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 — Shannon's property of confusion.

In general, an S-box takes some number of input bits, m, and transforms them into some number of output bits, n, where n is not necessarily equal to m.[1] An m×n S-box can be implemented as a lookup table with 2m 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).

One good example of a fixed table is the S-box from DES (S5), mapping 6-bit input into a 4-bit output:

S5Middle 4 bits of input
0000000100100011010001010110011110001001101010111100110111101111
Outer bits 00 0010110001000001011110101011011010000101001111111101000011101001
01 1110101100101100010001111101000101010000111110100011100110000110
10 0100001000011011101011010111100011111001110001010110001100001110
11 1011100011000111000111100010110101101111000010011010010001010011

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".[2]

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 (in Coppersmith 1994) after the public rediscovery of differential cryptanalysis, showing that they had been carefully tuned to increase resistance against this specific attack. Biham and Shamir found that even small modifications to an S-box could significantly weaken DES.[3]

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.

Any S-box where any linear combination of output bits is produced by a bent function of the input bits is termed a perfect S-box.[4]

See also

References
  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. (eds.). 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. Buchmann, Johannes A. (2001). "5. DES". Introduction to cryptography (Corr. 2. print. ed.). New York, NY [u.a.]: Springer. pp. 119–120. ISBN 978-0-387-95034-1.
  3. Gargiulo's "S-Box Modifications and Their Effect in DES-like Encryption Systems" Archived 2012-05-20 at the Wayback Machine p. 9.
  4. RFC 4086. Section 5.3 "Using S-Boxes for Mixing"

Further reading
  • Chuck Easttom (2018). A Generalized Methodology for Designing Non-Linear Elements in Symmetric Cryptographic Primitives. IEEE Computing and Communication Workshop and Conference (CCWC), 2018 IEEE 8th Annual. IEEE. pp. 444–449. doi:10.1109/CCWC.2018.8301643. ISBN 978-1-5386-4649-6.
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