Boolean functions play a central role in the design of most symmetric cryptosystems and in their security. In stream ciphers, they are usually used to combine the outputs to several linear feedback shift registers (see the corresponding entry and Combination generator), or to filter (and combine) the contents of a single one (see Filter generators). The sequence of their output, during a certain number of clock cycles, then produces the pseudorandom sequence which is used in a Vernam cipher (that is, which is bitwisely added to the plaintext to produce the ciphertext). In block ciphers (see Block cipher, Data Encryption Standard (DES), Advanced Encryption Standard (Rijndael/AES)), the S-boxes are designed by appropriate composition of nonlinear Boolean functions.
An n-variable Boolean function f is a function from the set \(F_2^n\) of all binary vectors \(x=(x_1,\dots,x_n)\) of length n to the field \(F_2=\{0,1\}\). The number nof variables is rarely large in practice. In the case of...
This is a preview of subscription content, log in via an institution to check access.
References
Evertse, J.H. (1988). “Linear structures in block ciphers.” Advances in Cryptology—EUROCRYPT'87, Lecture Notes in Computer Science, vol. 304, eds. David Chaum and Wyn L. Price. Springer-Verlag, Berlin, 249–266.
Massey, J.L. (1969). “Shift-register analysis and BCH decoding.” IEEE Trans. Inform. Theory, 15, 122–127.
Menezes, A., P. van Oorschot, and S. Vanstone (1996). Handbook of Applied Cryptography. CRC Press Series on Discrete Mathematics and its Applications. http://www.cacr.math.uwaterloo.ca/hac
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 International Federation for Information Processing
About this entry
Cite this entry
Carlet, C. (2005). Boolean Functions. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_40
Download citation
DOI: https://doi.org/10.1007/0-387-23483-7_40
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23473-1
Online ISBN: 978-0-387-23483-0
eBook Packages: Computer ScienceReference Module Computer Science and Engineering