# Cryptography/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 — Claude Shannon's property of confusion.[1] 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 can be implemented as a lookup table with $2^m$ words of n bits each. 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. Bruce Schneier describes IDEA's modular multiplication step as a key-dependent S-Box.

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 known only to its designers — might have been planted in the cipher. The S-Box design criteria were eventually published[2] 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.

## ReferencesEdit

1. Chandrasekaran, J. et al. (2011). "A Chaos Based Approach for Improving Non Linearity in the S-Box Design of Symmetric Key Cryptosystems". in Meghanathan, N. et al.. Advances in Networks and Communications: First International Conference on Computer Science and Information Technology, CCSIT 2011, Bangalore, India, January 2-4, 2011. Proceedings, Part 2. Springer. p. 516. ISBN 978-3-642-17877-1.
2. Coppersmith, Don (1994). "The Data Encryption Standard (DES) and its strength against attacks" (PDF). IBM Journal of Research and Development 38 (3): 243–250. doi:10.1147/rd.383.0243. Retrieved 2007-02-20.