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.

中文翻译：

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基于 Hermitian 曲线的物联网安全密码系统设计

现代密码学的最终目标是保护信息资源，使其绝对牢不可破、不可妥协。然而，纵观密码学的历史，数以千计的密码系统出现并被认为是不可战胜的，然而攻击者却能够破坏和破坏他们的安全。本文的主要目标是设计一个适合在物联网中实施的健壮密码系统。所提出的密码系统基于代数几何曲线，更具体地说是基于 Hermitian 曲线。新的密码系统设计称为基于 Hermitian 的密码系统 (HBC)。在 HBC 设计的开发过程中，Kerckhoffs 的需求是主要的指导原则，通过选择 Hermitian 曲线作为建议设计的核心，这一原则得到了满足。所提出的 HBC 继承了 Hermitian 曲线的所有优点，即满足曲线的点数多和高属曲线。上述特性在为 HBC 生成大尺寸加密密钥和确定明文块大小方面起着至关重要的作用。由于 HBC 在 Hermitian 曲线上使用了代数几何代码，因此除了数据加密之外，它还具有执行纠错的能力。与许多现有的密码系统（如 McEliece 密码系统）相比，纠错是 HBC 的另一个优势。HBC 可以纠正的错误数量比其他代数几何代码（例如椭圆曲线和超椭圆曲线）要大（高数据速率）。它还使用非二进制表示，这增加了其抗攻击性。在本文中，提出的 HBC 已在数学上与椭圆曲线密码系统进行了比较。结果表明，HBC在点数和曲线属方面比椭圆曲线有很多优势。