analysing cryptographic algorithms, potentially uncovering weaknesses in them (e.g. "breaking" them or casting doubts on their actual security)
Cryptanalysis is the analysis of cryptographic algorithms with the aim of finding weaknesses, which allow attackers to "break" them. For ciphers, the aim is to get the key or plaintext, for hashes it is to find collisions or preimages, for signatures/MACs it is to create forgeries. Methods include differential, linear and algebraic cryptanalysis.