RSA cryptosystems involves, a private key (which is kept private) and a public key, which is kept public i.e. known to everyone. The security of RSA hinges on the mathematically difficult problem of finding prime factorization of a very large number. Let's quickly disuss how a public, private key pair can be generated, Let, p and q be two large primes, then $n = q \times q$ $\phi(n) = (p-1) \times (q-1)$ Here, $\phi(n)$ is called euler's totient function Choose a random number $e$ such that, $e \in \left\{0,1,2...\phi(n)-1\right\}$ and $gcd(e,\phi(n)) = 1$ The gcd condition will ensure that we have an inverse of $e$ in $\mathbb{Z}_{26}$. Now, using extended euclidian algorithm one can get the inverse of e as d such that, $d \equiv e \pmod{\phi(n)}$ So, there we have it, the private key is $e$ and the public key is $(n,d)$. Few points to note here are, $p$ and $q$ are both $\geq 2^{512}$, although the recommened size is $2^{1024}$ $n$ is $\geq 2^{1024}$, although the recommended...
Universe from my perspective..