Analyzing and Optimizing the Combined Primality test with GCD Operation on Smart Mobile Devices
نویسندگان
چکیده
Fast generation of a large prime is important to enhance security. However, primality test of prime generation takes long time. Therefore, primality tests are combined to speed up. A combination of trial division and Miller-Rabin test (TD combined test hereafter) is the most popular combination. GCD operation and Miller-Rabin test combination (GCD combined test hereafter) is also popular and easily alternative to TD combined test. Although the performance of TD combined test has been analyzed and optimized, GCD combined test has scarcely been analyzed. In this paper, we present a probabilistic analysis on the total running time of GCD combined test for smart mobile devices. Our analysis and corresponding experiment result are very accurate with only 1-2% error. In addition, we propose a method to determine the optimal number of small primes used in GCD primality test to speed up.
منابع مشابه
On (Semi-) Edge-primality of Graphs
Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an ...
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