A Study on the Parameter of the Distinguished Point Method in Pollard’s Rho Method for ECDLP

2018 ◽  
Author(s):  
Ken Ikuta ◽  
Sho Joichi ◽  
Kazuya Kobayashi ◽  
Md. Al-Amin Khandaker ◽  
Takuya Kusaka ◽  
...  
Keyword(s):  
Point Method ◽  
Distinguished Point

scholarly journals An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ping Wang ◽  
Fangguo Zhang
Keyword(s):  
Collision Detection ◽  
Detection Method ◽  
Detection Algorithm ◽  
Point Method ◽  
Expected Number ◽  
Distinguished Point ◽  
Discrete Logarithms ◽  
Cyclic Groups ◽  
Space Requirements ◽  
Generic Algorithms

Pollard's rho method and its parallelized variant are at present known as the best generic algorithms for computing discrete logarithms. However, when we compute discrete logarithms in cyclic groups of large orders using Pollard's rho method, collision detection is always a high time and space consumer. In this paper, we present a new efficient collision detection algorithm for Pollard's rho method. The new algorithm is more efficient than the previous distinguished point method and can be easily adapted to other applications. However, the new algorithm does not work with the parallelized rho method, but it can be parallelized with Pollard's lambda method. Besides the theoretical analysis, we also compare the performances of the new algorithm with the distinguished point method in experiments with elliptic curve groups. The experiments show that the new algorithm can reduce the expected number of iterations before reaching a match from 1.309Gto 1.295Gunder the same space requirements for the single rho method.

Scanning Electron Microscopy of Dried and Acid Treated Shells of Difflugia

1973 ◽  
Vol 31 ◽  
pp. 448-449
Author(s):  
Barry S. Eckert ◽  
S. M. McGee-Russell
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Critical Point ◽  
Point Method ◽  
External Structure ◽  
Cell Locomotion ◽  
Single Opening ◽  
Scanning Electron

Difflugia lobostoma is a shelled amoeba. The shell is an external structure of considerable mass which presents the animal with special restrictions in cell locomotion which are met by the development of active pseudopodial lobopodia containing, apparently, an organized system of thick and thin microfilaments (Eckert and McGee-Russell, 1972). The shell is constructed of sand grains picked up from the environment, and cemented into place with a secretion. There is a single opening through which lobopods extend. The organization of the shell was studied by scanning electron microscopy (SEM).Intact shells or animals with shells were dried by the critical point method of Anderson (1966) or air dried, after primary fixation in glutaraldehyde.

Dermoscopy Analysis Easy by Three-Point Method

2007 ◽  
Vol 38 (3) ◽  
pp. 62
Author(s):  
SHERRY BOSCHERT
Keyword(s):  
Point Method

Application of GPS marker to the local treatment of hepatocellular carcinoma -GPS markers two-point method-

Choonpa Igaku ◽  
2011 ◽  
Vol 38 (5) ◽  
pp. 585-594
Author(s):  
Yasuhide MITSUMOTO ◽  
Ryuuki MINAMI ◽  
Takahiro MORI ◽  
Takuya UCHIDA ◽  
Koji FUJITA ◽  
...  
Keyword(s):  
Hepatocellular Carcinoma ◽  
Local Treatment ◽  
Point Method

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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