中文摘要：

在秘密共享方案中，存在欺骗者提供伪造分存参与秘密重构的行为，欺骗者可得到秘密而其他诚实参与者可能得不到秘密．靳蕃利用复数旋转码构造了（k，n）-秘密共享方案，分析靳蕃构造的基于复数旋转码的（k，n）-秘密共享方案，利用复数旋转码的性质对其进行防欺骗扩展——在分发过程中，计算一个检验值，利用该检验值进行欺骗检测与识别，使其可识别任意数目的欺骗者．改进靳蕃的（k，n）-秘密共享方案的重构算法，使其重构一个秘密码元的计算次数从2（p-1）次XOR运算减少到（P＋1）＋（p-1）／p^2次XOR运算．

英文摘要：

In a secret sharing scheme, there may be some cheaters who reconstruct the secret by presenting faked shares. The cheaters may recover the secret, while honest participants get no information on it. JIN Fan used complex-rotary codes to construct a （k,n）-secret sharing scheme. By analyzing JIN Fan＇s （k,n）- threshold secret sharing scheme based-on complex-rotary codes, the authors extended JIN Fan＇s secret sharing scheme and made it resistent to cheating. A secret detection value of the distribution phase of the JIN Fan＇s scheme was added, with which cheating can be detected and cheaters can be identified, no matter how many cheaters are involved in the secret reconstruction. Improving the reconstruction algorithm of JIN Fan＇s （k,n）-secret sharing scheme, makes it possible to reduce the number of computations to recover a secret code from 2（p-1） to （p＋1）＋（P-1）/P2.