Abstract: The linear complexity and the k-error linear complexity are important indicators to measure the strength of stream ciphers, and the higher of those two indicators could resistance the plaintext attack than others, generally. In order to research the sequence of stream cipher, this paper uses a structural approach and cube theory in investigating the 2ⁿ-periodic binary sequences with 6-error linear complexity as the second descent point, and gets all the possible value forms of 6-error linear complexity. This paper analyzes and derives the complete counting functions of 2ⁿ-periodic binary sequences with the given first descent point 2-error linear complexity and second descent point 6-error linear complexity. With the method proposed in this paper, other second or third descent point of the k-error linear complexity for 2n-periodic binary sequences can be obtained.

Key words: periodic sequence, linear complexity, k-error linear complexity, cube theory

摘要： 线性复杂度和k错线性复杂度是衡量流密码强度的重要指标，通常这两个指标越大就越能抗击明文攻击。为了更进一步地研究密钥流序列，利用构造方法和方体理论分析了具有第二下降点6错线性复杂度的2ⁿ周期序列，得到了所有可能6错线性复杂度的取值形式。分析并推导了具有2错线性复杂度为第一次下降点且6错线性复杂度为第二次下降点的2ⁿ周期序列的计数公式。使用这种方法也可以推导出其他具有第二次下降点或者第三次下降点的k错线性复杂度序列的相关性质。

关键词: 周期序列, 线性复杂度, k错线性复杂度, 方体理论