We consider a special type of sequence of arithmetic progressions, in which consecutive progressions are related by the property: i^thterms ofj^th, (j + 1)^thprogressions of the sequence are multiplicative inverses of each other modulo(i + 1)^thterm ofj^thprogression. Such a sequence is uniquely defined for any pair of co-prime numbers. A computational problem, defined in the context of such a sequence and its generalization, is shown to be equivalent to the integer factoring problem. The proof is probabilistic. As an application of the equivalence result, we propose a method for how users securely agree upon secret keys, which are ensured to be random. We compare our method with factoring based public key cryptographic systems: RSA (Rivest et al., ACM 21, 120–126, 1978) and Rabin systems (Rabin 1978). We discuss the advantages of the method, and its potential use-case in the post quantum scenario.

中文翻译：

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一定的算术级数序列和新的密钥共享方法

我们认为一种特殊类型的算术级数的序列，其中连续级数由酒店相关：我^吨ħ方面Ĵ^吨ħ，（Ĵ + 1）^吨ħ序列的级数彼此模的乘法逆（我+ 1）^吨ħ的术语Ĵ^吨ħ进展。这样的序列是针对任意一对互质数唯一定义的。在这种序列及其概括的上下文中定义的计算问题显示为等效于整数分解问题。证明是概率性的。作为等效结果的一种应用，我们提出了一种方法，用于确保用户如何安全地同意确保随机密钥的秘密密钥。我们比较我们的方法与基于保公钥密码系统：RSA（维斯特等人，ACM，21和拉宾系统（拉宾1978年），120-126，1978）。我们讨论了该方法的优点及其在后量子场景中的潜在用例。