Editing Product cipher (section)

{{refimprove|date=February 2009}}
In [[cryptography]], a '''product cipher''' combines two or more transformations in a manner intending that the resulting cipher is more secure than the individual components to make it resistant to [[cryptanalysis]].<ref>Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Fifth Printing (August 2001) page 251.</ref> The product cipher combines a sequence of simple transformations such as [[substitution cipher|substitution]] (S-box), [[transposition cipher|permutation]] (P-box), and [[modular arithmetic]].  The concept of product ciphers is due to [[Claude Shannon]], who presented the idea in his foundational paper, ''[[Communication Theory of Secrecy Systems]]''. A particular product cipher design where all the constituting transformation functions have the same structure is called an '''iterative cipher''' with the term "[[Round (cryptography)|rounds]]" applied to the functions themselves.{{sfn|Biryukov|2005}}

For transformation involving reasonable number of n message symbols, both of the foregoing cipher systems (the [[Substitution box|S-box]] and [[Permutation box|P-box]]) are by themselves wanting. Shannon suggested using a combination of S-box and P-box transformation—a product cipher. The combination could yield a cipher system more powerful than either one alone. This approach of alternatively applying substitution and permutation transformation has been used by IBM  in the [[Lucifer (cipher)|Lucifer]] cipher system, and has become the standard for national data encryption standards such as the [[Data Encryption Standard]] and the [[Advanced Encryption Standard]]. A product cipher that uses only substitutions and permutations is called a [[SP-network]]. [[Feistel cipher]]s are an important class of product ciphers.