Is there a name for this 'enhanced' caeser shift and if so, is it trivial to break? This cipher shifts the letter that it will shift to, after each shift...

I used to play with this when I was a kid. I was thinking about it recently and realized that it wasn't as simple as I thought. Here's the description:


  The second number makes the code much harder to break. It changes the number of letters above the letter to be replaced by a different amount each time. For example "a" will be subsituted by "b" (one place higher), "b" by "d" (two places higher), "c" by "f" (three places higher) and so on. Try changing the second code number in the code maker and see how much more difficult trying to break the code will be. 


Source: http://web.archive.org/web/20120818085711/http://www.puzzlepixies.com/activites/activites/make-secret-codes.html

Is there a name for this type of shift?
So if I understand correctly, the following describes your cipher:


Take letters A-Z to be numbers 0-25.
Let Mi represent letter i of the message
Let Ci represent letter i of the ciphertext
Let n be the ceasar shift number
Let m be the skip number
Let the key be described as the tuple (n,m)
Then, Ci = (Mi + n + m*i) modulo 26


The system is a type of polyalphabetic cipher. The Trithemus cipher is the same as your system, but it always used a key of (0,1). Your system is also equivalent to a Vigenere cipher that uses a key that is the full alphabet, but rotated a skip number of letters.

I can't find any reference to historical use of this system, so very likely there is no standard name for this type of cipher.

This cipher is still easy to break, because there are strict limits on the numbers you can choose for the shift and skip. 


The shift can only be from 0 to 25, because any higher numbers work the same as a number from 0 to 25.
The skip can also only be from 0 to 25, for exactly the same reason.
This means the total set of keys is 26*26 = 676


It's not hard to brute force 676 keys with a computer, but you usually don't have to. If you try all 26 skips, then you can figure out which skip is correct by doing a frequency analysis of the letters. The letter distribution that looks closest to the letter distribution of English is probably your skip. Then you just have to guess the shift based on the same frequency analysis you just did.