The Codes: Matrix Code Mystery Cache
Dr_B: I stopped by to check on this one and it appears it's missing. 'Tis time to hit the road, with Lander moving its baseball field also.
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Difficulty:
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Terrain:
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Size: 
(small)
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This cache is one of a series designed to introduce cachers to the
use of encryption codes. CACHE IS NOT AT THE POSTED COORDINATES,
but is within a mile. The answers to the questions below can be
answered at or near the posted coordinates, which will help in
finding the final coordinates.
Matrix Code
A Matrix Code is different from basic ciphers in that it
simultaneously alters blocks of text as opposed to individual
characters. This makes it much harder to decode unless you happen
to know the matrix used for encoding (or better yet, for decoding -
but we'll get to that).
The first step in encoding is to choose a square invertible
matrix, which I will call the "encoding matrix" or 'E'. Here is an
example of a 2x2 (rows x columns) invertible matrix. This is only
an example, but is the same size matrix as the one I used.
The second step is to write the message you wish to send as numbers
using the numbers below, ignoring spaces. The resulting chain of
numbers is then broken into pairs.
For example, "the code" turns into "20 8 5 3 15 4 5", and these
are divided into "20 8", "5 3", "15 4", and "5 0" (using a zero to
fill out the last group). The encoding matrix is now multiplied by
each of these pairs written as a column matrix (a 2x1 matrix with 2
rows and one column). If you do not know how to multiply matrices,
I refer you to
this very good tutorial.
Once you have finished, you string out all the resulting numbers
and send the whole chain of numbers. If someone intercepts the
message, it should hopefully look like gibberish to them.
The resulting coded message from the example above will be "-12 20
-2 5 -11 15 -5 5"
To decrypt, you need to find the inverse matrix of the encoding
matrix which I will call the "decoding matrix". Thankfully with 2x2
matrices there is a formula to do this.
If we have 
, the inverse matrix is 
.
At this point, all that remains is to multiply the decoding matrix
by groups of the coded message, then convert the result back to
letters.
The inverse of the example matrix above is 
. When you multiply this with the coded
message, it should give you the numbers you began with.
If you are REALLY good, you can figure out the matrix from me
telling you that the message starts with "north". If not, you can
visit the area at the posted coordinates and find the entries in
the ENCODING matrix as follows (letters correspond to the pattern
above). Note: one or more negative numbers should be expected!
- a = The second minus third digit of the distance down the left
field line.
- b = The first digit minus the second digit of the speed limit
here.
- c = The admission cost in dollars to a game minus 2.
- d = The number of letters in the mascot of the team whose home
field this is divided by 4.
-13 2 -16 4 4 24 2 20 -5 0
3 18 -24 -6 -16 -2 10 30 -31 -16
-33 -28 -39 -34 -13 2 -11 -6 -11 -4
4 24 -41 -36 -18 2 -1 8 -6 2
-20 0 -31 -16 -1 8 -6 2 -25 -10
-1 14 -23 -18 -33 -28 -39 -34 -28 -28
You're looking for a decon container with a few sports-related
items to start the cache off. Depending on your timing, you may
have muggle issues so please be discreet.
Additional Hints
(Decrypt)
[puzzle:] Zngevk zhygvcyvpngvba uryc ng uggc://jjj.rnflpnyphyngvba.pbz/zngevk/zngevk-zhygvcyvpngvba.cuc
Treasures
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