关于奥斯本循环中的密码身份
On A Cryptographic Identity In Osborn Loops
摘要：
本文挖掘了Osborn圈的一些新的代数性质，这将有助于揭示Osborn圈的中内映射$T_{(x)}$的奥秘。这些新的代数性质，将使我们对诸如CC-环的Osborn环的研究更加开阔，而在$21^\textrm{st}$和VD-环的研究中，CC-环已经受到了广泛的关注，而VD-环的研究还有待于进一步的探讨。在这项研究中，对非WIP Osborn环的一些代数性质进行了广泛的研究。Huthnance能够利用泛弱WIPL推导Osborn圈的一些代数性质。因此，这项工作免除了。首次引入了两个新的环恒等式，即左自逆性质环（LSIPL）恒等式和右自逆性质环（RSLPL）恒等式，并证明了它们在Osborn环中是等价的.一个CC-循环被证明是功率关联的，当且仅当它是RSLPL或LSIPL。在已经为Osborn循环建立的少数恒等式中，其中一个恒等式被认可并推荐用于密码学，其具有类似的精神，其中Keedwell已经使用了交叉逆属性，因为观察到Osborn循环不具有LSIP或RSIP或3-PAPL或更弱形式的逆属性，幂结合性和非结合性，仅举几例，会有周期（甚至是长周期）。这些身份被称为Osborn密码身份（或只是密码身份）。
英文摘要：
This study digs out some new algebraic properties of an Osborn loop that will help in the future to unveil the mystery behind the middle inner mappings $T_{(x)}$ of an Osborn loop. These new algebraic properties, will open our eyes more to the study of Osborn loops like CC-loops which has received a tremendious attention in this $21^\textrm{st}$ and VD-loops whose study is yet to be explored. In this study, some algebraic properties of non-WIP Osborn loops have been investigated in a broad manner. Huthnance was able to deduce some algebraic properties of Osborn loops with the WIP i.e universal weak WIPLs. So this work exempts the WIP. Two new loop identities, namely left self inverse property loop(LSIPL) identity and right self inverse property loop(RSLPL) are introduced for the first time and it is shown that in an Osborn loop, they are equivalent. A CC-loop is shown to be power associative if and only if it is a RSLPL or LSIPL. Among the few identities that have been established for Osborn loops, one of them is recognized and recommended for cryptography in a similar spirit in which the cross inverse property has been used by Keedwell following the fact that it was observed that Osborn loops that do not have the LSIP or RSIP or 3-PAPL or weaker forms of inverse property, power associativity and diassociativity to mention a few, will have cycles(even long ones). These identity is called an Osborn cryptographic identity(or just a cryptographic identity).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
