Number Theoretic Transforms and their Applications in Image Processing

“…which is the generator matrix of the Hamming code H (7,4,3). Note that 7 − log 2 (1 + 7) = 4 = dim V. Figure 1 shows the implementation of the binary Hamming Transform 7 × 7.…”

Section: (λ)mentioning

confidence: 99%

The Hamming and Golay Number-Theoretic Transforms

Paschoal¹,

Souza²,

Oliveira³

2018

Anais De XXXVI Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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“…NTTs use modular arithmetic operations on a field or ring of integers, without the errors inherent to normal floating-point operations, such as those found in the Discrete Fourier Transform (DFT) for example. NTTs have wide applications in different areas including; digital signal processing (Agarwal, 1980), digital filtering (Agarwal and Burrus, 1974;Boussakta and Holt, 1994), image processing (Boussakta and Holt, 1999), decoding (Reed et al, 1978) and cryptography (Yang et al, 2010;Yang and Boussakta, 2008).…”

Section: New Mersenne Number Transform (Nmnt)mentioning

confidence: 99%

New Mersenne Number Transform Diffusion Power Analysis

J.¹

2011

American Journal of Engineering and Applied Sciences

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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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“…Extensive experiment results suggest that the block cipher size has to be at least 128 bits or more in practical for security reason and it can be extended to a greater length with different requirements. Further to this, implementation of this transform can be computed through a radix-2 fast algorithm explained clearly in [3,4].…”

Section: New Algorithm Based On Nttsmentioning

confidence: 99%

“…The transform used in this proposed system is achieved through the derivation of a fast orthogonal transitional transform allowing the transition from one transform domain to another, called T transform [3,4]. The T transform is calculated by multiplying the WalshHadamard Transform (WHT) and the Fermat Number Transform (FNT) in a bit-row-reverse order:…”

Section: Introduction To T Transformmentioning

confidence: 99%

A New Development of Symmetric Key Cryptosystem

Yang

Boussakta

2008

2008 IEEE International Conference on Communications

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Security issues have become a main concern modern life. A powerful cryptosystem has to be practical, secure and able to be implemented on different platforms. The goal of this paper is to develop a basis of cryptographic scheme which utilizes some advanced transform techniques. A symmetric cryptographic system is proposed based on Shannon's concepts of "confusion" and "diffusion". It possesses high security levels as well as many other advantages.

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Number Theoretic Transforms and their Applications in Image Processing

Cited by 16 publications

References 72 publications

The Hamming and Golay Number-Theoretic Transforms

The Hamming and Golay Number-Theoretic Transforms

New Mersenne Number Transform Diffusion Power Analysis

A New Development of Symmetric Key Cryptosystem

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