scholarly journals Efficient Implementations of Sieving and Enumeration Algorithms for Lattice-Based Cryptography

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1618
Author(s):  
Hami Satılmış ◽  
Sedat Akleylek ◽  
Cheng-Chi Lee
Keyword(s):  
Software Package ◽  
Software Library ◽  
Memory Space ◽  
Vector Problem ◽  
Modular Software ◽  
Shortest Vector Problem ◽  
Hard Problems ◽  
Enumeration Algorithms ◽  
Run Time ◽  
Lattice Based Cryptography

The security of lattice-based cryptosystems is based on solving hard lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). Various cryptanalysis algorithms such as (Pro)GaussSieve, HashSieve, ENUM, and BKZ have been proposed to solve these hard problems. Several implementations of these algorithms have been developed. On the other hand, the implementations of these algorithms are expected to be efficient in terms of run time and memory space. In this paper, a modular software package/library containing efficient implementations of GaussSieve, ProGaussSieve, HashSieve, and BKZ algorithms is developed. These implementations are considered efficient in terms of run time. While constructing this software library, some modifications to the algorithms are made to increase the performance. Then, the run times of these implementations are compared with the others. According to the experimental results, the proposed GaussSieve, ProGaussSieve, and HashSieve implementations are at least 70%, 75%, and 49% more efficient than previous ones, respectively.

scholarly journals A Survey of Solving SVP Algorithms and Recent Strategies for Solving the SVP Challenge

2020 ◽  
pp. 189-207
Author(s):  
Masaya Yasuda
Keyword(s):  
Quantum Cryptography ◽  
Point Of View ◽  
Classical Lattice ◽  
Mathematical Point ◽  
Closest Vector Problem ◽  
Vector Problem ◽  
Shortest Vector Problem ◽  
Post Quantum Cryptography ◽  
Lattice Based Cryptography

Abstract Recently, lattice-based cryptography has received attention as a candidate of post-quantum cryptography (PQC). The essential security of lattice-based cryptography is based on the hardness of classical lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). A number of algorithms have been proposed for solving SVP exactly or approximately, and most of them are useful also for solving CVP. In this paper, we give a survey of typical algorithms for solving SVP from a mathematical point of view. We also present recent strategies for solving the Darmstadt SVP challenge in dimensions higher than 150.

scholarly journals An Efficient Algorithm for the Shortest Vector Problem

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 61478-61487 ◽  
Author(s):  
Yu-Lun Chuang ◽  
Chun-I Fan ◽  
Yi-Fan Tseng
Keyword(s):  
Efficient Algorithm ◽  
Vector Problem ◽  
Shortest Vector Problem

scholarly journals TPVTrack v1.0: a watershed segmentation and overlap correspondence method for tracking tropopause polar vortices

2018 ◽  
Vol 11 (12) ◽  
pp. 5173-5187 ◽  
Author(s):  
Nicholas Szapiro ◽  
Steven Cavallo
Keyword(s):  
Software Package ◽  
Unstructured Grids ◽  
Test Cases ◽  
Watershed Segmentation ◽  
Spatial Characterization ◽  
Modular Software ◽  
Mean Structure ◽  
Spatial Shape ◽  
Physical Features ◽  
Effective Representation

Abstract. A new free modular software package is described for tracking tropopause polar vortices (TPVs) natively on structured or unstructured grids. Motivated by limitations in spatial characterization and time tracking within existing approaches, TPVTrack mimics the expected dynamics of TPVs to represent their (1) spatial structure, with variable shapes and intensities, and (2) time evolution, with mergers and splits. TPVs are segmented from the gridded flow field into spatial objects as restricted regional watershed basins on the tropopause, described by geometric metrics, associated over time by overlap similarity into major and minor correspondences, and tracked along major correspondences. Simplified segmentation and correspondence test cases illustrate some of the appeal, sensitivities, and limitations of TPVTrack, including effective representation of spatial shape and reduced false positive associations in time. Tracked TPVs in more realistic historical conditions are consistent in bulk with expectations of life cycle and mean structure. Individual tracks are less reliable when discriminating among multiple overlaps. Modifications to track other physical features are possible, with each application requiring evaluation.

Shortest Vector Problem

2016 ◽  
pp. 1974-1977
Author(s):  
Daniele Micciancio
Keyword(s):  
Vector Problem ◽  
Shortest Vector Problem
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