Mathematics as a basis for the generation of cryptographic tools
This article is the product of the research “Mathematics as a basis for the generation of cryptographic tools”, developed at the Universidad de Cundinamarca, sectional Ubaté in the year 2021.
Problem: Improve the security of code with differential calculus, plane and spatial geometry, polar coordinates, and functions; the resulting encryption should improve on the standards of current encryption systems.
Objective: Explain the algorithm’s operation with fundamental issues that use and generate a modification proposal to make the algorithm more robust when subjected to an attack by unethical hackers.
Methodology: A bibliographic review, encryption codes, history of algorithms, and operation of SHA-256 in the Ethereum platform and Bitcoin explains how it works and gives an idea of how to improve security.
Result: The algorithm’s operation is explained step by step using subject topics such as precalculus and calculus. Also, topics such as functions, truth tables, logical operators, programming functions, and a way to complicate the algorithm were proposed by applying issues of plane geometry, space, polar coordinates, ceiling function, and absolute values.
Conclusion: It is possible to assimilate the operation of SHA-256 (256-bit secure hash algorithm) and the mathematical basis for generating codes in hexadecimal, depending on the message to be encrypted. Algebraic models allow taking different points of the figures generated in the Cartesian and polar planes to use them as a means of encryption.
Originality: Explaining an algorithm widely used in encryption issues; however, according to a survey conducted, only a few understood the code that explains the mathematics, all the aspects behind its operation, and why it is so secure. In addition, the project proposes a way to improve its security.
Limitations: The algorithm used was a hyperbolic and linear function combined. In this sense, common random points between the two functions are selected for encryption, and it is not aligned with the encryption systems used in blockchains; it is a restriction for the implementation. Currently, several updates are aligned with the SHA-256 system, involving limiting the inclusion of updated models.
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