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 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).

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

S₅		Middle 4 bits of input
S₅		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".^[2]

The eight 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.^{[citation needed]}

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]

References

^ 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.
^ 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.
^ Gargiulo's "S-box Modifications and Their Effect in DES-like Encryption Systems" Archived 2012-05-20 at the Wayback Machine p. 9.
^ RFC 4086. Section 5.3 "Using S-boxes for Mixing"

External links

[chandra-516-1] 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"

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S-box

See also

References

Further reading

External links