The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups

T. AdamskiCorresponding authorInstitute of Electronic Systems Warsaw University of Technology 15/19 Nowowiejska St. 00-662 Warsaw PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar; W. NowakowskiInstitute of Mathematical Machines 34 Krzywickiego St. 02-078 Warsaw PolandOther articles by this author:De Gruyter OnlineGoogle Scholar

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The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups

机译：在有限循环组中查找生成器的概率算法的平均时间复杂度

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Generators of finite cyclic groups play important role in many cryptographic algorithms like public key ciphers, digital signatures, entity identification and key agreement algorithms. The above kinds of cryptographic algorithms are crucial for all secure communication in computer networks and secure information processing (in particular in mobile services, banking and electronic administration). In the paper, proofs of correctness of two probabilistic algorithms (for finding generators of finite cyclic groups and primitive roots) are given along with assessment of their average time computational complexity.

机译：有限循环组的生成器在许多密码算法中扮演着重要的角色，例如公钥密码，数字签名，实体标识和密钥协商算法。对于计算机网络中的所有安全通信和安全信息处理（尤其是在移动服务，银行和电子管理中），上述类型的密码算法至关重要。在本文中，给出了两种概率算法（用于查找有限循环群和原始根的生成器）的正确性的证明，并评估了它们的平均时间计算复杂性。

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《Bulletin of the Polish Academy of Sciences. Technical Sciences》 |2015年第4期|共页
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T. AdamskiCorresponding authorInstitute of Electronic Systems Warsaw University of Technology 15/19 Nowowiejska St. 00-662 Warsaw PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar; W. NowakowskiInstitute of Mathematical Machines 34 Krzywickiego St. 02-078 Warsaw PolandOther articles by this author:De Gruyter OnlineGoogle Scholar;
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1. The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups [J] . Adamski T., Nowakowski W. Bulletin of the Polish Academy of Sciences. Technical Sciences . 2015,第4期

机译：在有限循环组中查找生成器的概率算法的平均时间复杂度
2. The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups [J] . T. Adamski, W. Nowakowski Bulletin of the Polish Academy of Sciences. Technical Sciences . 2015,第4期

机译：在有限循环组中查找生成器的概率算法的平均时间复杂度
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The average time complexity of probabilistic algorithms for finding generators in finite cyclic groups

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