基于抽象解密結(jié)構(gòu)的全同態(tài)加密構(gòu)造方法分析

宋新霞; 陳智罡

doi:10.11999/JEIT170997

基于抽象解密結(jié)構(gòu)的全同態(tài)加密構(gòu)造方法分析

doi: 10.11999/JEIT170997 cstr: 32379.14.JEIT170997

^①(浙江萬里學院基礎(chǔ)學院寧波 315100) ^②(浙江萬里學院電子與計算機學院寧波 315100) ^③(中國科學院信息工程研究所信息安全國家重點實驗室北京 100093)

基金項目:

浙江省科技廳公益性技術(shù)科研項目(2017C33079, LGG18F020001)，浙江省自然科學基金(LY17F020002)，密碼科學技術(shù)國家重點實驗室開放課題基金，寧波市自然科學基金(2017A610120)

詳細信息

作者簡介:
宋新霞：女，1973年生，副教授，研究方向為代數(shù)與編碼. 陳智罡：男，1972年生，教授，研究方向為全同態(tài)加密與格密碼.

中圖分類號: TP309.7
計量
- 文章訪問數(shù): 1527
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2017-10-24
- 修回日期: 2018-04-03
- 刊出日期: 2018-07-19

Analysis of Constructing Fully Homomorphic Encryption Based on the Abstract Decryption Structure

SONG Xinxia^① CHEN Zhigang^②③

Funds:

The Public Projects of Zhejiang Province (2017C33079, LGG18F020001), The Natural Science Foundation of Zhejiang Province (LY17F020002), The Foundation of the State Key Laboratory of Cryptology, The Ningbo Natural Science Foundation (2017A610120)

摘要

摘要: 為什么能夠在格上構(gòu)造全同態(tài)加密?密文矩陣的本質(zhì)及構(gòu)造方法是什么?該文提出一個重要的概念：抽象解密結(jié)構(gòu)。該文以抽象解密結(jié)構(gòu)為工具，對目前全同態(tài)加密構(gòu)造方法進行分析，得到抽象解密結(jié)構(gòu)、同態(tài)性與噪音控制之間的關(guān)系，將全同態(tài)加密的構(gòu)造歸結(jié)為如何獲得最終解密結(jié)構(gòu)的問題，從而形式化地建立全同態(tài)加密構(gòu)造方法。最后對GSW全同態(tài)加密方法分析，提出其密文矩陣是由密文向量堆疊而成?；诿芪亩询B法，研究密文是矩陣的全同態(tài)加密的通用性原因，給出密文矩陣全同態(tài)加密與其它全同態(tài)加密之間的包含關(guān)系。
- 全同態(tài)加密 /
- 構(gòu)造方法 /
- 抽象解密結(jié)構(gòu) /
- 密文堆疊 /
- 學習錯誤問題
Abstract: Why can fully homomorphic encryption be constructed based on lattice What is the essence and construction of the matrix An important concept is proposed: Abstract decryption structure. Based on the abstract decryption structure, the main factors related to the homomorphic encryption are analyzed and relationship between abstract decryption structure, homomorphism and noise control is studied. The construction of the homomorphic encryption is attributed to the problem of how to obtain the final decryption structure. So the formal method of homomorphic encryption can be established. Thus the essential law of the construction method of the homomorphic encryption construction is expounded, which provides the clue and clue for the construction of the new full homomorphic encryption. The general reason of the full homomorphic encryption of the ciphertext matrix from the point of view of the ciphertexts stack method is studied. The relation between the full homomorphic encryption and the other homomorphic encryption is obtained. Finally, this paper gives a general method of constructing fully homomorphic encryption.
- Fully homomorphic encryption、Construction method、Abstract decryption structure、Ciphertexts stack、Learning With Errors (LWE) /

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參考文獻(22)

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