Conic curve encryption and digital signature based on complex number theory for cybersecurity applications

Area of Science:

• Computer Science
• Cryptography
• Information Security

Background:

• Secure image transmission is critical, facing challenges from advanced cryptographic attacks.
• Elliptic Curve Cryptography (ECC) is widely used but vulnerable to side-channel and ECC-specific attacks.
• Existing methods require continuous innovation to address emerging security threats.

Purpose of the Study:

• To propose a novel authenticated and encrypted image scheme.
• To enhance security and performance by replacing ECC with Conic Curve Cryptography (CCC).
• To provide a robust solution for secure image transmission against modern cyber threats.

Main Methods:

• Implemented a public key cryptosystem based on multi-hard problems: Gaussian Conic Curve Integer Factorization Problem (GCC-IFP), Conic Curve Discrete Logarithm Problem (CC-DLP), and Conic Curve Integer Factorization Problem (CC-IFP).
• Integrated complex number theory with CCC for secure complex key exchange and utilized an Iterative Conic Curve Pseudorandom Number Generator (ICC-PRNG).
• Employed XOR operations for image encryption and developed a complex digital signature for encrypted images.

Main Results:

• Achieved high entropy (7.999) and low correlation (0.0001), indicating strong encryption.
• Demonstrated resilience against brute-force and statistical attacks with a large key space.
• Obtained an average PSNR of 8.51 dB and encryption times of 25 ms, suitable for real-time applications.
• NIST statistical tests confirmed the effectiveness of the ICC-PRNG.

Conclusions:

• The proposed Conic Curve Cryptography (CCC) based scheme offers superior security and efficiency compared to ECC.
• The integration of complex numbers and novel cryptographic problems provides robust protection for image data.
• This method presents a promising, secure, and efficient solution for advanced image encryption and transmission.