Take two distinct prime numbers of similar bit-length, $p$ and $q$. These numbers are not chosen from a reserve of known primes, but are instead generated using algorithms that find the nearest probable prime to a very large randomly-generated integer. Probable primes are numbers that are believed to be primes because they share certain properties with known primes. However, due to these numbers being extremely large, it is very difficult to verify that these numbers are in fact prime. As a result, the number's true primality may become irrelevant. Primality tests, such as the Miller-Rabin and Fermat's Little Theorem, are used to generate probable prime numbers that are hundreds of digits in length.

Let $n \= \mathrm{pq}$, where $n$ is the modulus for the public and private keys.

Compute the totient of $n$,  ɸ$\left(n\right) \= ɸ\left(p\right) \cdot ɸ\left(q\right) \= \left(p-1\right)\cdot \left(q-1\right)$. The totient of $n$ is the number of positive integers less than or equal to a given number $n$ that are relatively prime to $n$. Two integers $a$ and $b$ are relatively prime or coprime if they do not have a prime factors in common.

Let $e$ be any number such that: $1 < e < ɸ\left(n\right)$ and $e$ and $ɸ\left(n\right)$ are coprime.

$\left(n\&comma; e\right)$ is the public encryption key.

Compute $d \&equals; e^{-1 }$$\mathbf{mod}$ɸ$\left(n\right)$. The number $d$ is the private decryption key.

Apply padding techniques to the original plaintext message, such as random length padding, and permuting the message etc. as needed. Such padding techniques are necessary to subvert commonly know cryptographic attacks.

Convert the padded text to numeric form, by considering it as a representation of a number $m$ in some base (256-bit, 512-bit etc), such that $0 < m < n$.

Compute $c \&equals; m^e \mathbf{mod} n\&period;$ This $c$ is the ciphertext,

Send $c$ to the the private-key holder to be decrypted.