Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence
The module learning with errors (MLWE) problem has attracted considerable attention for its tradeoff between security and efficiency. The quantum/classical worst-case to average-case hardness for the MLWE problem (or more exactly, a family of problems) has been established, but most of the known res...
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Wiley
2023-01-01
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| Series: | IET Information Security |
| Online Access: | http://dx.doi.org/10.1049/2023/2104380 |
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| author | Wenjuan Jia Baocang Wang |
| author_facet | Wenjuan Jia Baocang Wang |
| author_sort | Wenjuan Jia |
| collection | DOAJ |
| description | The module learning with errors (MLWE) problem has attracted considerable attention for its tradeoff between security and efficiency. The quantum/classical worst-case to average-case hardness for the MLWE problem (or more exactly, a family of problems) has been established, but most of the known results require the seed distribution to be the uniform distribution. In the present paper, we show that, using the noise flooding technique based on the Rényi divergence, the search MLWE problem with uniform B-bounded secret distribution for 1≤B≪q can still be hard for some seed distributions that are not (even computationally indistinguishable from) the uniform distribution under the standard MLWE assumption. Specifically, we show that if the seed distribution is a semiuniform distribution (namely, the seed distribution can be publicly derived from and has a “small difference” to the uniform distribution), then for suitable parameter choices, the search MLWE problem with uniform bounded secret distribution is hard under the standard MLWE assumption. Moreover, we also show that under the appropriate setting of parameters, the search MLWE problem with uniform bounded noise distribution is at least as hard as the standard MLWE assumption using a different approach than the one used by Boudgoust et al. in [JoC 2023]. |
| format | Article |
| id | doaj-art-507e2faa644945fe8cb92e707221805d |
| institution | Kabale University |
| issn | 1751-8717 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
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| series | IET Information Security |
| spelling | doaj-art-507e2faa644945fe8cb92e707221805d2025-02-03T01:32:08ZengWileyIET Information Security1751-87172023-01-01202310.1049/2023/2104380Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi DivergenceWenjuan Jia0Baocang Wang1School of Telecommunications EngineeringState Key Laboratory of Integrated Service NetworksThe module learning with errors (MLWE) problem has attracted considerable attention for its tradeoff between security and efficiency. The quantum/classical worst-case to average-case hardness for the MLWE problem (or more exactly, a family of problems) has been established, but most of the known results require the seed distribution to be the uniform distribution. In the present paper, we show that, using the noise flooding technique based on the Rényi divergence, the search MLWE problem with uniform B-bounded secret distribution for 1≤B≪q can still be hard for some seed distributions that are not (even computationally indistinguishable from) the uniform distribution under the standard MLWE assumption. Specifically, we show that if the seed distribution is a semiuniform distribution (namely, the seed distribution can be publicly derived from and has a “small difference” to the uniform distribution), then for suitable parameter choices, the search MLWE problem with uniform bounded secret distribution is hard under the standard MLWE assumption. Moreover, we also show that under the appropriate setting of parameters, the search MLWE problem with uniform bounded noise distribution is at least as hard as the standard MLWE assumption using a different approach than the one used by Boudgoust et al. in [JoC 2023].http://dx.doi.org/10.1049/2023/2104380 |
| spellingShingle | Wenjuan Jia Baocang Wang Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence IET Information Security |
| title | Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence |
| title_full | Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence |
| title_fullStr | Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence |
| title_full_unstemmed | Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence |
| title_short | Hardness of (Semiuniform) MLWE with Short Distributions Using the Rényi Divergence |
| title_sort | hardness of semiuniform mlwe with short distributions using the renyi divergence |
| url | http://dx.doi.org/10.1049/2023/2104380 |
| work_keys_str_mv | AT wenjuanjia hardnessofsemiuniformmlwewithshortdistributionsusingtherenyidivergence AT baocangwang hardnessofsemiuniformmlwewithshortdistributionsusingtherenyidivergence |