In cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, an S-Box (Substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

s, they are typically used to obscure the relationship between the key and the ciphertext

Ciphertext

In cryptography, ciphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher...

 — Shannon's property of confusion

Confusion and diffusion

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Shannon in his paper Communication Theory of Secrecy Systems, published in 1949....

. In many cases, the S-Boxes are carefully chosen to resist cryptanalysis

Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

.

In general, an S-Box takes some number of input bit

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s, m, and transforms them into some number of output bits, n: an m×n S-Box can be implemented as a lookup table

Lookup table

In computer science, a lookup table is a data structure, usually an array or associative array, often used to replace a runtime computation with a simpler array indexing operation. The savings in terms of processing time can be significant, since retrieving a value from memory is often faster than...

 with 2^m words of n bits each. Fixed tables are normally used, as in the Data Encryption Standard

Data Encryption Standard

The Data Encryption Standard is a block cipher that uses shared secret encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 and which has subsequently enjoyed widespread use internationally. It is...

 (DES), but in some cipher

Cipher

In cryptography, a cipher is an algorithm for performing encryption or decryption — a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...

s the tables are generated dynamically from the key; e.g. the Blowfish

Blowfish (cipher)

Blowfish is a keyed, symmetric block cipher, designed in 1993 by Bruce Schneier and included in a large number of cipher suites and encryption products. Blowfish provides a good encryption rate in software and no effective cryptanalysis of it has been found to date...

 and the Twofish

Twofish

In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but was not selected for standardisation...

 encryption algorithms. Bruce Schneier

Bruce Schneier

Bruce Schneier is an American cryptographer, computer security specialist, and writer. He is the author of several books on general security topics, computer security and cryptography, and is the founder and chief technology officer of BT Managed Security Solutions, formerly Counterpane Internet...

 describes IDEA

International Data Encryption Algorithm

In cryptography, the International Data Encryption Algorithm is a block cipher designed by James Massey of ETH Zurich and Xuejia Lai and was first described in 1991. As a block cipher, it is also symmetric. The algorithm was intended as a replacement for the Data Encryption Standard[DES]...

's modular multiplication step as a key-dependent S-Box.

One good example of a fixed table is 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	1010	1011	1100	| 1101	1110	1111
Outer bits	00	0010	1100	0100	0001	0111	1010	1011	0110	1000	0101	0011	1111	1101	0000	1110	1001
	01	1110	1011	0010	1100	0100	0111	1101	0001	0101	0000	1111	1010	0011	1001	1000	0110
	10	0100	0010	0001	1011	1010	1101	0111	1000	1111	1001	1100	0101	0110	0011	0000	1110
	11	1011	1000	1100	0111	0001	1110	0010	1101	0110	1111	0000	1001	1010	0100	0101	0011

Given a 6-bit input, the 4-bit output is found by selecting the row using the outer two bits (the first and last 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 8 S-Boxes of DES were the subject of intense study for many years out of a concern that a backdoor — a vulnerability

Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

 known only to its designers — might have been planted in the cipher. The S-Box design criteria were eventually published (in ) after the public rediscovery of differential cryptanalysis

Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output...

, 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.

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

• Bijection
  Bijection
  A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements...
  
  
• Boolean function
• Nothing up my sleeve number
  Nothing up my sleeve number
  In cryptography, nothing up my sleeve numbers are any numbers which, by their construction, are above suspicion of hidden properties. They are used in creating cryptographic functions such as hashes and ciphers. These algorithms often need randomized constants for mixing or initialization purposes...
  
  
• Substitution cipher
  Substitution cipher
  In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
  
  
• Rijndael S-box
  Rijndael S-box
  This article describes the S-box used by the Rijndael cryptographic algorithm.- Forward S-box :The S-box is generated by determining the multiplicative inverse for a given number in GF = GF[x]/, Rijndael's finite field...
  
  
• Permutation box
  Permutation box
  In cryptography, a permutation box is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, retaining diffusion while transposing....
  
  

External links

• A literature survey on S-Box design
• John Savard's "Questions of S-Box Design"
• Gargiulo's "S-Box Modifications and Their Effect in DES-like Encryption Systems"