Sustainability and Time Complexity Estimation of Сryptographic Algorithms Main Operations on Elliptic Curves

2021 ◽  
Author(s):  
Igor Yakymenko ◽  
Mykhailo Kasianchuk ◽  
Vasyl Yatskiv ◽  
Ruslan Shevchuk ◽  
Vasyl Koval ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Time Complexity ◽  
Complexity Estimation

scholarly journals An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Naveed Ahmed Azam ◽  
Umar Hayat ◽  
Ikram Ullah
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Efficient Method ◽  
Time Complexity ◽  
Experimental Results ◽  
Rigorous Analysis ◽  
Design Scheme

Elliptic curves (ECs) are considered as one of the highly secure structures against modern computational attacks. In this paper, we present an efficient method based on an ordered isomorphic EC for the generation of a large number of distinct, mutually uncorrelated, and cryptographically strong injective S-boxes. The proposed scheme is characterized in terms of time complexity and the number of the distinct S-boxes. Furthermore, rigorous analysis and comparison of the newly developed method with some of the existing methods are conducted. Experimental results reveal that the newly developed scheme can efficiently generate a large number of distinct, uncorrelated, and secure S-boxes when compared with some of the well-known existing schemes.

scholarly journals On the Complexity of Impossible Differential Cryptanalysis

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Qianqian Yang ◽  
Lei Hu ◽  
Danping Shi ◽  
Yosuke Todo ◽  
Siwei Sun
Keyword(s):  
Time Complexity ◽  
Differential Analysis ◽  
Differential Attack ◽  
Symmetric Key ◽  
Impossible Differential ◽  
Complexity Estimation ◽  
Impossible Differential Attack ◽  
Differential Attacks ◽  
Impossible Differentials ◽  
Impossible Differential Cryptanalysis

While impossible differential attack is one of the most well-known and familiar techniques for symmetric-key cryptanalysts, its subtlety and complicacy make the construction and verification of such attacks difficult and error-prone. We introduce a new set of notations for impossible differential analysis. These notations lead to unified formulas for estimation of data complexities of ordinary impossible differential attacks and attacks employing multiple impossible differentials. We also identify an interesting point from the new formulas: in most cases, the data complexity is only related to the form of the underlying distinguisher and has nothing to do with how the differences at the beginning and the end of the distinguisher propagate in the outer rounds. We check the formulas with some examples, and the results are all matching. Since the estimation of the time complexity is flawed in some situations, in this work, we show under which condition the formula is valid and give a simple time complexity estimation for impossible differential attack which is always achievable.

scholarly journals Finding elliptic curves with a subgroup of prescribed size

2016 ◽  
Vol 13 (01) ◽  
pp. 133-152
Author(s):  
Igor E. Shparlinski ◽  
Andrew V. Sutherland
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Riemann Hypothesis ◽  
Time Complexity ◽  
Rational Functions ◽  
Deterministic Algorithm ◽  
Probabilistic Algorithm ◽  
Almost All

Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime [Formula: see text] and positive integer [Formula: see text], outputs an elliptic curve [Formula: see text] over the finite field [Formula: see text] for which the cardinality of [Formula: see text] is divisible by [Formula: see text]. The running time of the algorithm is [Formula: see text], and this leads to more efficient constructions of rational functions over [Formula: see text] whose image is small relative to [Formula: see text]. We also give an unconditional version of the algorithm that works for almost all primes [Formula: see text], and give a probabilistic algorithm with subexponential time complexity.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

Recognition of Birds in Blurred and Illumination Images by Local Features

2017 ◽  
Vol 7 (7) ◽  
pp. 243
Author(s):  
Suresha .M ◽  
. Sandeep
Keyword(s):  
Computer Vision ◽  
Time Complexity ◽  
Feature Detection ◽  
Feature Matching ◽  
Fast Algorithms ◽  
Local Features ◽  
Experimental Demonstration ◽  
Harris Corner ◽  
Blurred Image ◽  
Blurred Images

Local features are of great importance in computer vision. It performs feature detection and feature matching are two important tasks. In this paper concentrates on the problem of recognition of birds using local features. Investigation summarizes the local features SURF, FAST and HARRIS against blurred and illumination images. FAST and Harris corner algorithm have given less accuracy for blurred images. The SURF algorithm gives best result for blurred image because its identify strongest local features and time complexity is less and experimental demonstration shows that SURF algorithm is robust for blurred images and the FAST algorithms is suitable for images with illumination.

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