Conic curve encryption and digital signature based on complex number theory for cybersecurity applications
Abstract Secure image transmission requires robust algorithms to ensure authentication, integrity, non-repudiation, and confidentiality. Addressing emerging security challenges necessitates continuous advancements in cryptographic design. This paper presents an authenticated and encrypted image sche...
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| Format: | Article |
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-00334-6 |
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| author | Ahmed Kamal H. A. El-Kamchochi Adel El-Fahar Esam A. A. Hagras |
| author_facet | Ahmed Kamal H. A. El-Kamchochi Adel El-Fahar Esam A. A. Hagras |
| author_sort | Ahmed Kamal |
| collection | DOAJ |
| description | Abstract Secure image transmission requires robust algorithms to ensure authentication, integrity, non-repudiation, and confidentiality. Addressing emerging security challenges necessitates continuous advancements in cryptographic design. This paper presents an authenticated and encrypted image scheme that achieves all essential security services. While Elliptic curve cryptography (ECC) remains a fundamental component of recent encryption schemes, it is vulnerable to side-channel and inherent ECC-specific attacks. To overcome these vulnerabilities, the proposed scheme replaces ECC with Conic curve cryptography (CCC), offering enhanced security and performance. The integration of complex number theory with CCC enables a secure complex key exchange and incorporates a robust Iterative conic curve pseudorandom number generator (ICC-PRNG) to thwart all known attack types. The system is a public key cryptosystem based on multi-hard problems, including the Gaussian conic curve integer factorization problem (GCC-IFP), Conic curve discrete logarithm problem (CC-DLP), and Conic curve integer factorization problem (CC-IFP), combined with XOR operations for image encryption. Additionally, the scheme introduces a novel complex digital signature for encrypted images, leveraging complex arithmetic to enhance security. Experimental results demonstrate high entropy 7.999, correlation near 0.0001, key space $$>{2}^{688}$$ , and average PSNR of 8.51 dB, ensuring resilience against brute-force and statistical attacks. Additionally, the scheme achieves encryption times of 25 ms, making it suitable for real-time applications. Security analysis validates robustness against various attacks, with NIST statistical tests confirming ICC-PRNG effectiveness. By leveraging complex numbers over conic curves, the proposed method improves security and computational efficiency, establishing it as a promising solution for advanced image encryption. |
| format | Article |
| id | doaj-art-d841b171d0834a9ca5e433b1da9f3ccd |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-d841b171d0834a9ca5e433b1da9f3ccd2025-08-20T03:45:27ZengNature PortfolioScientific Reports2045-23222025-07-0115112810.1038/s41598-025-00334-6Conic curve encryption and digital signature based on complex number theory for cybersecurity applicationsAhmed Kamal0H. A. El-Kamchochi1Adel El-Fahar2Esam A. A. Hagras3Engineering Department, Air Defense College, Alexandria UniversityElectrical Department, Faculty of Engineering, Alexandria UniversityElectrical Department, Faculty of Engineering, Alexandria UniversityElectronics and Communications Department, Faculty of Engineering, Delta University for Science and TechnologyAbstract Secure image transmission requires robust algorithms to ensure authentication, integrity, non-repudiation, and confidentiality. Addressing emerging security challenges necessitates continuous advancements in cryptographic design. This paper presents an authenticated and encrypted image scheme that achieves all essential security services. While Elliptic curve cryptography (ECC) remains a fundamental component of recent encryption schemes, it is vulnerable to side-channel and inherent ECC-specific attacks. To overcome these vulnerabilities, the proposed scheme replaces ECC with Conic curve cryptography (CCC), offering enhanced security and performance. The integration of complex number theory with CCC enables a secure complex key exchange and incorporates a robust Iterative conic curve pseudorandom number generator (ICC-PRNG) to thwart all known attack types. The system is a public key cryptosystem based on multi-hard problems, including the Gaussian conic curve integer factorization problem (GCC-IFP), Conic curve discrete logarithm problem (CC-DLP), and Conic curve integer factorization problem (CC-IFP), combined with XOR operations for image encryption. Additionally, the scheme introduces a novel complex digital signature for encrypted images, leveraging complex arithmetic to enhance security. Experimental results demonstrate high entropy 7.999, correlation near 0.0001, key space $$>{2}^{688}$$ , and average PSNR of 8.51 dB, ensuring resilience against brute-force and statistical attacks. Additionally, the scheme achieves encryption times of 25 ms, making it suitable for real-time applications. Security analysis validates robustness against various attacks, with NIST statistical tests confirming ICC-PRNG effectiveness. By leveraging complex numbers over conic curves, the proposed method improves security and computational efficiency, establishing it as a promising solution for advanced image encryption.https://doi.org/10.1038/s41598-025-00334-6Elliptic curve cryptographyConic curve cryptographySecure image transmissionInteger factorization problemPublic key cryptosystemDiscrete logarithm problem |
| spellingShingle | Ahmed Kamal H. A. El-Kamchochi Adel El-Fahar Esam A. A. Hagras Conic curve encryption and digital signature based on complex number theory for cybersecurity applications Scientific Reports Elliptic curve cryptography Conic curve cryptography Secure image transmission Integer factorization problem Public key cryptosystem Discrete logarithm problem |
| title | Conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| title_full | Conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| title_fullStr | Conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| title_full_unstemmed | Conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| title_short | Conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| title_sort | conic curve encryption and digital signature based on complex number theory for cybersecurity applications |
| topic | Elliptic curve cryptography Conic curve cryptography Secure image transmission Integer factorization problem Public key cryptosystem Discrete logarithm problem |
| url | https://doi.org/10.1038/s41598-025-00334-6 |
| work_keys_str_mv | AT ahmedkamal coniccurveencryptionanddigitalsignaturebasedoncomplexnumbertheoryforcybersecurityapplications AT haelkamchochi coniccurveencryptionanddigitalsignaturebasedoncomplexnumbertheoryforcybersecurityapplications AT adelelfahar coniccurveencryptionanddigitalsignaturebasedoncomplexnumbertheoryforcybersecurityapplications AT esamaahagras coniccurveencryptionanddigitalsignaturebasedoncomplexnumbertheoryforcybersecurityapplications |