格上筛法研究现状与发展趋势

最短向量问题(shortest vector problem, SVP)是格上的基础困难问题之一, 是格密码方案安全性的基础假设, SVP求解算法是评估格密码算法具体安全性的关键技术. 实用的SVP精确求解算法主要包括筛法和枚举两种类型, 其中筛法的时间复杂性更低, 是目前实用化格密码算法安全性评估主要使用的算法. 筛法由Ajtai-Kumar-Sivakumar于2001年首次提出, 其主要思想是将指数多个格向量通过一系列的筛取过程, 互相约化, 以得到一定数量的长度为 O(λ1)的格向量, 然后将这些向量两两相减以得到最短非零格向量, 其中 λ1表示格中最短非零向量长度. 二十年来, 研究...

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Published inJournal of Cryptologic Research Vol. 8; no. 5; p. 735
Main Authors Lei, B I, Xian-Hui, LU, Kun-Peng, WANG, 毕蕾, 路献辉, 王鲲鹏
Format Journal Article
LanguageChinese
Published Beijing Chinese Association for Cryptologic Research, Journal of Cryptologic Research 01.01.2021
Subjects
Algorithms
Encryption
Enumeration
Heuristic methods
Reduction
Security
Online AccessGet full text
ISSN2097-4116
DOI10.13868/j.cnki.jcr.000474

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Abstract 最短向量问题(shortest vector problem, SVP)是格上的基础困难问题之一, 是格密码方案安全性的基础假设, SVP求解算法是评估格密码算法具体安全性的关键技术. 实用的SVP精确求解算法主要包括筛法和枚举两种类型, 其中筛法的时间复杂性更低, 是目前实用化格密码算法安全性评估主要使用的算法. 筛法由Ajtai-Kumar-Sivakumar于2001年首次提出, 其主要思想是将指数多个格向量通过一系列的筛取过程, 互相约化, 以得到一定数量的长度为 O(λ1)的格向量, 然后将这些向量两两相减以得到最短非零格向量, 其中 λ1表示格中最短非零向量长度. 二十年来, 研究者们不仅在理论上对筛法进行研究和改进, 同时也给出了一系列在实际应用中更为高效的启发式算法. 针对筛法中复杂度最高的部分, 即约化时遍历指数多个格向量的过程, 研究者们使用了多种技术对其进行改进, 包括生日悖论、局部敏感技术、层次化、元组化、线性化等. 本文按照技术发展及时间顺序介绍了格上筛法的发展历史、研究现状和将来的发展趋势.
AbstractList 最短向量问题(shortest vector problem, SVP)是格上的基础困难问题之一, 是格密码方案安全性的基础假设, SVP求解算法是评估格密码算法具体安全性的关键技术. 实用的SVP精确求解算法主要包括筛法和枚举两种类型, 其中筛法的时间复杂性更低, 是目前实用化格密码算法安全性评估主要使用的算法. 筛法由Ajtai-Kumar-Sivakumar于2001年首次提出, 其主要思想是将指数多个格向量通过一系列的筛取过程, 互相约化, 以得到一定数量的长度为 O(λ1)的格向量, 然后将这些向量两两相减以得到最短非零格向量, 其中 λ1表示格中最短非零向量长度. 二十年来, 研究者们不仅在理论上对筛法进行研究和改进, 同时也给出了一系列在实际应用中更为高效的启发式算法. 针对筛法中复杂度最高的部分, 即约化时遍历指数多个格向量的过程, 研究者们使用了多种技术对其进行改进, 包括生日悖论、局部敏感技术、层次化、元组化、线性化等. 本文按照技术发展及时间顺序介绍了格上筛法的发展历史、研究现状和将来的发展趋势.
Author Lei, B I
Xian-Hui, LU
路献辉
毕蕾
Kun-Peng, WANG
王鲲鹏
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Snippet 最短向量问题(shortest vector problem, SVP)是格上的基础困难问题之一, 是格密码方案安全性的基础假设, SVP求解算法是评估格密码算法具体安全性的关键技术. 实用的SVP精确求解算法主要包括筛法和枚举两种类型, 其中筛法的时间复杂性更低, 是目前实用化格密码算法安全性评估主要使用的算法....
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SubjectTerms Algorithms
Encryption
Enumeration
Heuristic methods
Reduction
Security
Title 格上筛法研究现状与发展趋势
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