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Cryptosystem design based on Hermitian curves for IoT security

机译:基于Hermitian曲线对IoT安全的密码系统设计

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The ultimate goal of modern cryptography is to protect the information resource and make it absolutely unbreakable and beyond compromise. However, throughout the history of cryptography, thousands of cryptosystems emerged and believed to be invincible and yet attackers were able to break and compromise their security. The main objective of this paper is to design a robust cryptosystem that will be suitable to be implemented in Internet of Things. The proposed cryptosystem is based on algebraic geometric curves, more specifically on Hermitian curves. The new cryptosystem design is called Hermitian-based cryptosystem (HBC). During the development of the HBC design, Kerckhoffs's desideratum was the main guidance principle, which has been satisfied by choosing the Hermitian curves as the core of the proposed design. The proposed HBC inherits all the advantageous characteristics of Hermitian curve which are large number of points that satisfy the curve and high genus curves. The aforementioned characteristics play a crucial role in generating a large size encryption key for HBC and determine the block size of plaintext. Due to the fact that HBC used algebraic geometric codes over Hermitian curve, it has the ability to perform error correction in addition to data encryption. The error correction is another advantage of HBC compared with many existing cryptosystems such as McEliece cryptosystem. The number of errors that can be corrected by HBC is larger (high data rate) than other algebraic geometric codes such as elliptic and hyperelliptic curves. It also uses non-binary representation which increases its attack resistance. In this paper, the proposed HBC has been mathematically compared with elliptic curve cryptosystem. The results show that HBC has many advantages over the elliptic curves in terms of number of points and genus of the curve.
机译:现代密码学的最终目标是保护信息资源,使其绝对不可用,超越妥协。然而,在整个密码学的历史中,出现了数千个密码系统并认为是不可实现的,但攻击者能够打破和妥协他们的安全。本文的主要目的是设计一种强大的密码系统,这些系统将适合在物联网中实施。所提出的密码系统基于代数几何曲线,更具体地说在隐士曲线上。新的密码系统设计被称为基于Hermitian的密码系统(HBC)。在HBC设计的发展期间,Kerckhoffs的船长是主要指导原则,通过选择隐士曲线作为所提出的设计的核心,已经满足。所提出的HBC继承了密封曲线的所有有利特征,这些特征是满足曲线和高属曲线的大量点。上述特征在为HBC生成大尺寸加密密钥并确定明文的块大小来发挥至关重要的作用。由于HBC使用了Hermitian曲线上的代数几何代码,除了数据加密之外,它还能够执行纠错。纠错是HBC与诸如MECELIES密码系统的许多现有密码系统相比的另一个优点。可以由HBC校正的错误数量比其他代数几何代码(如椭圆形和超细曲线)更大(高数据速率)。它还使用非二进制表示,这增加了其攻击阻力。在本文中,与椭圆曲线密码系统进行了拟议的HBC。结果表明,HBC在曲线的点数和属的数量方面具有椭圆曲线的许多优点。

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