How Miller Rabin test is used for primality testing? Show whether the | Cryptography 2080

Cryptography20805 marksNumerical: Miller-Rabin test 561Number Theory

How Miller Rabin test is used for primality testing? Show whether the number 561 passes the test. [5]

Number to test: $n = 561$ - Test base (chosen): $a = 2$ Miller-Rabin is a probabilistic primality test based on the fact that for a prime $n$ , the only square roots of $1 \pmod n$ are $\pm 1$ . Algorithm: 1. Write $n - 1 = 2^k \cdot m$ where $m$ is odd. 2. Pick a base $a$ with $1 < a < n-1$ . 3. ...

Number to test: $n = 561$ - Test base (chosen): $a = 2$ Miller-Rabin is a probabilistic primality test based on the fact that for a prime $n$, the only square roots of $1 \pmod n$ are $\pm 1$. Algorithm: 1. Write $n - 1 = 2^k \cdot m$ where $m$ is odd. 2. Pick a base $a$ with $1 < a < n-1$. 3. ...