具有小規(guī)模公開參數(shù)的適應(yīng)安全的非零內(nèi)積加密方案
doi: 10.11999/JEIT190510 cstr: 32379.14.JEIT190510
-
信息工程大學(xué) 鄭州 450001
基金項(xiàng)目: 國家自然科學(xué)基金(61702548, 61601515)，河南省基礎(chǔ)與前沿技術(shù)課題(162300410192)
Adaptive Secure Non-zero Inner Product Encryption Scheme with Small-scale Public Parameters
-
University of Information Engineering, Zhengzhou 450001, China
Funds: The National Natural Science Foundation of China (61702548, 61601515), The Fundamental and Frontier Technology Research of Henan Province (162300410192)
-
摘要: 內(nèi)積加密是一種支持內(nèi)積形式的函數(shù)加密，已有內(nèi)積加密方案的公開參數(shù)規(guī)模較大，為解決該問題，該文基于素?cái)?shù)階熵?cái)U(kuò)張引理，利用雙對偶向量空間(DPVS)技術(shù)，提出一個公開參數(shù)規(guī)模較小的具有適應(yīng)安全性的內(nèi)積加密方案。在方案的私鑰生成算法中，將用戶的屬性向量的分量與主私鑰向量結(jié)合，生成一個可與熵?cái)U(kuò)張引理中密鑰分量結(jié)合的向量；在方案的加密算法中，將內(nèi)積向量的每一分量與熵?cái)U(kuò)張引理中的部分密文分量結(jié)合。在素?cái)?shù)階熵?cái)U(kuò)張引理和
${\rm{MDDH}}_{k, k + 1}^n$ 困難假設(shè)成立條件下，證明了方案具有適應(yīng)安全性。該文方案公開參數(shù)僅有10個群元素，與現(xiàn)有內(nèi)積加密方案相比，公開參數(shù)規(guī)模最小。-
關(guān)鍵詞:
- 內(nèi)積加密 /
- 素?cái)?shù)階熵?cái)U(kuò)張引理 /
- $ {\rm{MDDH}}_{k,k+1}^n$困難假設(shè) /
- 適應(yīng)安全
Abstract: Inner product encryption is a kind of function encryption which supports inner product form. The public parameter scale of the existing inner product encryption schemes are large. In order to solve this problem, based on prime-order bilinear entropy expansion lemma and Double Pairing Vector Space (DPVS), an inner product encryption scheme is proposed in this paper, which has fewer public parameters and adaptive security. In the private key generation algorithm of the scheme, the components of the user’s attribute with the main private key are combined to generate a vector that can be combined with the key components in the entropy expansion lemma, and in encryption algorithm of the scheme, each component of the inner product vector is combined with ciphertext component in the entropy expansion lemma. Finally, under the condition of prime order bilinear entropy extension lemma and$\textstyle{{\rm{MDDH}}_{k, k + 1}^n}$ difficult assumption, the adaptive secure of the scheme is proved. The proposed scheme has only 10 group elements as public parameters, which is the smallest compared with the existing inner product encryption schemes. -
表 1
${\rm{Game}}$ 序列Game ct sk $\kappa < i$ $\kappa = i$ $\kappa > i$ 0 標(biāo)準(zhǔn) 標(biāo)準(zhǔn) 0’ 熵?cái)U(kuò)張 熵?cái)U(kuò)張 $i$ 熵?cái)U(kuò)張 半功能 熵?cái)U(kuò)張 熵?cái)U(kuò)張 $i,1$ – – 偽標(biāo)準(zhǔn) – $i,2$ – – 偽半功能 – $i,3$ – – 半功能 – Final 隨機(jī)消息 半功能 
下載: 導(dǎo)出CSV
表 2 與現(xiàn)有內(nèi)積加密方案的數(shù)據(jù)長度比較
方案 公開參數(shù)長度 私鑰長度 密文長度 安全性假設(shè) 安全性 文獻(xiàn)[5] $(4{n^2} + 3)|{G_1}|$ $(2n + 1)|{G_1}|$ $(2n + 1)|{G_1}|$ 2 variants of GSD 選擇安全 文獻(xiàn)[7] $(4{n^2} + 2n)|{G_1}|$ $(2n + 3)|{G_1}|$ $(2n + 3)|{G_1}|{\rm{ + }}|{G_T}|$ n-eDDH 適應(yīng)安全 文獻(xiàn)[8] $(4{n^2} + 3)|{G_1}|$ $(3n + 2)|{G_1}|$ $(3n + 2)|{G_1}| + |{G_T}|$ DLIN 適應(yīng)安全 文獻(xiàn)[9](type1) $105|{G_1}|$ $(3n + 2)|{G_1}|$ $(3n + 2)|{G_1}| + |{G_T}|$ DLIN 適應(yīng)安全 文獻(xiàn)[10] $28|{G_1}|$ $7n|{G_2}|{\rm{ + }}\alpha $ $7n|{G_1}|$ SXDH 適應(yīng)安全 本方案 $9|{G_1}| + {G_T}$ $8n|{G_2}|$ $(5n + 3)|{G_1}|{\rm{ + |}}{G_T}{\rm{|}}$ ${\rm{MDDH}}_{k,k + 1}^n$ 適應(yīng)安全 注：其中n表示系統(tǒng)屬性的個數(shù)，$|{G_1}|,|{G_2}|,|{G_T}|$分別表示${G_1},{G_2},{G_T}$中群元素的長度。
下載: 導(dǎo)出CSV
-
BALTICO C E Z, CATALANO D, and FIORE D. Practical functional encryption for quadratic functions with applications to predicate encryption[C]. The 37th Annual International Cryptology Conference on Advances in Cryptology, Santa Barbara, USA, 2017: 67–100. BONEH D, SAHAI A, and WATERS B. Functional encryption: Definitions and challenges[C]. The 8th conference on Theory of Cryptography, Providence, USA, 2011: 253–273. 曹丹, 王小峰, 王飛, 等. SA-IBE: 一種安全可追責(zé)的基于身份加密方案[J]. 電子與信息學(xué)報(bào), 2011, 33(12): 2922–2928.CAO Dan, WANG Xiaofeng, WANG Fei, et al. SA-IBE: A secure and accountable identity-based encryption scheme[J]. Journal of Electronics &Information Technology, 2011, 33(12): 2922–2928. BONEH D and WATERS B. Conjunctive, subset, and range queries on encrypted data[C]. The 4th conference on Theory of Cryptography. Amsterdam, Netherlands, 2007: 535–554. KATZ J, SAHAI A, and WATERS B. Predicate encryption supporting disjunctions, polynomial equations, and inner products[C]. The 27th Annual International Conference on Advances in Cryptology, Istanbul, Turkey: 2008: 146–162. DATTA P, OKAMOTO T, and TAKASHIMA K. Adaptively simulation-secure attribute-hiding predicate encryption[C]. The 24th International Conference on the Theory and Application of Cryptology and Information Security, Brisbane, Australia, 2018: 640–672. LEWKO A, OKAMOTO T, and SAHAI A. Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption[C]. The 29th Annual International Conference on Theory and Applications of Cryptographic Techniques, French Riviera, 2010: 62–91. OKAMOTO T and TAKASHIMA K. Fully secure functional encryption with general relations from the decisional linear assumption[C]. The 30th Annual Conference on Advances in Cryptology, Santa Barbara, USA, 2010: 191–208. OKAMOTO T and TAKASHIMA K. Fully secure unbounded inner-product and attribute-based encryption[C]. The 18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, 2012: 349–366. TOMIDA J and TAKASHIMA K. Unbounded inner product functional encryption from bilinear maps[C]. The 24th International Conference on the Theory and Application of Cryptology and Information Security, Brisbane, Australia, 2018: 609–639. WATERS B. Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions[C]. The 29th Annual International Cryptology Conference on Advances in Cryptology, Santa Barbara, USA, 2009: 619–636. CHEN Jie, GAY R, and WEE H. Improved dual system ABE in prime-order groups via predicate encodings[C]. The 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, 2015: 595–624. CHEN Jie, GONG Junqing, KOWALCZYK L, et al. Unbounded ABE via bilinear entropy expansion, revisited[C]. The 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, 2018: 503–534. WEE H. Dual system encryption via predicate encodings[C]. The 11th Theory of Cryptography Conference, San Diego, USA, 2014: 616–637. LEWKO A B and WATERS B. New techniques for dual system encryption and fully secure HIBE with short ciphertexts[C]. The 7th International Conference on Theory of Cryptography, Zurich, Switzerland, 2010: 455–479. -
表(2)
計(jì)量
- 文章訪問數(shù): 1467
- HTML全文瀏覽量: 349
- PDF下載量: 56
- 被引次數(shù): 0
下載:
