# How many combinations does the Enigma machine have?

## How many combinations does the Enigma machine have?

Since in the new enigma machine, one extra rotor had been added, which had 26 wired discs. So total possible combinations are 264.

## How did the Enigma Plugboard work?

Adding to the scrambling was a plugboard, sitting between the main rotors and the input and output, which swapped pairs of letters. In the earliest machines, up to six pairs could be swapped in that way; later models pushed it to 10, and added a fourth rotor.

What is the Enigma encryption machine?

The Enigma machine was a field unit used in World War II by German field agents to encrypt and decrypt messages and communications. Similar to the Feistel function of the 1970s, the Enigma machine was one of the first mechanized methods of encrypting text using an iterative cipher.

### What was the plugboard on the Enigma machine called?

On the front of the machine was another section called the “plugboard”. The Enigma machine had several cables with a plug at each end that could be used to plug pairs of letters together. If A were plugged to B then, on typing the letter A, the electric current would follow the path that was normally associated with the letter B, and vice versa.

### How to count the possible plugboard settings for Enigma?

Given a set of n distinct objects there are C(n,r) ways of dividing it into two sets of size r and (n-r), where C(n,r) means n! / r! (n-r)! However it is not immediately obvious how we apply this to the Enigma plugboard problem where the 26 letters have to be divided into 6 unpaired letters and 10 pairs of pairwise connected letters.

How are the rotors of the Enigma machine connected?

The output of the plugboard is connected via an entry plate (a so called static wheel) to the position corresponding to the letter K on the input terminal of the first rotor known as the fast rotor.

## How many pairs of letters are there on the Enigma machine?

Enigma machines had 10 cables with which to link up pairs of letters. Question 4: How many ways are there to link up pairs of letters on the Enigma machine? The answer is that there are approximately 150,000,000,000,000 – that is, 150 million million – possible combinations of 10 pairs of 26 letters on the plug board.