【摘要】：目前全同態(tài)加密的效率亟待提高,為了提高全同態(tài)加密的效率,提出一個(gè)LWE(learning with errors)上的短公鑰多位全同態(tài)加密方案.方案中從離散高斯分布上選取LWE樣例,并且將高斯噪音與之相加,導(dǎo)致LWE樣例從2nlogq下降到n+1,使得方案的公鑰長度變短.詳細(xì)給出了該方案的噪音增長分析與安全性證明;此外,對(duì)目前密鑰交換技術(shù)進(jìn)行了優(yōu)化,并且針對(duì)多位全同態(tài)加密,給出了密鑰交換優(yōu)化版本的形式化描述;最后,針對(duì)目前全同態(tài)加密的實(shí)踐應(yīng)用,給出了分析全同態(tài)加密具體安全參數(shù)的方法.分析了該方案與BGH13方案的具體安全參數(shù),數(shù)據(jù)顯示該方案的具體參數(shù)長度要優(yōu)于BGH13方案.
[Abstract]:At present, the efficiency of full homomorphism encryption needs to be improved urgently. In order to improve the efficiency of full homomorphism encryption, a short public key multi-bit full homomorphism encryption scheme on LWE (learning with errors) is proposed. In the scheme, the LWE sample is selected from the discrete Gao Si distribution, and Gao Si noise is added to it, which leads to the decrease of LWE sample from 2nlogq to n 1, which makes the public key length of the scheme shorter. The noise growth analysis and security proof of the scheme are given in detail. In addition, the current key exchange technology is optimized, and the formal description of the optimized version of key exchange is given for multi-bit homomorphism encryption. Finally, according to the practical application of full homomorphism encryption, the method of analyzing the specific security parameters of full homomorphism encryption is given. The specific security parameters of the scheme and the BGH13 scheme are analyzed. The data show that the specific parameter length of the scheme is better than that of the BGH13 scheme.
【作者單位】： 浙江萬里學(xué)院電子與計(jì)算機(jī)學(xué)院;浙江萬里學(xué)院基礎(chǔ)學(xué)院;信息工程大學(xué)三院;
【基金】：浙江省自然科學(xué)基金項(xiàng)目(LY17F020002) NSFC-浙江兩化融合聯(lián)合基金項(xiàng)目(U1509219) 寧波市自然科學(xué)基金項(xiàng)目(2016A610226)~~
【分類號(hào)】：TN918.4

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