CAJ | 학술논문

本文利用 Li-York 混沌判别定理，构造了一类分段线性连续混沌映射．基于此类映射，建立了一个构造一类分段非线性鲁棒混沌映射的判别定理．作为应用，构造了一个由多项式函数和三角函数映射合成的分段非线性鲁棒混沌映射．通过计算该混沌映射的分岔图，验证了映射在参数范围内的混沌性．作为鲁棒混沌的应用，设计了三个基于分段非线性鲁棒混沌映射的伪随机数发生器．在此基础上，利用混沌映射对初始参数的敏感性，提出了批量生成 S盒的算法．S 盒密码性能的分析结果表明，生成的 S 盒具有良好的密码学性能，可以较好的抵抗线性与差分攻击，为密码算法的研究发展提供基础与条件．
본문이용 Li-York 혼돈판별정리，구조료일류분단선성련속혼돈영사．기우차류영사，건립료일개구조일류분단비선성로봉혼돈영사적판별정리．작위응용，구조료일개유다항식함수화삼각함수영사합성적분단비선성로봉혼돈영사．통과계산해혼돈영사적분차도，험증료영사재삼수범위내적혼돈성．작위로봉혼돈적응용，설계료삼개기우분단비선성로봉혼돈영사적위수궤수발생기．재차기출상，이용혼돈영사대초시삼수적민감성，제출료비량생성 S합적산법．S 합밀마성능적분석결과표명，생성적 S 합구유량호적밀마학성능，가이교호적저항선성여차분공격，위밀마산법적연구발전제공기출여조건．
Using the judgment theorem of Li-York chaos,this paper generates a class of piecewise linear chaotic maps.Based on the chaotic maps,a constructing theorem of piecewise nonlinear robust chaotic map is proposed.As an application,this theorem is used to construct a piecewise nonlinear robust chaotic map with a polynomial function and a trigonometric function.This study com-putes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseu-do-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis,the generation algo-rithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography perfor-mance is tested and the tested results show that generated S-boxes have good cryptographic properties,and can not only better resist the linear and differential attacks,but also provide the foundation and conditions for the research and development of cryptography.