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| 1 | A new discrete Fourier transform randomness test显示文摘The randomness of random number generators(RNGs) is important for the reliability of cryptographic systems since the outputs of RNGs are usually utilized to construct cryptographic parameters.Statistical tests are employed to evaluate the randomness of the RNG outputs. The discrete Fourier transform(DFT) test is an important test item of the most popular statistical test suite NIST SP800-22. In the standard NIST DFT test and related improved studies, there exist accuracy and efficiency issues. First, the bit sequences generated by known good RNGs have a high probability to be rejected when the sequences are long or the sequence number is large, due to the deviation between the actual distribution of the test statistic values and the assumed normal distribution. Second, the long test time and high memory consumptions of the complex DFT test algorithm also affect its practicability. To solve these problems, we propose a new DFT test method for long sequences(106 or more bits). Different from the previous DFT test methods focusing on making the distribution of the test statistic values closer to the normal distribution, we reconstruct the statistic to follow the chi-square distribution. Our experiment result shows that our method has higher reliability in the two-level test, and could effectively reduce the test time and the memory consumptions.When applying our method on randomness test, the test efficiency has been increased to about 4 times for 106-bit sequences and 7 times for 107-bit sequences. In conclusion, our method has lower probability of making errors, and is more suitable for practical application scenarios. | Meihui CHEN Hua CHEN Limin FAN Shaofeng ZHU Wei XI Dengguo FENG | 2019 | Science China(Information Sciences)2019，62，3： | 3 |
| 2 | Period analysis of the Logistic map for the finite field显示文摘Usually, the security of traditional cryptography which works on integer numbers and chaotic cryptosystem which works on real numbers is worthy of study. But the classical chaotic map over the real domain has a disadvantage that the calculation accuracy of the floating point number can be doubled when the map is implemented by computer. This is a serious drawback for practical application. The Logistic map is a classical chaotic system and it has been used as a chaotic cipher in the real number field. This inevitably leads to the degradation of finite precision under computer environment, and it is also very difficult to guarantee security.To solve these drawbacks, we extend the Logistic map to the finite field. In this paper, we consider the Logistic map for the finite field N = 3~n, and analyze the period property of sequences generated by the Logistic map over ZN. Moreover, we discuss the control parameters which may influence the behavior of the mapping, and show that the Logistic map over ZN may be suitable for application by performance analysis. Ultimately, we find that there exists an automorphic map between two Logistic maps with the different control parameters, which makes them suitable for sequence generator in cryptosystem. The automorphic sequence generated algorithm based on the Logistic map over ZN is designed and analyzed in detail. These sequences can be used in the pseudorandom number generator, the chaotic stream cipher, and the chaotic block cipher, etc. | Bo YANG Xiaofeng LIAO | 2017 | Science China(Information Sciences)2017，60，2： | 2 |
| 3 | Some characteristics of logistic map over the finite field显示文摘Dear editor,Chaotic maps have good characteristics,which include randomness,sensitivity to the initial value,and unpredictability.Hence,there have been many attempts to discuss the dynamic behavior of chaotic maps in the field of chaotic cryptography.However,the limited computation,finite memory,and restricted communication capabilities in application causes the state space of the chaotic map to possibly be discrete[1].How to choose a chaos system that conforms to the cryptographic conditions is a very important issue of study. | Bo YANG Xiaofeng LIAO | 2019 | Science China(Information Sciences)2019，62，3： | 0 |
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