CAJ | 학술논문

密码学意义上强的序列不仅应该具有高的线性复杂度而且其线性复杂度必须稳定,k-错线性复杂度用来反应线性复杂度的稳定性.本文基于xpm2n-1在GF(2)上具有明确的分解式,研究了pm2n-周期二元序列的线性复杂度和k-错线性复杂度之间的关系,然后说明了同时使得线性复杂度和k-错线性复杂度都达到最大值的pm2n-周期二元序列是存在的.这里p是一个奇素数,2是模p2的本原根.
밀마학의의상강적서렬불부응해구유고적선성복잡도이차기선성복잡도필수은정,k-착선성복잡도용래반응선성복잡도적은정성.본문기우xpm2n-1재GF(2)상구유명학적분해식,연구료pm2n-주기이원서렬적선성복잡도화k-착선성복잡도지간적관계,연후설명료동시사득선성복잡도화k-착선성복잡도도체도최대치적pm2n-주기이원서렬시존재적.저리p시일개기소수,2시모p2적본원근.
Cryptographically strong sequences should not only have a high linear complexity, but also altering a few terms should not cause a significant decline of the linear complexity. This requirement leads to the concept of the k-error linear complexity of periodic sequences.Based on the explicit factorization of xpm2n - 1 over GF(2), this correspondence focuses on the relationship between the linear complexity and the k-error linear complexity of the pm2n-periodic binary sequences, where p is an odd prime number, 2 is a primitive root modulo p2. Then we establish the existence of pm2n-periodic sequences which simultaneously achieve the maximum value of the linear complexity and the k-error linear complexity.