol from Lattice

2013 ◽  
Vol 380-384 ◽  
pp. 2262-2266 ◽  
Author(s):  
Guo Yan Zhang
Keyword(s):  
Encryption Scheme ◽  
Secret Key ◽  
Worst Case ◽  
Average Case ◽  
Identity Based Encryption ◽  
Identity Based ◽  
Learning With Errors ◽  
Fuzzy Identity ◽  
Security Guarantees ◽  
Lattice Based Cryptography

Due to their conjectured resistance to quantum cryptanalysis, strong worst-case/average-case security guarantees, ease of implementation and increasing practicality, lattice-based cryptography is one of the hottest and fastest moving areas in mathematical cryptography today. In this paper, we give a fuzzy certificateless identity-based encryption scheme from lattice, whose security is based on the hardness of the Learning With Errors (LWE) problem. In the scheme, the user can choose his own secret key that the KGC cannot obtain, which is an efficient approach to mitigate the key escrow problem in fuzzy identity-based encryption scheme.

Rule Based Classifiers for Suspect Detection from CCTV Footages

2020 ◽  
Vol 13 ◽  
Author(s):  
Sunil Pathak
Keyword(s):  
Answer Sheet ◽  
Normal Activity ◽  
Contact Detection ◽  
Accuracy Rate ◽  
Hand Detection ◽  
Worst Case ◽  
Average Case ◽  
The Face ◽  
Case Simulation ◽  
Material Exchange

Background: The significant work has been present to identify suspects, gathering information and examining any videos from CCTV Footage. This exploration work expects to recognize suspicious exercises, i.e. object trade, passage of another individual, peeping into other's answer sheet and individual trade from the video caught by a reconnaissance camera amid examinations. This requires the procedure of face acknowledgment, hand acknowledgment and distinguishing the contact between the face and hands of a similar individual and that among various people. Methods: Segmented frames has given as input to obtain foreground image with the help of Gaussian filtering and background modeling method. Suh foreground images has given to Activity Recognition model to detect normal activity or suspicious activity. Results: Accuracy rate, Precision and Recall are calculate for activities detection, contact detection for Best Case, Average Case and Worst Case. Simulation results are compare with performance parameter such as Material Exchange, Position Exchange, and Introduction of a new person, Face and Hand Detection and Multi Person Scenario. Conclusion: In this paper, a framework is prepared for suspect detection. This framework will absolutely realize an unrest in the field of security observation in the training area.

scholarly journals A Splay Tree-Based Approach for Efficient Resource Location in P2P Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wei Zhou ◽  
Zilong Tan ◽  
Shaowen Yao ◽  
Shipu Wang
Keyword(s):  
Routing Algorithm ◽  
Adaptive Routing ◽  
Upper And Lower Bounds ◽  
Resource Location ◽  
Hop Count ◽  
Worst Case ◽  
Average Case ◽  
Splay Tree ◽  
Efficient Resource ◽  
P2p System

Resource location in structured P2P system has a critical influence on the system performance. Existing analytical studies of Chord protocol have shown some potential improvements in performance. In this paper a splay tree-based new Chord structure called SChord is proposed to improve the efficiency of locating resources. We consider a novel implementation of the Chord finger table (routing table) based on the splay tree. This approach extends the Chord finger table with additional routing entries. Adaptive routing algorithm is proposed for implementation, and it can be shown that hop count is significantly minimized without introducing any other protocol overheads. We analyze the hop count of the adaptive routing algorithm, as compared to Chord variants, and demonstrate sharp upper and lower bounds for both worst-case and average case settings. In addition, we theoretically analyze the hop reducing in SChord and derive the fact that SChord can significantly reduce the routing hops as compared to Chord. Several simulations are presented to evaluate the performance of the algorithm and support our analytical findings. The simulation results show the efficiency of SChord.

scholarly journals Average-Case Approximation Ratio of Scheduling without Payments

Algorithmica ◽  
2021 ◽  
Author(s):  
Jie Zhang
Keyword(s):  
Mechanism Design ◽  
Case Analysis ◽  
Theoretical Computer Science ◽  
Approximation Ratio ◽  
Approximation Schemes ◽  
Worst Case Analysis ◽  
Algorithmic Mechanism Design ◽  
Worst Case ◽  
Average Case ◽  
Optimal Mechanism

AbstractApart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and design of approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design—the scheduling problem (Nisan and Ronen, in: Proceedings of the 31st annual ACM symposium on theory of computing (STOC), 1999). One version of this problem, which includes a verification component, is studied by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014). It was shown that the problem has a tight approximation ratio bound of $$(n+1)/2$$ ( n + 1 ) / 2 for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014) is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio. It indicates that the optimal mechanism devised for a worst-case guarantee works well on average.

scholarly journals Motion Estimation Architecture Using Efficient Adder-Compressors for HDTV Video Coding

2010 ◽  
Vol 5 (1) ◽  
pp. 78-88 ◽  
Author(s):  
Marcelo Porto ◽  
André Silva ◽  
Sergo Almeida ◽  
Eduardo Da Costa ◽  
Sergio Bampi
Keyword(s):  
Motion Estimation ◽  
Real Time ◽  
Search Algorithm ◽  
Absolute Difference ◽  
High Definition ◽  
Case Processing ◽  
Worst Case ◽  
Average Case ◽  
High Definition Television ◽  
Internal Structures

This paper presents real time HDTV (High Definition Television) architecture for Motion Estimation (ME) using efficient adder compressors. The architecture is based on the Quarter Sub-sampled Diamond Search algorithm (QSDS) with Dynamic Iteration Control (DIC) algorithm. The main characteristic of the proposed architecture is the large amount of Processing Units (PUs) that are used to calculate the SAD (Sum of Absolute Difference) metric. The internal structures of the PUs are composed by a large number of addition operations to calculate the SADs. In this paper, efficient 4-2 and 8-2 adder compressors are used in the PUs architecture to achieve the performance to work with HDTV (High Definition Television) videos in real time at 30 frames per second. These adder compressors enable the simultaneous addition of 4 and 8 operands respectively. The PUs, using adder compressors, were applied to the ME architecture. The implemented architecture was described in VHDL and synthesized to FPGA and, with Leonardo Spectrum tool, to the TSMC 0.18μm CMOS standard cell technology. Synthesis results indicate that the new QSDS-DIC architecture reach the best performance result and enable gains of 12% in terms of processing rate. The architecture can reach real time for full HDTV (1920x1080 pixels) in the worst case processing 65 frames per second, and it can process 269 HDTV frames per second in the average case.

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