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 ciphertext — Shannon's property of confusion. In many cases, the S-boxes are carefully chosen to resist cryptanalysis.

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.

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.

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.

Table of contents

1 See also 2 References 3 External links

See also

• Boolean function
• Substitution cipher

References

• Coppersmith, Don. (1994). The data encryption standard (DES) and its strength against attacks. The IBM Journal of Research and Development, 38(3), pp243–250.
• 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

• A literature survey on S-box design
• John Savard's "Questions of S-Box Design"
• Practical S-Box Design by S. Mister and C. Adams (PDF)

Block ciphers

Algorithms: 3-Way | AES | Akelarre | Blowfish | Camellia | CAST-128 | CAST-256 | CMEA | DEAL | DES | DES-X | FEAL | G-DES | GOST | IDEA | Iraqi | KASUMI | KHAZAD | Khufu and Khafre; | LOKI89/91 | LOKI97 | Lucifer | MacGuffin | Madryga | MAGENTA | MARS | MISTY1 | MMB | NewDES | RC2 | RC5 | RC6 | 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;

Help build the largest human-edited directory on the web.

Submit a Site - Open Directory Project - Become an Editor