A new approach to analyze the independence of statistical tests of randomness

Luengo, Elena Almaraz; Cerna, Marcos Brian Leiva; Villalba, Luis Javier García; Hernández-Castro, Julio

doi:10.1016/j.amc.2022.127116

Cited by 6 publications

(6 citation statements)

References 18 publications

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“…This tool specifically scrutinizes the presence of repetitive bit strings. Additionally, it is worth highlighting that this parameter is incorporated into the NIST 800-22 standard [38]. In the computation of this parameter, the variables defined in Equations ( 6)-( 8) are utilized, where m represents the length of the analyzed string, M 0 in Equation ( 6) is a constant value, and l in Equation ( 7) is a boundary.…”

Section: Discrete Fourier Transformmentioning

confidence: 99%

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy

Silva-García,

Flores-Carapia,

Cardona-López

2024

Entropy

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Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie–Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are necessary for the symmetrical aspect to generate dynamic permutations, substitution boxes, and round keys. Following an encryption process with fourteen rounds, the encrypted images are processed by an algorithm proposed to enhance entropy, a critical metric for assessing encryption quality. It increases the frequencies of the basic colors to achieve a histogram closely resembling a uniform distribution, but it increases the image size by approximately 8%. This improves the entropy values achieved by the hybrid cryptosystem, bringing them remarkably close to the ideal value of 8.0. In specific instances, the entropy values were elevated from 7.99926 to 8.0. The proposed method exhibits resilience against various attacks, including differential, linear, brute force, and algebraic attacks, as evaluated through the entropy, correlation, goodness of fit, Discrete Fourier Transform (DFT), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Avalanche Criteria (AC), contrast, energy, and homogeneity. Further, encrypted images are subjected to noise attacks ranging from 20% to 50% noise, including additive, multiplicative, occlusion noise, as well as the newly introduced χ2 noise. The noise damage is quantified using the proposed Similarity Parameter (SP), and a 3×3 median filter is employed to enhance the visual quality.

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Section: Discrete Fourier Transformmentioning

confidence: 99%

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy

Silva-García,

Flores-Carapia,

Cardona-López

2024

Entropy

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“…The procedure to calculate the goodnes-of-fit test parameter is also a statistical hypothesis test [38]. In this sense, this parameter assesses how much the distribution of information adjusts to one that is uniform, which will determine that the information is random, although it is clarified that it is possible to construct a theoretical distribution which is not random, but is adjusts to a uniform distribution; However, in practice it is considered that if the information fits a uniform distribution, it is said to be random; In addition, the randomness of the information is evaluated with other parameters.…”

Section: Goodness-of-fit Testmentioning

confidence: 99%

Digital signature algorithm based on ElGamal, Diffie-Hellman protocol and the number π

Flores-Carapia,

Silva-García,

González-Ramírez

et al. 2023

Preprint

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This research proposes an algorithm to sign messages using the ElGamal asymmetric cryptosystem, called: Digital signature algorithm based on ElGamal, Diffie-Hellman protocol and the number π (DSAπ). This proposal has a high level of security like the DSA standard, in addition, execution times are reduced in relation to it. The Diffie-Hellman protocol and the number π were used in the construction of the digital signature algorithm in conjunction with the Hash-Sha-512 function. Some experiments are presented to provide evidence that the bits on the right side of the decimal point of π appear randomly, such as: a color image was constructed of a string of consecutive bits chosen at random, of the number π. Subsequently, parameters such as: entropy, correlation, discrete Fourier transform, goodness-of-fit test χ2 were evaluated. It is mentioned that an S-box 8×8 is involved in the signature. The sensitivity of the signature was measured, that is, when small changes are made to the sender’s private key, or small changes to the message. Finally, an image was constructed using the signatures of random texts, and subsequently the randomness of its pixels was obtained, to verify that there is no relationship between the different signatures.

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“…Different articles have verified the effectiveness of mutual information in studying the correlation between the randomness tests of different batteries. In [18], DieHarder, TufTest, and SmallCrush batteries were studied, and in [19], the FIPS 140-2 battery was analyzed using the method proposed in [17]. Mutual information can detect the correlations found by Pearson correlation and new nonlinear dependencies between tests.…”

Section: Introductionmentioning

confidence: 99%

“…In [20], the complexity of the method proposed in [17] was estimated, and its high complexity was pointed out as a disadvantage, which prevents testing batteries with more tests or longer sequences. However, mutual information as a new measure of independence between randomness tests represents a significant advance and an important piece for building a definitive test battery [18].…”

Section: Introductionmentioning

confidence: 99%

Complexity Reduction in Analyzing Independence between Statistical Randomness Tests Using Mutual Information

Karell-Albo,

Legón-Pérez,

Socorro-Llanes

et al. 2023

Entropy

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The advantages of using mutual information to evaluate the correlation between randomness tests have recently been demonstrated. However, it has been pointed out that the high complexity of this method limits its application in batteries with a greater number of tests. The main objective of this work is to reduce the complexity of the method based on mutual information for analyzing the independence between the statistical tests of randomness. The achieved complexity reduction is estimated theoretically and verified experimentally. A variant of the original method is proposed by modifying the step in which the significant values of the mutual information are determined. The correlation between the NIST battery tests was studied, and it was concluded that the modifications to the method do not significantly affect the ability to detect correlations. Due to the efficiency of the newly proposed method, its use is recommended to analyze other batteries of tests.

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A new approach to analyze the independence of statistical tests of randomness

Cited by 6 publications

References 18 publications

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy

Digital signature algorithm based on ElGamal, Diffie-Hellman protocol and the number π

Complexity Reduction in Analyzing Independence between Statistical Randomness Tests Using Mutual Information

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