From Wikipedia, "Cryptography or cryptology is the practice and study of techniques for secure communication in the presence of third parties called adversaries."
Cryptography CTF challenges often require the players to break or otherwise decrypt a secure message by taking advantage of vulnerabilities in the encryption process, such as the use of weak keys.
A list of tips from OTA CTF members, mostly focusing on reverse engineering and binary exploitation, plus a bit of crypto. This links to the crypto section.
Browser tools for solving simple crypto challenges