周期序列的線性復(fù)雜度及其穩(wěn)定性是序列密碼評價的重要度量指標(biāo).k-錯線性復(fù)雜度是線性復(fù)雜度穩(wěn)定性的一個重要評價指標(biāo).然而,目前對于大部分周期序列（除周期為2ⁿ、pⁿ、2pⁿ外）,尚無有效的算法求解其k-錯線性復(fù)雜度.因此,本文提出了一種混合的遺傳算法來近似計算任意周期序列的k-錯線性復(fù)雜度.采用輪盤賭、最優(yōu)保留策略、兩點交叉和單點隨機變異,并引入自適應(yīng)算子來調(diào)整交叉概率和變異概率,以保證遺傳算法的收斂性.通過并行計算適應(yīng)度函數(shù)來提高算法的效率,同時與模擬退火算法相結(jié)合,加速算法收斂并避免早熟.結(jié)果表明:當(dāng)k<8且周期小于256時,k-錯線性復(fù)雜度的實驗值僅比精確值高8%. 

【文章來源】：上海交通大學(xué)學(xué)報. 2020,54(06)北大核心

【文章頁數(shù)】：8 頁

【部分圖文】：

序列s1的k-錯線性復(fù)雜度實驗值和準(zhǔn)確值對比

s2={111001001011110001101100000011010110101 11110110110111111011100110101001011100101011 10001100010001010000001110001101000000101001 1},N=128s3={01011011011010000010011101010110110010 11010000011101011110010000010110110111011011 10101110011100110101010100100101111011011101 00101000101100000001100000111111010001111110 01100001110011010111010101111001100010010011 001010011111100001000011000101111000011010},N=256

s3={01011011011010000010011101010110110010 11010000011101011110010000010110110111011011 10101110011100110101010100100101111011011101 00101000101100000001100000111111010001111110 01100001110011010111010101111001100010010011 001010011111100001000011000101111000011010},N=256對比文獻[16]的實驗結(jié)果,周期為32的二元序列的5-錯線性復(fù)雜度的實驗結(jié)果比準(zhǔn)確值平均高19.5%.而本文算法可以計算周期為256的二元序列的8-錯線性復(fù)雜度,其實驗值僅比準(zhǔn)確值高8%.因此,本文算法不僅使可計算的N、k增加,還提高了算法的準(zhǔn)確性和效率.

【參考文獻】：
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