Research Article Open Access

New Mersenne Number Transform Diffusion Power Analysis

M. F. Al-Gailani1 and S. Boussakta1
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American Journal of Engineering and Applied Sciences
Volume 4 No. 4, 2011, 461-469

DOI: https://doi.org/10.3844/ajeassp.2011.461.469

Submitted On: 19 September 2011 Published On: 12 January 2012

How to Cite: Al-Gailani, M. F. & Boussakta, S. (2011). New Mersenne Number Transform Diffusion Power Analysis. American Journal of Engineering and Applied Sciences, 4(4), 461-469. https://doi.org/10.3844/ajeassp.2011.461.469

Abstract

Problem statement: Due to significant developments in the processing power and parallel processing technologies, the existing encryption algorithms are increasingly susceptible to attacks, such as side-channel attacks, for example. Designing new encryption algorithms that work efficiently on different platforms and security levels to protect the transmitted data from any possible attacks is one of the most important issues in today’s information and network security. The aim is to find more secure, reliable and flexible systems that can run as a ratified standard, with reasonable computational complexity for a sufficient service time. To expand the longevity of the algorithm, it is important to be designed to work efficiently on a variety of block sizes and key lengths according to the security demand. A sensible solution is the suggested use of a parameter transform. Approach: The present study evaluates the appropriateness of the New Mersenne Number Transform for security applications by analyzing and estimating its avalanche and diffusion power. Results: The results confirm that the transform in general reflects good avalanche characteristics that are for most cases over 50% and can be up to 100%. The lower bound can be further improved by increasing the modulus and/or the transform length. Conclusion: This New Mersenne Number Transform is highly flexible and adaptable for this application. It can be involved in the design of a secure cryptosystem for the following reasons; changing a single input element makes drastic changes in the output elements and vice versa (sensitivity), provides variable block size and key length (parameterization). Has long transform length (power of two), is error free and its inverse is the same with a scale factor of (1/N) which simplifies implementation of both encryption and decryption. Finally, it is appropriate for real time implementations such as fast algorithms, which can be applied to it, to speed up processing.

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Keywords

  • Diffusion power
  • Number Theoretic Transform (NTT)
  • fast algorithms
  • parameter transform
  • Maximum Distance Separable (MDS)
  • Discrete Fourier Transform (DFT)