A chaotic digital signature algorithm based on a dynamic substitution box
Abstract Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In...
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Nature Portfolio
2025-01-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-83943-x |
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| author | Rolando Flores-Carapia Víctor Manuel Silva-García Manuel Alejandro Cardona-López Miguel Gabriel Villarreal-Cervantes |
| author_facet | Rolando Flores-Carapia Víctor Manuel Silva-García Manuel Alejandro Cardona-López Miguel Gabriel Villarreal-Cervantes |
| author_sort | Rolando Flores-Carapia |
| collection | DOAJ |
| description | Abstract Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In this research, we propose the DSADH $$\pi$$ algorithm, which introduces a confusion step directly into the signature itself, rather than only applying it to the message, using a dynamic substitution box. It is generated with the number pi and changes with each signing. In addition, to enhance security, this work uses a 2048-bit prime, double the length frequently used. This proposal induces chaotic behavior in the signature, making it highly sensitive to any changes in the signer’s private key or message content, thereby enhancing authentication and integrity verification. Moreover, the proposed algorithm computes a single multiplicative modular inverse during verification and none during signing, unlike other approaches that require inverse computation in both stages. Since the required inverse is for the Diffie-Hellman session key, it always exists and can be precomputed per communication rather than per message. Consequently, DSADH $$\pi$$ is on average 45 times faster than DSA. Additionally, we introduce a method to assess signature security by constructing images from signature bytes generated by slight changes to the signer’s private key and message. Then, their chaotic behavior is evaluated with cryptographic metrics. |
| format | Article |
| id | doaj-art-7470dac0edeb4aa59d50de15189462ce |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-7470dac0edeb4aa59d50de15189462ce2025-01-19T12:22:39ZengNature PortfolioScientific Reports2045-23222025-01-0115111310.1038/s41598-024-83943-xA chaotic digital signature algorithm based on a dynamic substitution boxRolando Flores-Carapia0Víctor Manuel Silva-García1Manuel Alejandro Cardona-López2Miguel Gabriel Villarreal-Cervantes3Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico NacionalCentro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico NacionalCentro de Investigación en Computación, Instituto Politécnico NacionalCentro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico NacionalAbstract Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In this research, we propose the DSADH $$\pi$$ algorithm, which introduces a confusion step directly into the signature itself, rather than only applying it to the message, using a dynamic substitution box. It is generated with the number pi and changes with each signing. In addition, to enhance security, this work uses a 2048-bit prime, double the length frequently used. This proposal induces chaotic behavior in the signature, making it highly sensitive to any changes in the signer’s private key or message content, thereby enhancing authentication and integrity verification. Moreover, the proposed algorithm computes a single multiplicative modular inverse during verification and none during signing, unlike other approaches that require inverse computation in both stages. Since the required inverse is for the Diffie-Hellman session key, it always exists and can be precomputed per communication rather than per message. Consequently, DSADH $$\pi$$ is on average 45 times faster than DSA. Additionally, we introduce a method to assess signature security by constructing images from signature bytes generated by slight changes to the signer’s private key and message. Then, their chaotic behavior is evaluated with cryptographic metrics.https://doi.org/10.1038/s41598-024-83943-xChaosDiffie-Hellman ProtocolDigital SignatureNumber PiSubstitution Box |
| spellingShingle | Rolando Flores-Carapia Víctor Manuel Silva-García Manuel Alejandro Cardona-López Miguel Gabriel Villarreal-Cervantes A chaotic digital signature algorithm based on a dynamic substitution box Scientific Reports Chaos Diffie-Hellman Protocol Digital Signature Number Pi Substitution Box |
| title | A chaotic digital signature algorithm based on a dynamic substitution box |
| title_full | A chaotic digital signature algorithm based on a dynamic substitution box |
| title_fullStr | A chaotic digital signature algorithm based on a dynamic substitution box |
| title_full_unstemmed | A chaotic digital signature algorithm based on a dynamic substitution box |
| title_short | A chaotic digital signature algorithm based on a dynamic substitution box |
| title_sort | chaotic digital signature algorithm based on a dynamic substitution box |
| topic | Chaos Diffie-Hellman Protocol Digital Signature Number Pi Substitution Box |
| url | https://doi.org/10.1038/s41598-024-83943-x |
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