Is the Caesar cipher really a cipher?

In this lecture by Dan Boneh on Coursera it was stated at minute 03:37 that

The Caesar cipher, actually, is not a cipher at all. And the reason is that it doesn't have a key. What a Caesar cipher is, is basically a substitution cipher where the substitution is fixed.

Can someone elaborate what he said? I don't get the part that he says that it doesn't have a key.

• There are 26 possible key for caesar. ROT13 on the other hand only has a single valid key, so the above argument might apply. – CodesInChaos Nov 14 '16 at 22:23
• – CodesInChaos Nov 14 '16 at 22:43

He is talking about the original version of the Caesar Cipher where the substitution was just a +3:

A -> D
B -> E
C -> F
D -> G
E -> H
F -> I
G -> K
H -> L
...
X -> A
Y -> B
Z -> C


Because the shift is fixed, it does not have a key (but you could say it is a substitution cipher with a key equal to +3).

However it is common usage to call a substitution cipher as a Caesar Cipher because the idea the same but where you change the value of the shift.

The Caesar cipher is named after Julius Caesar, who, according to Suetonius, used it with a shift of three to protect messages of military significance. While Caesar's was the first recorded use of this scheme, other substitution ciphers are known to have been used earlier.

If he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others. — Suetonius, Life of Julius Caesar 56 [source]

• just to be pedantic (sorry), Caesar's latin alphabet did not have a letter J simple.wikipedia.org/wiki/… (sorry again, I just couldn't help it) – Mawg says reinstate Monica Nov 15 '16 at 11:01
• k is non existent in latin aswell, or do I err? It's probably confusing to anyone hearing about the cipher the first time here to omit letters just because they haven't been in the alphabet. – HopefullyHelpful Nov 15 '16 at 13:46
• If we want to be extra pedantic, we could say that it has a key length $n = 0$. At least some of the math works out, for example, an attacker that attempts $2^n$ keys will decipher the message with a probability of $2^{-n}$. – Luis Casillas Nov 15 '16 at 19:07
• @HopefullyHelpful K is rare in Latin, but it wasn't unknown in Caesar's day. It was mostly used with Greek-derived terms. The most common one that comes to mind would be "Kalends" where we get Calendar – eques Nov 15 '16 at 19:31
• Latin during Caesar's time had 23 letters and did not have the letters J, U, W. – Zvi Kedem Mar 28 '17 at 17:59

According to Fred B. Wrixon as well as Simon Singh, the definition of a cipher is: "Any means of encryption which can be manipulated according to a key." Anything with a fixed substitution can be called a code.