Browsing by Author "Orhon, Neriman Gamze"

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Citation - WoS: 6
Citation - Scopus: 10
Convergence Detection in Epidemic Aggregation
(SPRINGER-VERLAG BERLIN, 2014) Pasu Poonpakdee; Neriman Gamze Orhon; Giuseppe Di Fatta; Orhon, Neriman Gamze; Di Fatta, Giuseppe; Poonpakdee, Pasu; DA Mey; M Alexander; P Bientinesi; M Cannataro; C Clauss; A Costan; G Kecskemet; C Morin; L Ricci; J Sahuquillo; M Schulz; V Scarano; SL Scott; J Weidendorfer
Emerging challenges in ubiquitous networks and computing include the ability to extract useful information from a vast amount of data which are intrinsically distributed. Epidemic protocols are a bio-inspired approach that provide a communication and computation paradigm for large and extreme-scale networked systems. These protocols are based on randomised communication which provides robustness scalability and probabilistic guarantees on convergence speed and accuracy. This work investigates the convergence detection problem in epidemic aggregation which is critical to minimise the execution time for a given approximation error of the estimated aggregate. Global and local convergence criteria are presented and compared. The experimental analysis shows that a local convergence criterion can be adopted to minimise and adapt the number of cycles in epidemic aggregation protocols.
Huff eliptik eğri modeli üzerinde hızlı nokta toplama formülleri
(2017) Orhon, Neriman Gamze; Hışıl, Hüseyin
Elliptic curves were being used only for mathematical studies until Miller and Koblitz introduced elliptic curves to crypto-community in 1985 with independent works. Since then, elliptic curves became one of the most significant tools in cryptography. Elliptic curve cryptography (ECC) started to be used for commercial purposes after 1990's. It provides a better level of security with the same key size than the widely used public key crypto-systems such as RSA. Nevertheless, time complexity is not at the desired stage. Hence, there have been several studies so far that aims to increase the time efficiency. The curve forms that are being used for speed oriented operations came a long way in terms of gathering lower degree formulas for scalar multiplication which is the core operation of ECC. However, one of the curve forms which is called Huff curve could not get competitive with the other forms such as Twisted Edwards, Jacobi Quartic, despite the studies have been made so far. This thesis focuses on increasing the efficiency of Huff form of elliptic curve by making use of mathematical and computational primitives. Inversion-free point addition and doubling formulas which are being used in scalar multiplication algorithms, are proposed for the Huff curve which is defined y(1 + ax2 ) = cx(1 + dy2 ) First idea is rather to embed the curve into a different projective space than the preferred for Huff curve previously. Thus, P 1×P 1 embedding is used instead of P 2 embedding. The second idea is to make the use of isogenies in order to obtain an alternative doubling formula. Thanks to these two ideas, an improvement is achieved. The best algorithm for point doubling on Huff curve was computed with 6M+ 5S. 1 The proposed doubling formula in this thesis can be computed with 8M. Also, operation count of mixed addition is decreased from 10M to 8M. Both sets of formulas are leading to an effective cost of 2M. Furthermore, they are shown to be 4-way parallel. Key Words: Elliptic curves, 2-isogeny, efficient, scalar multiplication, Huff curves, inversion-free point addition, parallel computation.
Citation - WoS: 4
Citation - Scopus: 6
Speeding up Huff form of elliptic curves
(SPRINGER, 2018) Neriman Gamze Orhon; Huseyin Hisil; Orhon, Neriman Gamze; Hisil, Huseyin
This paper presents faster inversion-free point addition formulas for the curve y(1+ ax2) = cx(1+ dy2). The proposed formulas improve the point doubling operation count record (I M S D a are arithmetic operations over a field. I: inversion M: multiplication S: squaring D: multiplication by a curve constant a: addition/ subtraction) from 6M + 5S to 8M and mixed addition operation count record from 10M to 8M. Both sets of formulas are shown to be 4-way parallel leading to an effective cost of 2M per either of the group operations.