New transform using the Mersenne numbers

Boussakta, S.; Holt, A.G.J.

doi:10.1049/ip-vis:19952323

Cited by 39 publications

(12 citation statements)

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“…The 2-D transform will increase the strength of confusion, although it would not change the data diffusion. However, if the T transform is replaced by any other member of NTTs, such as the New Mersene Number Transform (NMNT) [10,11], the diffusion and confusion will be both strengthened by PT '=(112,190,171,199,71,54,111,47,31,192,205 CipherText: ¶ # ¤ ì 6 ù Y à i ë É Á L î…”

Section: System Discussionmentioning

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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Section: System Discussionmentioning

confidence: 99%

A New Development of Symmetric Key Cryptosystem

Yang

Boussakta

2008

2008 IEEE International Conference on Communications

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“…However, if this NMNT is employed in the convolution calculation, these sign choices will not affect the final output. 9 Then, 1 (n) and 2 (n) must obey 9 In real-world applications, N can be smaller than the N max in Table I, such as the choice of (N, M p , 1 , 2 ) = (8, 31, −4, 4).…”

Section: New Mersenne Number Transformmentioning

confidence: 99%

“…5 Among all NTTs, there are two kinds of transform attracted much attentions, ie, the Fermat number transform (FNT) and the Mersenne number transform (MNT). In order to tackle this issue, people proposed the NMNT in Boussakta and Holt, 9 in which both the Mersenne number and the FNT-like transform length were derived, leading to a fast realization through FFT. 6,7 Specifically, the FNT length can be power of two, then the multiplication can be replaced by the shift-addition operation, resulting in faster computation than conventional FFT or Hartley transform.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, there does not exist the fast realization of NMT analogous to FFT. In order to tackle this issue, people proposed the NMNT in Boussakta and Holt, 9 in which both the Mersenne number and the FNT-like transform length were derived, leading to a fast realization through FFT. The fast realization of NMNT could be found as the radix-2 NMNT, 10 radix-4 NMNT, 11 and the Rader-Brenner NMNT.…”

Section: Introductionmentioning

confidence: 99%

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A fast realization of new Mersenne number transformation and its applications

Hua

Liu

et al. 2019

Circuit Theory & Apps

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The new Mersenne number transform (NMNT) can be realized by the fast Fourier transform (FFT) with power-of-two length, which results in great flexibility in real-world fixed-point computations, such as the convolution-based signal processing in the embedded device. Yet the FFT realization exists the truncation errors and in order to further reduce the computations, this paper puts forward a novel realization structure for the NMNT, where the Walsh-Hadamard transform (WHT) is employed to accelerate the NMNT computation. Moreover, we also propose the refined computing structure using the matrix decomposition and multiple constant multiplication (MCM), and then all multiplications can be replaced by the shift-addition operations without precision loss. Besides, the use of lookup table (LUT) to reduce the complexity is also discussed in our study. A typical convolution application is tested by computer simulations, while the result demonstrates that the proposed scheme produces precise computing results with reduced complexity. KEYWORDS computing complexity, fast realization, Walsh-Hadamard new mersenne number transform, Walsh Hadamard transform 738

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“…The introduction of the new Mersenne number transform (NMNT) [4], [5] introduced a highly scalable transform with potential applications for security systems [6]. This transform has very versatile long power-of-two blocks based over a finite field modulo a Mersenne prime, which are highly efficient to calculate.…”

Section: Introductionmentioning

confidence: 99%

Assessment of the One-Dimensional Generalized New Mersenne Number Transform for Security Systems

Rutter

Boussakta

Bystrov

2013

2013 IEEE 77th Vehicular Technology Conference (VTC Spring)

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With increased reliance on encryption for e-commerce, communications and data storage, new techniques are constantly being developed to meet the demand for secure encryption systems requiring higher levels of security and integrity. A significant aspect of integrity is the diffusion and avalanche effect, which is measured by its sensitivity to a single bit change between the cipher text and the plaintext. This effect should yield a catastrophic result which is measurable and can therefore be readily assessed for its suitability as part of a security system. This paper measures the standard one-dimensional implementations of the generalized new Mersenne number transform suite for its suitability in security applications. The generalized suite is expanded from the existing new Mersenne number transform, by the addition of two new transforms, which have yet to be fully assessed in this aspect. The two new transforms offer the same long power-of-two run lengths and efficient calculations over a field of integers modulo a Mersenne prime. Sharing similar characteristics with the original transform, they also have the cyclic-convolution property, suggesting that they too can wield significant impact in the fields of image-, signal-processing as well as cryptography.

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New transform using the Mersenne numbers

Cited by 39 publications

References 0 publications

A New Development of Symmetric Key Cryptosystem

A New Development of Symmetric Key Cryptosystem

A fast realization of new Mersenne number transformation and its applications

Assessment of the One-Dimensional Generalized New Mersenne Number Transform for Security Systems

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