Fermat's Little Theorem is used in cryptography in several ways. One of the most common applications is in the generation of so-called "public-key" cryptography systems, which are used to securely transmit messages over the internet and other networks.

In a public-key cryptography system, each user has a pair of keys: a public key, which is widely known and can be used by anyone to encrypt a message intended for that user, and a private key, which is known only to the user and is used to decrypt messages that have been encrypted with the corresponding public key.

One way to generate these keys is to use prime numbers and Fermat's Little Theorem. For example, suppose we want to generate a public-key cryptography system for a user with the initials "ABC". We might choose two large prime numbers, $p$ and $q$, and then compute the product $n=pq$.

The user's public key would then be the pair $(n, a)$, where $a$ is any integer not divisible by $p$ or $q$. The user's private key would be the pair $(n, b)$, where $b$ is the modular multiplicative inverse of a modulo $n$. This means that when we multiply $a$ and $b$ together, the result is congruent to $1$ modulo $n$.

To encrypt a message with the user's public key $(n, a)$, we first convert the message into a number $m$ (using some agreed-upon scheme), and then compute the encrypted message $c$ as $c=m^a \bmod n$. To decrypt the message, the recipient simply computes $m=c^b \bmod n$, which (by Fermat's Little Theorem) is equivalent to $m=(m^a)b \bmod n=m^(ab) \bmod n=m^1 \bmod n=m \bmod n$.

In this way, Fermat's Little Theorem allows us to perform modular exponentiation efficiently, which is a crucial operation in public-key cryptography. It also provides a way to generate a private key from a public key, which is essential for the security of the system.