XOR and cipher stream

Question

I am new to cryptography and I am very confused. In fact, I am so confused that I have trouble providing a suitable title for my thread...

I know that a Substitution Cipher is designed to substitute one letter or character for another, to produce a ciphertext as shown in the picture below

With most symmetric cipher, the final step is to combine the cipher stream with the plaintext to create a ciphertext using XOR binary logic encryption.

My question is

1. why is the plain text, cipher stream and cipher text all in binary? In the first picture, it is all in letters, now in the second picture, it is all in binary.
2. Where does the single key from the symmetric cryptography take place?

Answer 1

For #1, binary is used for a number of reasons. First, XOR is a logical operator, so it only operates on bits. Modern computers store everything as bits, too, so that makes XOR convenient.

As for why the first picture is not in bits, that is because no one uses (or at least should) use substitution ciphers such as the one proposed on modern computers. That substitution cipher is extremely insecure. Those sorts of ciphers were typically seen in the pre-computing age, so showing it with an alphabet instead of in bits makes sense. You could, however, show the same graphic with binary text. You'd first have to break up the binary into groups of values (maybe 4 or 5 bits per group) and show a substitution table for the 4 bit values.

For #2, the key is used to produce the cipher stream. That is not shown in the picture.

Answer 2

why is the plain text, cipher stream and cipher text all in binary? In the first picture, it is all in letters, now in the second picture, it is all in binary.

Because classical cryptography (e.g., substitution ciphers) usually was done on text represented as sequences of letters, whereas modern cryptography is usually done on data (not necessarily textual) represented as bits. Although there have been ternary computers, they are a historical curiosity for the most part; computers in practice work in binary, so modern cryptography does so as well.

This is however an incidental, not essential distinction. Mathematically you could formulate modern algorithms to work on letters instead of bits. One way to perceive this is to think of one-time pads, and in particular historical pen-and-paper instantiations thereof. It's relatively straightforward to write a program that, given a password and page number as input, uses a modern stream cipher to reproducibly generate a page with pseudorandom characters that looks very much like the one in the latter link, which you could then use with pen and paper to encrypt messages. That would be a stream cipher, but based on letters instead of bits.

Note that, mathematically, the same sort of thing is going on:

1. Messages are encoded into sequences of symbols drawn out of some abstract finite, ordered "alphabet" (in the mathematical sense, not the everyday sense). In the alphabetical ciphers the alphabet is the familiar one with 26 letters, while in the binary ciphers it's the set $\{0, 1\}$.
2. Messages are encrypted by shifting the symbol at each position by an amount that is randomly and independently chosen for each position.
3. The sequence of shifts to be applied to each position in the message is called the keystream. In historical one-time pads this keystream and the shifts are encoded as letters, while in modern bit-based ciphers it's encoded as a sequence of bits.

The difference is that in one-time pads the key is the random keystream, while modern stream ciphers are algorithms for generating long pseudorandom keystreams from short random keys.