Substitution box
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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.
See also
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 (http://www.ciphersbyritter.com/RES/SBOXDESN.HTM)
- John Savard's "Questions of S-Box Design" (http://home.ecn.ab.ca/~jsavard/crypto/co4513.htm)
- Practical S-Box Design (http://adonis.ee.queensu.ca:80/sac/sac96/papers.html) by S. Mister and C. Adams (PDF)
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