Definition
Product Cipher
A product cipher is a cipher that consists of the combination of multiple, possibly iterated transformations. Its goal is to produce a cipher stronger than its individual components.
Composition
Modern product ciphers consist of the iterative combination of substitutions, transpositions, and modular arithmetic. An example is AES.
Caution
Not All Combinations Strengthen the Cipher
Two consecutive monoalphabetic substitutions are equivalent to another monoalphabetic substitution. Composition does not automatically increase security if the component transformations belong to the same class.