scholarly journals The Additive Differential Probability of ARX

2011 ◽  
pp. 342-358 ◽  
Author(s):  
Vesselin Velichkov ◽  
Nicky Mouha ◽  
Christophe De Cannière ◽  
Bart Preneel
Keyword(s):  
Differential Probability

scholarly journals Resonant Effect of High-Energy Electron–Positron Pairs Production in Collision of Ultrarelativistic Electrons with an X-ray Electromagnetic Wave

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 210
Author(s):  
Georgii K. Sizykh ◽  
Sergei P. Roshchupkin ◽  
Victor V. Dubov
Keyword(s):  
High Energy ◽  
Energy Electron ◽  
Opening Angle ◽  
High Energy Electron ◽  
Scattered Electron ◽  
Differential Probability ◽  
X Ray ◽  
Electron Positron ◽  
Pulsar Radiation ◽  
Resonant Effect

The process of resonant high-energy electron–positron pairs production by electrons in an X-ray pulsar electromagnetic field is studied theoretically. Under the resonance conditions, the second-order process under consideration effectively reduces into two sequential first-order processes: X-ray-stimulated Compton effect and X-ray–stimulated Breit–Wheeler process. The kinematics of the process is studied in detail: the dependencies of the energy of the scattered electron on its outgoing angle and the energies of the particles of the pair on the outgoing angle of the scattered electron and the opening angle of the pair are obtained. The analysis of the number of different possible particles energies values in the entire range of the angles is also carried out, according to which the energies of the particles of the pair can take up to eight different values at a fixed outgoing angle of the scattered electron and opening angle of the pair. The estimate of the resonant differential probability per unit time of the process, which reaches the maximum value of 24 orders of the value of the non-resonant differential probability per unit time, is obtained. The angular distribution of the differential probability per unit time of the process is analyzed, particularly for the case of high-energy positrons presenting in pulsar radiation.

scholarly journals Maximums of the Additive Differential Probability of Exclusive-Or

2021 ◽  
pp. 292-313
Author(s):  
Nicky Mouha ◽  
Nikolay Kolomeec ◽  
Danil Akhtiamov ◽  
Ivan Sutormin ◽  
Matvey Panferov ◽  
...  
Keyword(s):  
Differential Probability ◽  
Recurrence Formulas ◽  
Minimum Value ◽  
Symmetric Key ◽  
Addition Modulo 2N ◽  
Exclusive Or ◽  
Insight Into

At FSE 2004, Lipmaa et al. studied the additive differential probability adp⊕(α,β → γ) of exclusive-or where differences α,β,γ ∈ Fn2 are expressed using addition modulo 2n. This probability is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as the increasingly popular Addition-Rotation-XOR (ARX) constructions. The focus of this paper is on maximal differentials, which are helpful when constructing differential trails. We provide the missing proof for Theorem 3 of the FSE 2004 paper, which states that maxα,βadp⊕(α,β → γ) = adp⊕(0,γ → γ) for all γ. Furthermore, we prove that there always exist either two or eight distinct pairs α,β such that adp⊕( α,β → γ) = adp⊕(0,γ → γ), and we obtain recurrence formulas for calculating adp⊕. To gain insight into the range of possible differential probabilities, we also study other properties such as the minimum value of adp⊕(0,γ → γ), and we find all γ that satisfy this minimum value.

scholarly journals Resonant Ultrarelativistic Electron–Positron Pair Production by High-Energy Electrons in the Field of an X-ray Pulsar

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 132 ◽  
Author(s):  
Georgii K. Sizykh ◽  
Sergei P. Roshchupkin ◽  
Victor V. Dubov
Keyword(s):  
Pair Production ◽  
Threshold Energy ◽  
Structure Constant ◽  
High Energy ◽  
Differential Probability ◽  
X Ray ◽  
Initial Electron ◽  
Ultrarelativistic Electron ◽  
Electron Positron ◽  
Electron Positron Pair

The process of resonant high-energy electron–positron pair production by an ultrarelativistic electron colliding with the field of an X-ray pulsar is theoretically investigated. Resonant kinematics of the process is studied in detail. Under the resonance condition, the intermediate virtual photon in the X-ray pulsar field becomes a real particle. As a result, the initial process of the second order in the fine structure constant effectively reduces into two successive processes of the first order: X-ray-stimulated Compton effect and X-ray-stimulated Breit–Wheeler process. For a high-energy initial electron all the final ultrarelativistic particles propagate in a narrow cone along the direction of the initial electron momentum. The presence of threshold energy for the initial electron which is of order of 100 MeV for 1-KeV-frequency field is shown. At the same time, the energy spectrum of the final particles (two electrons and a positron) highly depends on their exit angles and on the initial electron energy. This result significantly distinguishes the resonant process from the non-resonant one. It is shown that the resonant differential probability significantly exceeds the non-resonant one.

Bloodtyping and Twin Zygosity. Reassessment and Extension

1980 ◽  
Vol 29 (2) ◽  
pp. 103-120 ◽  
Author(s):  
Ronald S. Wilson
Keyword(s):  
Direct Method ◽  
Individual Case ◽  
Differential Probability ◽  
Dizygotic Twins ◽  
Similarities And Differences ◽  
Diagnostic Question ◽  
The Individual

The determination of twin zygosity by bloodtyping is reconsidered, and the model for the individual case is reformulated. The crucial diagnostic question may be phrased as follows: Given the particular array of bloodgroup phenotypes that the twins display and are concordant for, how might this array have been obtained by a pair of dizygotic twins, and how might the array have been obtained by a monozygotic pair? The solution yields a differential probability value that is uniquely tailored to the actual phenotype array shown. The procedure offers a coherent and more direct method for arriving at the needed probability figures, and it is recommended to supersede previous methods. Some similarities and differences between the methods are discussed.

scholarly journals Lossless Compression of Medical Images based on the Differential Probability of Images

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Medical Image ◽  
Large Scale ◽  
Medical Images ◽  
Lossless Compression ◽  
Differential Method ◽  
Huffman Coding ◽  
Difference Matrix ◽  
Differential Probability ◽  
Compression Effect ◽  
The Difference

Lossless compression is crucial in the remote transmission of large-scale medical image and the retainment of complete medical diagnostic information. The lossless compression method of medical image based on differential probability of image is proposed in this study. The medical image with DICOM format was decorrelated by the differential method, and the difference matrix was optimally coded by the Huffman coding method to obtain the optimal compression effect. Experimental results obtained using the new method were compared with those using Lempel–Ziv–Welch, modified run–length encoding, and block–bit allocation methods to verify its effectiveness. For 2-D medical images, the lossless compression effect of the proposed method is the best when the object region is more than 20% of the image. For 3-D medical images, the proposed method has the highest compression ratio among the control methods. The proposed method can be directly used for lossless compression of DICOM images.

scholarly journals Optimal Differential Trails in SIMON-like Ciphers

2017 ◽  
pp. 358-379 ◽  
Author(s):  
Zhengbin Liu ◽  
Yongqiang Li ◽  
Mingsheng Wang
Keyword(s):  
Upper Bound ◽  
Efficient Algorithm ◽  
Search Algorithm ◽  
Hamming Weight ◽  
Differential Probability ◽  
Smt Solvers ◽  
Round Function ◽  
Input Size ◽  
Automatic Search ◽  
First Time

In the present paper, we propose an automatic search algorithm for optimal differential trails in SIMON-like ciphers. First, we give a more accurate upper bound on the differential probability of SIMON-like round function. It is shown that when the Hamming weight of the input difference α , which is denoted by wt(α), is less than one half of the input size, the corresponding maximum differential probability of SIMON-like round function is less than or equal to 2−wt(α)−1. Based on this, we adapt Matsui’s algorithm and propose an efficient algorithm for searching for optimal differential trails. With the proposed algorithm, we find the provably optimal differential trails for 12, 16, 19, 28 and 37 rounds of SIMON32/48/64/96/128. To the best of our knowledge, it is the first time that the provably optimal differential trails for SIMON64, SIMON96 and SIMON128 are reported. The provably optimal differential trails for 13, 19 and 25 rounds of SIMECK32/48/64 are also found respectively, which confirm the results given by Kölbl et al. [KR15]. Besides the optimal differential trails, we also find the 14, 17, 23, 31 and 41-round differentials for SIMON32/48/64/96/128, and 14, 21 and 27-round differentials for SIMECK32/48/64, respectively. As far as we know, these are the best differential distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers used by K¨olbl et al., our algorithm is more efficient and more practical to evaluate the security against differential cryptanalysis in the design of SIMON-like ciphers.

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