2
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Encoded text:

9, 15, 15, 16, 25, 6, 11, 2, 9, 6, 11, 2, 21, 1, 14, 9, 19, 23, 25, 17, 19, 18, 1

Hint 1:

Look up n-bonacci

Hint 2:

Starting numbers are different

Hint 3:

Message length is the same as encoded length

Hint 4 (slightly changed):

All the numbers are in a certain range. What is the modulo for that range?

Hint 5

This cipher has no key.

Hint 6 (basically gives it away)

n-bonacci starting numbers are the message.

Hint 7 (literally just describes the encryption algorithm)

Start with the letter values of the message, and repeat as many times as there are letters in the message: Change the current letter values to the values except the first, and then the sum of the values, including the first, mod 26. In code: for _ in range(len(message)): message = message[1:] + sum(message) % 26

I will add more if it is not solved soon.

Hints are in no particular order, but some might be less helpful than others.

Notes:

This will probably be very tedious without computers, so they are allowed. The message is all lowercase letters, with no spaces, but it is more than one word.

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  • $\begingroup$ Perhaps, individual numbers can be comma separated, rather than by currently used space for better clarity. $\endgroup$ – Mea Culpa Nay Nov 5 '17 at 5:09
  • $\begingroup$ is the message a common phrase? $\endgroup$ – Dr t Nov 5 '17 at 19:24
  • $\begingroup$ Computers allowed or not? $\endgroup$ – ABcDexter Nov 5 '17 at 19:44
  • $\begingroup$ It is not a common phrase, and computers are allowed. $\endgroup$ – internet_user Nov 5 '17 at 21:56
  • $\begingroup$ “Message length is the same as encoded length” Is that the quantity of individual numbers or digits? $\endgroup$ – Ambo100 Nov 6 '17 at 14:30
3
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The message is

CONGRATULATIONSYOUGOTIT

though really

not much congratulation is in order for simply inverting the algorithm OP has kindly provided :-).

Algorithm:

once per number in the list: compute last number minus sum of others, mod 26, put that at the start of the list, and drop the last one. (This is just doing the encoding algorithm in reverse.)

Remark:

although no one got this until the answer was more or less handed to us on a plate, I don't think it was particularly unreasonable; there are only so many things to try and this should have been one of the earlier ones. On the other hand, I did spend a little while staring at it earlier when there weren't so many hints, and this wasn't one of the things I thought of trying :-).

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