本文選題：格 + 帶錯誤學(xué)習(xí)問題��； 參考：《北京交通大學(xué)學(xué)報》2017年05期

【摘要】：基于帶錯誤學(xué)習(xí)問題(Learning With Errors,LWE)構(gòu)造的密碼體制能夠抵御量子攻擊,它的應(yīng)用效率與LWE問題的采樣過程密切相關(guān).而在LWE問題采樣中,對其中的錯誤因子(Error Factor)采樣占采樣過程絕大部分時間,本文對LWE問題中的錯誤因子的采樣算法進行研究,將在高斯分布上效率較高的金字塔(Ziggurat)采樣算法,應(yīng)用到了一種高效的LWE問題采樣算法中.基于在連續(xù)域上的采樣比離散域上采樣效率高的思路,對LWE問題采樣算法在離散域上采樣的過程進行了優(yōu)化,提出了一種將連續(xù)域上的采樣結(jié)果進行取整的方法,.對優(yōu)化前后的兩種LWE問題的采樣算法進行了對比實驗,結(jié)果表明:改進后的算法在不占用大量內(nèi)存并且保證安全性的情況下,將采樣速度提高了38%~200%.
[Abstract]:The cryptosystem based on Learning With errors LW with error learning problem can resist quantum attack. Its application efficiency is closely related to the sampling process of LWE problem. In the sampling of LWE problem, the sampling of error factor (error factor) takes up most of the time in the sampling process. In this paper, the sampling algorithm of error factor in the LWE problem is studied, and the sampling algorithm of pyramid Ziggurat, which is more efficient in Gao Si distribution, is studied in this paper. It is applied to an efficient sampling algorithm for LWE problem. Based on the idea that sampling in continuous domain is more efficient than that in discrete domain, the sampling process of sampling algorithm for LWE problem in discrete domain is optimized, and a method of rounding the sampling results in continuous domain is proposed. Two sampling algorithms for LWE problems before and after optimization are compared. The results show that the improved algorithm increases the sampling speed by 38 / 200 without occupying a lot of memory and ensuring security.
【作者單位】： 北京交通大學(xué)計算機與信息技術(shù)學(xué)院;
【基金】：國家自然科學(xué)基金青年基金項目(61402035) 中央高�；A(chǔ)科研業(yè)務(wù)費專項資金(2014JBM033)~~
【分類號】：TN918.4

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