When a block cipher is used in a given mode of operation, the resulting algorithm should ideally be about as secure as the block cipher itself. ECB (discussed above) emphatically lacks this property: regardless of how secure the underlying block cipher is, ECB mode can easily be attacked. On the other hand, CBC mode can be proven to be secure under the assumption that the underlying block cipher is likewise secure. Note, however, that making statements like this requires formal mathematical definitions for what it means for an encryption algorithm or a block cipher to "be secure". This section describes two common notions for what properties a block cipher should have. Each corresponds to a mathematical model that can be used to prove properties of higher level algorithms, such as CBC.
This general approach to cryptography---proving higher-level algorithms (such as CBC) are secure under explicitly stated assumptions regarding their components (such as a block cipher)---is known as provable security.