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A graph theoretic method for securing key fobs
Mathematical Sciences ( IF 2 ) Pub Date : 2020-11-26 , DOI: 10.1007/s40096-020-00363-4
Farideh Heydari , Alireza Ghahremanian

Key fobs are small security hardware devices that are used for controlling access to doors, cars and etc. There are many types of these devices, more secure types of them are rolling code. They often use a light weight cryptographic schemas to protect them against the replay attack. In this paper, by the mean of constructing a Hamiltonian graph, we propose a simple to implement and secure method which overrides some drawbacks of traditional ones. Let \(m,n>1\) be two integers, and \({\mathbb {Z}}_n\) be a \({\mathbb {Z}}_m\)-module. Here, we determine the values of m and n for which the \({\mathbb {Z}}_n\)-intersection graph of ideals of \({\mathbb {Z}}_m\) is Hamiltonian. Then a suitable sequence will be produced which by some criteria can be used as the authenticator.



中文翻译:

一种保护密钥卡的图论方法

密钥卡是用于控制对门,汽车等的访问的小型安全硬件设备。这些设备有很多类型,其中更安全的类型是滚动代码。他们经常使用轻量级的加密模式来保护它们免受重放攻击。在本文中,通过构造哈密顿图,我们提出了一种易于实现且安全的方法,该方法克服了传统方法的一些缺点。令\(m,n> 1 \)为两个整数,而\({\ mathbb {Z}} _ n \)\({\ mathbb {Z}} _ m \)-模块。在这里,我们确定的值Ñ的量,\({\ mathbb {Z}} _Ñ\)的理想曲线图-intersection \({\ mathbb {Z}} _米\)是哈密尔顿。然后将产生合适的序列,该序列可以通过某些标准用作验证者。

更新日期:2020-11-27
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