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首页> 外文会议>International Conference on Mathematical Sciences and Technology >Some Properties of Continued Fraction Expansions Related to Certain Sequence of Integers and its Applications in Elliptic Curve Cryptography
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Some Properties of Continued Fraction Expansions Related to Certain Sequence of Integers and its Applications in Elliptic Curve Cryptography

机译：与某些整数序列相关的持续分数扩展的一些性质及其在椭圆曲线密码中的应用

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摘要

In this paper, we consider the sequence of integers r_i, S_i, t_i ∈ Z of regular continued fraction (RCF) expansions generated from the extended Euclidean algorithm. These sequences always satisfy r_i = s_ia + t_ib where r_i is a remainder whereas s_i and t_i arising from the extended Euclidean algorithm are equal, up to sign, to the convergent of the continued fraction expansion of a/b. We discuss the behavior of these sequences and provide their full proof in detail with their simple calculation of sample. Throughout this work, we deal with the concept of Euclidean algorithm and extended Euclidean algorithm together with continued fraction algorithm. These algorithms are involved in the improvement of computational efficiency of the elliptic curve cryptography (ECC). Henceforth from that, we tend to associate these sequences in ECC. Last but not least, we found that the value of integers (r_i, s_i, t_i) satisfy various properties in RCF which then used to solve the shortest vector problem in representing point multiplications in ECC, namely the Gallant, Lambert & Vanstone (GLV) integer decomposition method and the integer sub decomposition (ISD) method.
机译：在本文中，我们考虑了从扩展欧几里德算法产生的常规持续分数（RCF）扩展的整数R_I，S_I，T_I∈Z的序列。这些序列总是满足R_I = S_IA + T_IB，其中R_I是剩余的，而从扩展的欧几里德算法产生的S_I和T_I等于符号，以签署A / B的持续分数扩展的会聚。我们讨论了这些序列的行为，并通过简单计算样品来提供完整的证明。在这项工作中，我们处理欧几里德算法的概念和扩展欧几里德算法以及持续的分数算法。这些算法涉及提高椭圆曲线密码学（ECC）的计算效率。从此以上，我们倾向于将这些序列与ECC相关联。最后但并非最不重要的是，我们发现整数（R_I，S_I，T_I）的值满足RCF中的各种属性，然后用于解决ECC中代表点乘法的最短传感器问题，即巫师，Lambert＆Vanstone（GLV）整数分解方法和整数子分解（ISD）方法。

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