In 1978, a public key encryption system was developed by three MIT scientists (Rivest, Shamir, and Aldeman). This encryption method is known by their initials RSA. It is asymmetrical. That is, the keys used to encode the message cannot be used to decode it. The encryption method uses two public keys and one private key. One of the public keys is the product of two prime numbers. The remaining two keys are derived from the two prime numbers. Typically the numbers used are very large in the order of 200 digits each. The factors of the resulting multiplication are extremely hard to determine. If keys one and two are used to encode the message only keys one and three will decode it. Therefore if you know my two public keys and I send you a message encoded with my private key that you are able to decode using the public keys, you can be assured that I sent it. This is the basis of the security certificates used on the web today. I have used much smaller primes to encode the coordinates of this cache.
WIKIPEDIA explanation:
The public key is (n = 3233, e = 17). For a padded message m the encryption function is:
c = me mod n
The private key is (n = 3233, d = 2753). The decryption function is:
m = cd mod n
For example, to encrypt m = 123, we calculate
c = 12317 mod 3233 = 855
To decrypt c = 855, we calculate
m = 8552753 mod 3233 = 123
The decoding keys are N = 1142411 and D=7. The encoded coordinates are 698496.
The result of your decoding will be a six-digit number. The left three digits of the result are the last three digits of the latitude. The right three digits are the last three digits of the longitude. .
Consider yourself lucky, as I had to multiply over 300,000 times to determine the encoded message. (Not really I used a mathematical shortcut).
