A Novel Image Encryption Technique Based on Mobius Transformation

Area of Science:

• Cryptography
• Galois Fields
• Number Theory

Background:

• S-boxes are crucial for block cipher security, providing nonlinear transformation.
• Existing S-box constructions require rigorous cryptographic analysis for effectiveness.
• The projective general linear group PGL(2, GF(2^8)) offers a novel algebraic structure for S-box design.

Purpose of the Study:

• To propose novel S-boxes with enhanced cryptographic properties.
• To evaluate the performance of these S-boxes using established cryptographic tests.
• To demonstrate the application of these S-boxes in a secure image encryption scheme.

Main Methods:

• Constructing S-boxes using Mobius transformations and elements from the Galois field GF(2^8).
• Applying the projective general linear group PGL(2, GF(2^8)) for S-box generation.
• Evaluating S-box strength via tests including BIC, SAC, DP, LP, and nonlinearity.

Main Results:

• The proposed S-boxes exhibit strong algebraic properties and confusion capabilities.
• Image encryption using the proposed S-boxes showed improved contrast, entropy, correlation, energy, and homogeneity.
• The developed S-boxes outperformed previous ones in cryptographic analysis.

Conclusions:

• The novel S-boxes provide robust security for block ciphers and image encryption.
• The use of PGL(2, GF(2^8)) and Mobius transformations yields high-quality cryptographic primitives.
• The proposed image encryption scheme effectively secures confidential image data during transmission.