We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotie...We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.展开更多
When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical ...When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.展开更多
We design a practical and provablysecure block ciper over small domain and non-binary inputs,which is also can be considered as a pseudorandom permutation on N elements.Our work is based on a relation we found between...We design a practical and provablysecure block ciper over small domain and non-binary inputs,which is also can be considered as a pseudorandom permutation on N elements.Our work is based on a relation we found between the small domain ciper and the negative hypergeometric probability(NHG) distribution.We prove that our block ciper achieves ideal security,that is,it is indistinguishable from a random permutation even if the adversary had already observed N plaintext-cipertext pairs.In particular,we initiate an efficient and sufficiently precise sampling algorithm for negative hypergeometric distribution.展开更多
The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we ...The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.展开更多
In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and pr...In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.展开更多
基金the National Natural Science Foundation of China，the Open Funds of State Key Laboratory of Information Security (Chinese Academy of Sciences)，the Program for New Century Excellent Talents in Fujian Province University
文摘We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFB0802000)the Cryptography Theoretical Research of National Cryptography Development Fund,China(Grant No.MMJJ20170109).
文摘When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.
基金National 973 Fundamental Basic Research Program under grant No.2014CB340600 and by the National Natural Science Foundations of China
文摘We design a practical and provablysecure block ciper over small domain and non-binary inputs,which is also can be considered as a pseudorandom permutation on N elements.Our work is based on a relation we found between the small domain ciper and the negative hypergeometric probability(NHG) distribution.We prove that our block ciper achieves ideal security,that is,it is indistinguishable from a random permutation even if the adversary had already observed N plaintext-cipertext pairs.In particular,we initiate an efficient and sufficiently precise sampling algorithm for negative hypergeometric distribution.
基金supported by Overseas Scholars Research Fund of Heilongjiang Provinicial Education Department
文摘The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60973162)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009GM037)+1 种基金the Science and Technology of Shandong Province, China(Grant No. 2010GGX10132)the Key Program of the Natural Science Foundation of Shandong Province, China (Grant No. Z2006G01)
文摘In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.
