基于Keedwell交叉逆群的双重密码体制
A Double Cryptography Using The Keedwell Cross Inverse Quasigroup
摘要：
本研究进一步加强了使用Keedwell CIPQ对系统的攻击。这是按照如下方式完成的。研究了AIPQ（AIPL）和CIPQ（CIPL）的全纯结构.建立了拟群（圈）的全形是AIPQ（AIPL）或CIPQ（CIPL）的充要条件。证明了若拟群（圈）的全形是AIPQ（AIPL）或CIPQ（CIPL），则全形同构于拟群（圈）。因此，一个拟群（圈）的全同态是AIPQ（AIPL）或CIPQ（CIPL）当且仅当它的自同构群是平凡的，并且这个拟群（圈）是AIPQ（AIPL）或CIPQ（CIPL）。进一步证明了若拟群（圈）的全形是CIPQ（CIPL），则拟群（圈）是柔性幂幺CIPQ（指数为2的柔性CIPL）.通过构造两个同位素拟群（环）$U$和$V$使得它们的自同构群不是平凡的，证明了$U$是AIPQ或CIPQ（AIPL或CIPL）的充要条件是$V$是AIPQ或CIPQ（AIPL或CIPL）.给出了如何使用这些CIPQ对信息进行双重加密的说明和过程。
英文摘要：
The present study further strenghtens the use of the Keedwell CIPQ against attack on a system. This is done as follows. The holomorphic structure of AIPQs(AIPLs) and CIPQs(CIPLs) are investigated. Necessary and sufficient conditions for the holomorph of a quasigroup(loop) to be an AIPQ(AIPL) or CIPQ(CIPL) are established. It is shown that if the holomorph of a quasigroup(loop) is a AIPQ(AIPL) or CIPQ(CIPL), then the holomorph is isomorphic to the quasigroup(loop). Hence, the holomorph of a quasigroup(loop) is an AIPQ(AIPL) or CIPQ(CIPL) if and only if its automorphism group is trivial and the quasigroup(loop) is a AIPQ(AIPL) or CIPQ(CIPL). Furthermore, it is discovered that if the holomorph of a quasigroup(loop) is a CIPQ(CIPL), then the quasigroup(loop) is a flexible unipotent CIPQ(flexible CIPL of exponent 2). By constructing two isotopic quasigroups(loops) $U$ and $V$ such that their automorphism groups are not trivial, it is shown that $U$ is a AIPQ or CIPQ(AIPL or CIPL) if and only if $V$ is a AIPQ or CIPQ(AIPL or CIPL). Explanations and procedures are given on how these CIPQs can be used to double encrypt information.
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