Product ciphers are ciphers that are built as a composition of several different functions. In a special case when all the functions are the same, the cipher is called iterative cipher and the functions are called rounds. The intuition behind such constructions is inspired by the analogy with mixing transformations studied in the theory of Dynamical Systems, which was first noted by Shannon 3. The IBM team followed this approach in the design of Lucifer and the Data Encryption Standard (DES). Rounds of iterative ciphers are typically keyed with different subkeys or at least involve different round constants to break self-similarity, which otherwise would be vulnerable to slide attacks. Note that the individual round transformation might be cryptographically weak. The strength of the whole construction relies on the number of iterations. The choice of the proper number of rounds is a difficult task, which is performed via cryptanalysis of the cipher. Most of the modern block-ciphers...
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References
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Biryukov, A. (2005). Product Cipher, Superencryption. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_320
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