Construction of a cryptographic function based on Bose-type Sidon sets

Julian Osorio; Carlos Trujillo; Diego Ruiz; Julian Osorio; Carlos Trujillo; Diego Ruiz

doi:10.3934/math.2024855

AIMS Mathematics

2024, Volume 9, Issue 7: 17590-17605. doi: 10.3934/math.2024855

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Construction of a cryptographic function based on Bose-type Sidon sets

Department of Mathematics, Universidad del Cauca, Cauca, Colombia

Received: 30 January 2024 Revised: 21 March 2024 Accepted: 25 March 2024 Published: 22 May 2024
MSC : Primary: 43A46, 11T71; Secondary: 12E20

Sidon sets have several applications in mathematics and in real-world problems, including the generation of secret keys in cryptography, error-correcting codes, and the physical problem of compression of signals in telecommunications. In particular, in cryptography, the design of cryptographic functions with optimal properties like nonlinearity and differential uniformity plays a fundamental role in the development of secure cryptographic systems. Based on the construction of Bose-type Sidon sets, in this paper we present the construction of a new cryptographic function with good properties of nonlinearity and differential uniformity.
- cryptography,
- linearity,
- differential uniformity,
- Sidon sets,
- APN functions
Citation: Julian Osorio, Carlos Trujillo, Diego Ruiz. Construction of a cryptographic function based on Bose-type Sidon sets[J]. AIMS Mathematics, 2024, 9(7): 17590-17605. doi: 10.3934/math.2024855

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Abstract

Sidon sets have several applications in mathematics and in real-world problems, including the generation of secret keys in cryptography, error-correcting codes, and the physical problem of compression of signals in telecommunications. In particular, in cryptography, the design of cryptographic functions with optimal properties like nonlinearity and differential uniformity plays a fundamental role in the development of secure cryptographic systems. Based on the construction of Bose-type Sidon sets, in this paper we present the construction of a new cryptographic function with good properties of nonlinearity and differential uniformity.

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