Below are some problems related to computer security (specifically poorly implemented security). Do Them. You are free to use any language and environment you like to complete them. The problems require familiarity with programming, but not necessarily with applied cryptography or computer security in general. An understanding of how some of the algorithms and tools in the problems work will be of use, so as a starting point you can find some resources to help you begin here. If this topic is new to you, you may want to start with the Tutorial Problems.
Fast Hashing Passwords
Cryptographic hash functions shouldn't be used to hash passwords directly
CCA on Textbook RSA
Turns out padding is important
Salt Alone Won't Save You
Salting password hashes is important, but not enough on it's own
It's easy to generate bad symmetric keys