So I was checking out where/how the Chinese Remainder Theorem is used outside the classroom and I found some pretty interesting stuff. The best way I saw its uses described is by "the three c's": computing, coding, and *cryptography*. Of these I found the last to be the most interesting. I used to watch a lot of X-Files…

Cryptography is the practice and study of hiding information. I found a paragraph in an article titled "Applications to the Chinese Remainder Theorem" from http://neworder.box.sk/files/CRT.pdf that I thought described pretty well how cryptography and the CRT are related:

"Let N be a very large secret integer. To prevent misuse, the secret N is split among n servers

nation wide. During an emergency, the partial secrets are collected and worked together to

retrieve N. However, if p servers are down (for a number of reasons), N can be retrieved from

the remaining k = n-p servers, as long as n-p >= k, the threshold value. Such a scheme is

called k-threshold system for secret sharing. If we choose p1, p2, …,pr to be r different

primes such that kth root of N < pi much< k-1th root of N, for each pi, then the secret N can be

unlocked using k servers but not by a fewer number of servers."

What is more interesting is that the use of cryptography is extremely controversial, and continues to get more controversial as the technological age advances. The prohibition of cryptography has been an interest to law enforcement and intelligence agencies for a long time. Their argument is based on the idea that its use tends be related to criminal, treasonous, and even civil-rights-violating behaviors. Both the control of the export of cryptography and NSA's previous uses of cryptography were also of major concerns in the 1980's and 1990's.

Who knew the CRT could get so dangerous?