This puzzle cache requires you to crack a message that has been encoded using a method similar to that used to encrypt the data passed around the internet.
The method used on the internet is the RSA algorithm that was publicly described in 1978 by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT; the letters RSA are the initials of their surnames
Here is a link to the wikipedia article on the subject, I'll use the notation from that to set out the puzzle below: https://en.wikipedia.org/wiki/RSA_(cryptosystem)
And to another article that you should find useful: http://www.cs.princeton.edu/courses/archive/spr05/cos126/lectures/22.pdf
I'll give you the Public Key and a sequence of encrypted numbers, you need to decrypt them, giving another sequence of numbers. I won’t tell you the Private key, d, you have to act as code-breaker to work out what it is. To convert these into co-ordinates you need to use the code A=1, B=2, C=3, etc.
To make this (fairly) easy to solve d will be less than 100. In practice the numbers used in commercial encryptions are often 1024-bit numbers. That is, numbers up to 2^1024, which is around 1 followed by 300 zeros. That is why its so hard to crack, and so why it is secure. (The ' ^ ' symbol is ' to the power of ' in spreadsheets, so 2^3 = 8 for example)
To show you how it works here is a simple example:
The Public Key is (N=38, e = 11)
The Private Key is (N=38, d = 5)
The code, C, is 32,3,18,20,12
To decrypt this:
m = c^d Mod N
[Hint: " x Mod N" means the remainder if you divide x by N a whole number of times.
For example, 19 Mod 4 is 3, 101 Mod 5 is 1.
To work this out on a spreadsheet you can use a formula like:
m mod N = m - N * INT( m / N) ]
| Code |
m=C^d |
m Mod N |
Means |
| 32 |
33,554,432 |
14 |
N |
| 3 |
243 |
15 |
O |
| 18 |
1,889,568 |
18 |
R |
| 20 |
3,200,000 |
20 |
T |
| 12 |
248,832 |
8 |
H |
PUZZLE:
The Public Key is (n=403, e = 47)
The Private Key is (n=403, d = ?)
The cache is found at
N 51 30.X
W 000.05.Y
Where
X = 242,81,80,343,28,292,292,85,196,242,129,130,206,81,292,1,345
Y = 130,242,138,85,1,345,28,343,138,242,242,292,129,336,81,198,242,345,1
Clue = 345,242,343,81,196,140,292,345,259,1,22,344,292,242,292,138,242,140,292,28,277,85
You can check your answers for this puzzle on Geochecker.com.