A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings

Area of Science:

• Cryptography
• Computer Science
• Applied Mathematics

Background:

• Elliptic curve (EC) cryptography offers high security with smaller key sizes compared to traditional cryptosystems.
• ECs over finite rings present enhanced security by increasing computational complexity for factorization and discrete logarithm problems.

Purpose of the Study:

• To propose a novel image encryption scheme utilizing elliptic curves over finite rings.
• To enhance image security against sophisticated cryptanalytic attacks.
• To improve encryption efficiency, particularly for color images.

Main Methods:

• The proposed scheme involves three main steps: masking the plain image using EC points over a finite ring.
• Diffusion is achieved through a mapping from EC over a finite ring to EC over a finite field.
• Confusion is generated using a substitution box (S-box) derived from an ordered EC for pixel permutation.

Main Results:

• The developed cryptosystem demonstrates higher security against linear, differential, and statistical attacks compared to existing methods.
• Computational experiments confirm the proposed scheme's effectiveness.
• The average encryption time for color images is found to be lower than that of other existing schemes.

Conclusions:

• The novel image encryption scheme based on ECs over finite rings provides a robust and efficient solution for secure image transmission.
• The method effectively balances high security with improved performance, making it a promising advancement in image cryptography.