Ars Paradoxica: 24 - Dilemma - Green

In episode 24: Dilemma, the second of season 3, our friendly nemesis the numbers station provides us with this:

GREEN

08 02 28 19 22 28 09 12 11 18 19 16 31 20 40 25 30 41 25 30 38 38 33 28 38 47

WEATHER: arid
MARKETS: rising

The first hint that this is something different is that there are two pass codes, as there were in 23. I REALLY wanted this to be a two-keyed Vigenere, because I love the concept - combining the best of the Playfair cipher and the Vigenere and generally being absolutely insane to crack - unless you use the handy code on Rumkin. I thought I had it all made.... 

And then I noticed that not all of the numbers were under 26. Ok, fine, I'll subtract 26 from the high ones - no problem (essentially mod 26). Still complete nonsense. And yes, I tried it multiple ways, backwards and forwards, trying to use the keyed system. No luck. 26 characters of absolute unintelligible blah. 

Staring at it, eventually got to the point where I'll try anything, even really annoying things. If markets are rising and the numbers are essentially getting higher towards the right, maybe I have to do some falling. Fast forward through multiple attempts at rotating them 'down' uniformly - not going to work. Ok, what if I rotate them down in an ascending order (more negative towards the right), subtracting 1 from the first, 2 from the second, 3 from the 3rd, etc.

My first attempt gave me 7 0 25 15 17 22 2 4 2 8 8 4 18 6 25 9 13 23 6 10 17 16 10 4 13 21, which doesn't work as the second character becomes a 0. Thankfully, I was working on an excel table at this point, so I could simply shift the subtraction over by one. 

This gave me: 8 1 26 16 18 23 3 5 3 9 9 5 19 7 26 10 14 24 7 11 18 17 11 5 14 22, and there was much rejoicing as everything was, at least, 26 or under. 

From there, follow the standard GREEN procedure.

Converting the cipher text into A=01 alphabet gives H A Z P R W C E C I I E S G Z J N X G K R Q K E N V.

Converting the pass code ARID into A=26, Z=01 gives 26-09-18-23. Re-encoding that with A=01 gives you ZIRW. 

From there, run a Vigenere with ZIRW as the key and H A Z P R W C E C I I E S G Z J N X G K R Q K E N V as the cipher text any way you would prefer (I must admit at this point I went straight to Rumkin). 

Is It Solidarity In Opposition

TL;DR: To solve this particular code, starting at 0, subtract 0 to 25 from the numbers provided, then follow the standard GREEN procedure. 

Here is the math method, remembering that when we use the math method, we subtract 01 from each of the numbers in the key, so that ARID (26-09-18-23) becomes 25-08-17-22

Ciphertext	8	2	28	19	22	28	9	12	11	18	19	16	31	20	40	25	30	41	25	30	38	38	33	28	38	47
Falling	0	-1	-2	-3	-4	-5	-6	-7	-8	-9	-10	-11	-12	-13	-14	-15	-16	-17	-18	-19	-20	-21	-22	-23	-24	-25
Falling Solution	8	1	26	16	18	23	3	5	3	9	9	5	19	7	26	10	14	24	7	11	18	17	11	5	14	22
Arid A=25	25	8	17	22	25	8	17	22	25	8	17	22	25	8	17	22	25	8	17	22	25	8	17	22	25	8
Subtraction (Decoding)	-17	-7	9	-6	-7	15	-14	-17	-22	1	-8	-17	-6	-1	9	-12	-11	16	-10	-11	-7	9	-6	-17	-11	14
Mod 26	9	19	9	20	19	15	12	9	4	1	18	9	20	25	9	14	15	16	16	15	19	9	20	9	15	14
A=01	I	S	I	T	S	O	L	I	D	A	R	I	T	Y	I	N	O	P	P	O	S	I	T	I	O	N

Many thanks to Table Generator for making it easier to display