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Encyclopedia > Substitution box

In cryptography, a substitution box (or S-box) is a basic component of symmetric key algorithms. In block ciphers, they are typically used to obscure the relationship between the plaintext and the ciphertextShannon's property of confusion. In many cases, the S-boxes are carefully chosen to resist cryptanalysis. See also: Topics in cryptography The security of all practical encryption schemes remains unproven, both for symmetric and asymmetric schemes. ... A symmetric-key algorithm is an algorithm for cryptography that uses the same cryptographic key to encrypt and decrypt the message. ... In cryptography, a block cipher is a type of symmetric key cipher which operates on groups of bits of a fixed length, termed blocks. ... In cryptography, plaintext is information used as input to an encryption algorithm; the output is termed ciphertext. ... This article is about algorithms for encryption and decryption. ... Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ... In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Shannon in his paper, Communication Theory of Secrecy Systems published in 1949. ... For the Game Boy Advance cheat device, see CodeBreaker (Game Boy) Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ...


In general, an S-box takes some number of input bits, m, and transforms them into some number of output bits, n: an m×n S-box, implemented as a lookup table. Fixed tables are normally used, as in the Data Encryption Standard (DES), but in some ciphers the tables are generated dynamically from the key; e.g. the Blowfish and the Twofish encryption algorithms. A bit (abbreviated b) is the most basic information unit used in computing and information theory. ... In computer science, a lookup table is a data structure, usually an array or associative array, used to replace a runtime computation with a simpler lookup operation. ... General Designer(s) IBM First published 1975 (January 1977 as the standard) Derived from Lucifer (cipher) Cipher(s) based on this design Triple DES, G-DES, DES-X, LOKI89, ICE Algorithm detail Block size(s) 64 bits Key size(s) 56 bits Structure Feistel network Number of rounds 16 Best... This article is about algorithms for encryption and decryption. ... A key is a piece of information that controls the operation of a cryptography algorithm. ... General Designer(s) Bruce Schneier First published 1993 Derived from - Cipher(s) based on this design - Algorithm detail Block size(s) 64 bits Key size(s) 32-448 bits in steps of 8 bits; default 128 bits Structure Feistel network Number of rounds 16 Best cryptanalysis Four rounds of Blowfish... In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. ...


As a concrete illustration, consider this 6×4-bit S-box from DES (S5):

S5 Middle 4 bits of input
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1100 1011 1100 1101 1110 1111
Outer bits 00 0010 1100 0100 0001 0111 1100 1011 0110 1000 0101 0011 1111 1101 0000 1110 1001
01 1110 1011 0010 1100 0100 0111 1101 0001 0101 0000 1111 1100 0011 1001 1000 0110
10 0100 0010 0001 1011 1100 1101 0111 1000 1111 1001 1100 0101 0110 0011 0000 1110
11 1011 1000 1100 0111 0001 1110 0010 1101 0110 1111 0000 1001 1100 0100 0101 0011

Given a 6-bit input, the 4-bit output is found by selecting the row using the outer two bits, and the column using the inner four bits. For example, an input "011011" has outer bits "01" and inner bits "1101"; the corresponding output would be "1001".


The S-boxes of DES were the subject of intense study for many years out of a concern that a backdoor — a vulnerability known only to its designers — might have been planted in the cipher. The S-box design criteria were eventually published (Don Coppersmith, 1994) after the public rediscovery of differential cryptanalysis, showing that they had been carefully tuned to increase resistance against this specific attack. Other research had already indicated that even small modifications to an S-box could significantly weaken DES. A backdoor in a computer system (or a cryptosystem, or even in an algorithm) is a method of bypassing normal authentication or obtaining remote access to a computer, while intended to remain hidden to casual inspection. ... For the Game Boy Advance cheat device, see CodeBreaker (Game Boy) Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ... Don Coppersmith is a cryptographer and mathematician who was involved in the design of the Data Encryption Standard block cipher at IBM. He has also worked on algorithms for computing discrete logarithms, the cryptanalysis of RSA, methods for rapid matrix multiplication and IBMs MARS cipher, In 1972, Coppersmith obtained... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ...


There has been a great deal of research into the design of good S-boxes, and much more is understood about their use in block ciphers than when DES was released.


See also

In mathematics, a Boolean function is usually a function F(b1, b2, ... , bn) of a number n of Boolean variables bi from the two-element Boolean algebra {0,1}, and such that F also takes values in {0, 1}. A function on a general domain of a function taking values... In cryptography, a substitution cipher is a method of encryption by which units of plaintext are substituted with ciphertext according to a regular system; the units may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. ...

References

  • Coppersmith, Don. (1994). The data encryption standard (DES) and its strength against attacks. IBM Journal of Research and Development, 38(3), 243–250. [1] (http://www.research.ibm.com/journal/rd/383/coppersmith.pdf)
  • S. Mister and C. Adams, "Practical S-Box Design," Workshop on Selected Areas in Cryptography (SAC '96) Workshop Record, Queens University, 1996, pp. 61–76

External links


Block ciphers edit  (http://en.wikipedia.org/w/index.php?title=Template:Block_ciphers&action=edit)
Algorithms: 3-Way | AES | Akelarre | Blowfish | Camellia | CAST-128 | CAST-256 | CMEA | DEAL | DES | DES-X | FEAL | FOX | FROG | G-DES | GOST | ICE | IDEA | Iraqi | KASUMI | KHAZAD | Khufu and Khafre | LOKI89/91 | LOKI97 | Lucifer | MacGuffin | Madryga | MAGENTA | MARS | MISTY1 | MMB | NewDES | RC2 | RC5 | RC6 | REDOC | Red Pike | S-1 | SAFER | SEED | Serpent | SHACAL | SHARK | Skipjack | Square | TEA | Triple DES | Twofish | XTEA
Design: Feistel network | Key schedule | Product cipher | S-box | SPN   Attacks: Brute force | Linear / Differential cryptanalysis | Mod n | XSL   Standardisation: AES process | CRYPTREC | NESSIE   Misc: Avalanche effect | Block size | IV | Key size | Modes of operation | Piling-up lemma | Weak key

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Substitution — after mixing in the subkey, the block is divided into eight 6-bit pieces before processing by the S-boxes, or substitution boxes.
Permutation — finally, the 32 outputs from the S-boxes are rearranged according to a fixed permutation, the P-box.
The alternation of substitution from the S-boxes, and permutation of bits from the P-box and E-expansion provides so-called "confusion and diffusion" respectively, a concept identified by Claude Shannon in the 1940s as a necessary condition for a secure yet practical cipher.
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