八維廣義同步系統(tǒng)在偽隨機數(shù)發(fā)生器中的應(yīng)用

韓丹丹; 閔樂泉; 趙耿

doi:10.11999/JEIT150899

八維廣義同步系統(tǒng)在偽隨機數(shù)發(fā)生器中的應(yīng)用

doi: 10.11999/JEIT150899

1.
(北京科技大學(xué)自動化學(xué)院北京 100083) ②(北京科技大學(xué)數(shù)理學(xué)院北京 100083) ③(北京電子科技學(xué)院北京 100070)

基金項目:

國家自然科學(xué)基金(61074192, 61170037)

計量
- 文章訪問數(shù): 1267
- HTML全文瀏覽量: 120
- PDF下載量: 278
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2015-07-30
- 修回日期: 2015-12-18
- 刊出日期: 2016-05-19

Application of 8-dimensional Generalized Synchronization System in Pseudorandom Number Generator

1.
(School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China)
2.
(School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)

Funds:

The National Natural Science Foundation of China (61074192, 61170037)

摘要

摘要: 該文提出一類4維離散系統(tǒng)。利用系統(tǒng)平衡點處 Jacobi 矩陣的特征值來分析系統(tǒng)在平衡點處的穩(wěn)定性，建立了一個判別這類系統(tǒng)為周期或混沌的定理。依據(jù)該定理構(gòu)造了一個新的4維離散系統(tǒng)。該系統(tǒng)具有正的Lyapunov指數(shù)，數(shù)值模擬顯示該系統(tǒng)的動力學(xué)行為具有混沌特性。結(jié)合該系統(tǒng)和系統(tǒng)廣義同步定理構(gòu)造了一個8維廣義同步混沌系統(tǒng)。利用該系統(tǒng)構(gòu)造了一個16 bit混沌偽隨機數(shù)發(fā)生器 (CPRNG)，其密鑰空間大于21245。利用FIPS 140-2 檢測/廣義FIPS 140-2檢測判別標(biāo)準(zhǔn)分別檢測由CPRNG, Narendra RBG, RC4 PRNG和ZUC PRNG生成的1000個長度為20000 bit的密鑰流的隨機性。檢測結(jié)果表明，分別有100%/99%, 100%/82.9%, 99.9%/ 98.8%和100%/97.9%密鑰流通過FIPS 140-2檢測/廣義FIPS 140-2 檢測標(biāo)準(zhǔn)。數(shù)值仿真顯示不同密鑰流之間有平均50.004%不同碼。結(jié)果說明設(shè)計的偽隨機數(shù)發(fā)生器有好的隨機性，可以抵抗窮盡攻擊。該文提出的CPRNG為密碼安全的研究與發(fā)展提供了新的工具。
- 偽隨機數(shù)發(fā)生器 /
- 混沌系統(tǒng) /
- 收斂性 /
- 廣義同步 /
- 隨機性檢測
Abstract: This paper proposes a class of 4-Dimensional Discrete Systems (4DDSs). Using the eigenvalues of Jacobian matrix of the system at the equilibrium, the?stability of the system at the equilibrium is analyzed. A theorem is set up, which is used to determine whether the class systems are periodic or chaotic. Based on the theorem, a 4DDS is constructed. The 4DDS has positive Lyapunov exponent. Numerical simulations show that the dynamic behaviors of the 4DDS have chaotic attractor characteristics as they expects. Combining the 4DDS with Generalized Synchronization (GS) theorem, an 8-Dimensional GS Chaotic System (8DGSCS) is designed. Using this system, this paper designs a 16 bit string Chaotic Pseudo Random Number Generator (CPRNG). Theoretically the key space of the CPRNG is larger than 21245. The FIPS 140-2 test suit/Generalized FIPS 140-2 test suit are used to test the randomness of the 1000-key streams consisting of 20000 bit generated by the CPRNG, Narendra RBG, RC4 PRNG and ZUC PRNG, respectively. The results show that there are 100%/99%, 100%/ 82.9%, 99.9%/98.8% and 100%/97.9% key streams passing the FIPS 140-2 test suit/Generalized FIPS 140-2 test suit, respectively. Numerical simulations show that the different key-streams have 50.004% different codes. The results show that the generated CPRNG has good randomness properties, can better resist the brute attack. The designed CPRNG provides a novel tool for the research and development of cryptography.
- Pseudo-Random Number Generator (PRNG) /
- Chaotic system /
- Convergence /
- Generalized synchronization /
- Randomness test

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