cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (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 Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic se ...

.Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Fifth Printing (August 2001) page 251. The product cipher combines a sequence of simple transformations such as substitution (S-box),

permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...

(P-box), and

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...

. The concept of product ciphers is due to

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...

, who presented the idea in his foundational paper, ''

Communication Theory of Secrecy Systems "Communication Theory of Secrecy Systems" is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory Information theory is the mathematical study of the quantification (science), quantifica ...

''. A particular product cipher design where all the constituting transformation functions have the same structure is called an iterative cipher with the term " rounds" applied to the functions themselves. For transformation involving reasonable number of n message symbols, both of the foregoing cipher systems (the S-box and 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 The most common meaning for Lucifer in English is as a name for the Devil in Christian theology. He appeared in the King James Version of the Bible in Isaiah and before that in the Vulgate (the late-4th-century Latin translation of the Bib ...

cipher system, and has become the standard for national data encryption standards such as the

Data Encryption Standard The Data Encryption Standard (DES ) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cryp ...

and the

Advanced Encryption Standard The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant ...

. A product cipher that uses only substitutions and permutations is called a SP-network.

Feistel cipher In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering resear ...

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