The purposes of this geoart series are twofold: to bring cachers to the watershed of the North Fork of the Broad River in Stephens and Franklin Counties and to serve as an introduction to the fascinating field of cryptography.
We use a decimal numeral system -- each digit represents a multiple of a power of 10. For example,
43,125 = 4×104 + 3×103 + 1×102 + 2×101 + 5×100
Ten digits are required -- 0, 1, 2, ..., 9.
An alternative to this is the binary numeral system, in which each digit represents a multiple of a power of 2. Only two digits are required -- 0 and 1. For example,
43,125 = 32,768 + 8,192 + 2,048 + 64 + 32 + 16 + 4 + 1
= 1×215 + 0×214 + 1×213 + 0×212 + 1×211 + 0×210 + 0×29 + 0×28 + 0×27 + 1×26 + 1×25
+ 1×24 + 0×23 + 1×22 + 0×21 + 1×20,
and so it is denoted in binary by 1010100001110101.
Now suppose we have two binary numbers. The bitwise XOR (for eXclusive OR) operation, denoted by ⊕, takes the corresponding digits from each number and returns a 1 if they are different and a 0 if they are the same. For example, 1010 ⊕ 0110 = 1100.
In the XOR cipher, Alices wants to send her friend Bob a plaintext message m. She encodes it as a binary number and performs a bitwise XOR with some key k to compute the ciphertext c, i.e., m ⊕ k = c.
Bob also knows k, and he is able to recover the plaintext by performing another bitwise XOR, i.e., c ⊕ k = m.
The XOR cipher is susceptible to a known plaintext attack. Indeed, if someone knows how one plaintext message has been encrypted, then they can recover the key and use it to decrypt any further messages.
To find this geocache below, decrypt the coordinates below. The degrees are correct, but the minutes have been encrypted using a XOR cipher (ignoring the decimal point). Furthermore, you are given that the plaintext 22,795 is encrypted as the ciphertext 46,649.
N 34° 40.299' W 083° 55.044'
Congratulations to fanasfreaks for FTF!