cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

, 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 sec ...

.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 Substitution may refer to: Arts and media *Chord substitution, in music, swapping one chord for a related one within a chord progression * Substitution (poetry), a variation in poetic scansion * "Substitution" (song), a 2009 song by Silversun Pi ...

(S-box),

permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

(P-box), and

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ...

. The concept of product ciphers is due to

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-o ...

, 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. It is one of the foundational treatments (arguably ''the'' foundational treatment) of modern c ...

''. For transformation involving reasonable number of n message symbols, both of the foregoing cipher systems (the

S-box In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Sha ...

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 Lucifer is one of various figures in folklore associated with the planet Venus. The entity's name was subsequently absorbed into Christianity as a name for the devil. Modern scholarship generally translates the term in the relevant Bible passage ...

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 cry ...

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 research ...

s are an important class of product ciphers.

References

External links

The Cryptography FAQ
Block ciphers {{crypto-stub