Gauss Sieve Algorithm on GPUs

Yang, Shengyi; Kuo, Po-Chun; Yang, Bo‐Yin; Cheng, Chen-Mou

doi:10.1007/978-3-319-52153-4_3

Cited by 14 publications

(9 citation statements)

References 19 publications

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“…Efforts have been made to decrease the asymptotic time complexity at the cost of using more space [32][33][34][35] and to study the trade-offs in reducing the space complexity [35][36][37][38]. Attempts have been made to make these algorithms competitive in high-performance computing environments [39][40][41][42][43]. The theoretically fastest heuristic algorithm that is conjectured to solve SVP runs in a time of 2 0.29n+o(n) [33] (LD-Sieve).…”

Section: Sieving Algorithms In the Euclidean Normmentioning

confidence: 99%

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

Mukhopadhyay

2021

Algorithms

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In this work, we give provable sieving algorithms for the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) on lattices in ℓp norm (1≤p≤∞). The running time we obtain is better than existing provable sieving algorithms. We give a new linear sieving procedure that works for all ℓp norm (1≤p≤∞). The main idea is to divide the space into hypercubes such that each vector can be mapped efficiently to a sub-region. We achieve a time complexity of 22.751n+o(n), which is much less than the 23.849n+o(n) complexity of the previous best algorithm. We also introduce a mixed sieving procedure, where a point is mapped to a hypercube within a ball and then a quadratic sieve is performed within each hypercube. This improves the running time, especially in the ℓ2 norm, where we achieve a time complexity of 22.25n+o(n), while the List Sieve Birthday algorithm has a running time of 22.465n+o(n). We adopt our sieving techniques to approximation algorithms for SVP and CVP in ℓp norm (1≤p≤∞) and show that our algorithm has a running time of 22.001n+o(n), while previous algorithms have a time complexity of 23.169n+o(n).

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Section: Sieving Algorithms In the Euclidean Normmentioning

confidence: 99%

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

Mukhopadhyay

2021

Algorithms

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“…In addition, there are various parallel implementations [? ], [39], [59], [62], [81] of Gauss Sieve algorithm.…”

Section: List Sieve Algorithm Gauss Sieve Algorithm and Their Impmentioning

confidence: 99%

“…In 2017, Yang et al [81] implemented Ishiguro et al's parallel Gauss Sieve algorithm on a single GPU and Bos et al's on multiple GPUs. Both implementation behaved efficiently in solving the shortest vector problem.…”

Section: G Parallelizationmentioning

confidence: 99%

A Review of Sieve Algorithms in Solving the Shortest Lattice Vector Problem

Sun

Yan

2020

IEEE Access

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As a category of algorithms to solve the shortest lattice vector problem, sieve algorithms have drawn more and more attention due to the prominent performance in recent years. Enumeration algorithms used to perform better in practice even though sieve algorithms are asymptotically faster. Combined with techniques like locality-sensitive hashing and rank reduction, sieve algorithms now are capable of competing with enumeration algorithms. In this work, we study sieve algorithms in solving the shortest vector problem on lattices by categorizing various sieve algorithms and elaborating on ideas and techniques used to improve sieve algorithms. In addition, we present several prospective directions worth future research.

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“…Some recent work in energy‐efficient cloud computing benefits from virtualization capabilities, such as load balancing, resource allocation, and virtual machine scheduling, to make the environment more sustainable . Another study proposes power models to quantify the energy consumption of different workloads .…”

Section: Background and State Of The Artmentioning

confidence: 99%

Modeling and simulation of global and sleep states in ACPI‐compliant energy‐efficient cloud environments

Xavier

Rossi

Rose

et al. 2016

Concurrency and Computation

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SUMMARYThe more large-scale data centers infrastructure costs increase, the more simulation-based evaluations are needed to understand better the trade-off between energy and performance and support the development of new energy-aware resource allocation policies. Specifically, in the cloud computing field, various simulators are able to predict and measure the behavior of applications on different architectures using different resource allocation policies. Yet, only a few of them have the ability to simulate energy-saving strategies, and none of them support the complete advanced configuration and power interface (ACPI) specification. ACPI defines a terminology for all possible power states of a machine and their associated power rate. The hardware industry has relied on ACPI to provide up-to-date standard interfaces for hardware discovery, configuration, power management, and monitoring, enabling a better understanding of the energy consumption level of different hardware states, referred to as ACPI G-states, S-states, and P-states. In this paper, we improve the modeling and simulation of the ACPI G/S-states and show not only that these states offer different energy-saving levels but also that state transitions consume energy. In addition, we model the latency to transit between two states and the effects on the turnaround time when the transitions are not performed conservatively. Furthermore, the equations provide essential information to quantify the trade-off between energy consumption and performance and assist in the analysis/decision on which strategy fits better in the environment and how it could be refined. Our expanded energy model was implemented in CloudSim and validated with simulation-based experiments with a very high level of accuracy, with a standard deviation of at most 6%.

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Gauss Sieve Algorithm on GPUs

Cited by 14 publications

References 19 publications

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

A Review of Sieve Algorithms in Solving the Shortest Lattice Vector Problem

Modeling and simulation of global and sleep states in ACPI‐compliant energy‐efficient cloud environments

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