NTRU格上無(wú)證書加密
doi: 10.11999/JEIT150380
基金項(xiàng)目:
國(guó)家自然科學(xué)基金(61472309, 61173151)，安徽省自然科學(xué)基金(1208085MF108, KJ2012B157)
Certificateless Encryption over NTRU Lattices
Funds:
The National Natural Science Foundation of China (61472309, 61173151), The Natural Science Foundation of Anhui Province (1208085MF108, KJ2012B157)
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摘要: 為降低密鑰尺寸，利用陷門抽樣算法在優(yōu)選的NTRU格上抽取部分私鑰并使用多項(xiàng)式環(huán)上帶誤差的學(xué)習(xí)問(wèn)題計(jì)算公鑰等方法來(lái)構(gòu)造格上無(wú)證書加密方案。它的安全性基于多項(xiàng)式環(huán)上帶誤差學(xué)習(xí)的判定問(wèn)題和小多項(xiàng)式比判定問(wèn)題等兩個(gè)困難問(wèn)題假設(shè)。為獲取更好的效率，該文還提出一個(gè)無(wú)證書并行加密方案。該方案用中國(guó)剩余定理分解擴(kuò)大后的明文空間為多個(gè)不同素理想之積來(lái)實(shí)現(xiàn)并行加密。它還用中國(guó)剩余定理分解加密運(yùn)算所在的多項(xiàng)式環(huán)獲取中國(guó)剩余基來(lái)優(yōu)化算法，使算法只涉及整數(shù)間運(yùn)算。結(jié)果顯示該方案具有計(jì)算和通信復(fù)雜度低等特點(diǎn)。
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關(guān)鍵詞:
- 無(wú)證書密碼系統(tǒng) /
- 格密碼 /
- 環(huán)上帶誤差的學(xué)習(xí)問(wèn)題 /
- 判定小多項(xiàng)式比問(wèn)題
Abstract: To lower the sizes of keys, a certificateless encryption scheme is put forward by using a trapdoor sampling algorithm over a selected NTRU lattice to extract partial private keys and using Ring Learning With Errors (RLWE) problem to generate public keys. Its security is based on both assumptions of the decisional ring learning with errors problem and the decisional Small Polynomial Ratio (SPR) problem. To further improve efficiency, a certificateless parallel encryption scheme with more efficient algorithms only using arithmetic in integers is also given by respectively using the Chinese Remainder Theorem (CRT) to decompose the enlarged plaintext space into the product of distinct prime ideals and to break down the ring, over which encryption operations work, for obtaining the Chinese Remainder basis. The given results show that the proposed schemes are characterized by low computation complexity and small communication complexity. -
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