This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the res...This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6展开更多
In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that t...In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).展开更多
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank appr...We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.展开更多
1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact ...1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.展开更多
文摘This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6
基金supported by National Natural Science Foundation of China(Grant Nos.61070172,10990011 and 61170257)the External Science and Technology Cooperation Program of Hubei Province(Grant No.2012IHA01402)+1 种基金National Key Basic Research Program of China(Grant No.2013CB834203)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA06010702)
文摘In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).
基金This work was supported in part by the Special Funds for Major State Basic Research Projectsthe National Natural Science Foundation of China(Grants No.60372033 and 9901936)NSF CCR9901986,DMS 0311800.
文摘We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos. 10831003,61072147,11071159)+2 种基金the Shanghai Municipal Natural Science Foundation (No. 09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)TUBITAK (the Scientific and Technological Research Council of Turkey) for its financial support and grant for the research entitled "Integrable Systems and Soliton Theory" at University of South Florida
文摘1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.
