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A highly nonlinear S-box based on a fractional linear transformation.
Shabieh Farwa1, Tariq Shah2, Lubna Idrees1
1Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, Pakistan.
Springerplus
|October 13, 2016
Summary
This study introduces a new S-box, created using fractional linear transformations, offering strong data confusion. Its cryptographic strength is validated through rigorous analysis for potential use in image encryption.
Area of Science:
- Cryptography
- Number Theory
- Computer Science
Background:
- S-boxes are crucial components in symmetric-key cryptography, providing confusion.
- Fractional linear transformations over Galois fields offer a basis for constructing cryptographic primitives.
Purpose of the Study:
- To design and analyze a novel S-box using fractional linear transformations.
- To evaluate the cryptographic strength and suitability of the proposed S-box for image encryption.
Main Methods:
- Constructing an S-box via fractional linear transformation on the Galois field GF(2^8).
- Analyzing S-box properties: nonlinearity, strict avalanche criterion, bit independence, linear approximation probability, and differential approximation probability.
- Applying the majority logic criterion for image encryption effectiveness assessment.
Main Results:
- The proposed S-box exhibits a high degree of confusion.
- Key cryptographic properties were rigorously analyzed and found to be favorable.
- The S-box demonstrated effectiveness in preliminary image encryption tests.
Conclusions:
- The novel S-box, based on fractional linear transformations, presents a strong candidate for cryptographic applications.
- Its robust performance in confusion and other cryptographic metrics supports its use in secure systems, particularly image encryption.
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