Cryptographic Criteria on Vector Boolean Functions
Jos Antonio, Pedro J. · InTech eBooks · 2012
Cryptographic Criteria on Vector Boolean Functions 3 Preliminaries DefinitionsLet be the finite field of order 2, where GF(2)=Z 2 = {0, 1},'+' the 'integer addition modulo 2' and '•' the 'integer multiplication modulo 2'.V n is the vector space of n-tuples of elements from GF(2).The direct sum of x ∈ V n 1 and y ∈ V n 2 is defined as x ⊕ y =(x 1 ,...,x n 1 , y 1 ,...,y n 2 ) ∈ V n 1 +n 2 .The inner product of x, y ∈ V n is denoted by x • y, and of real vectors x, y ∈ R n is denoted by x, y .Let x, y ∈ R n , the pointwise product is defined as 2) is called a Boolean function and F n is the set of all Boolean functions on V n .L n is the set of all linear Boolean functions on V n :59 Cryptographic Criteria on Vector Boolean Functions www.intechopen.comThis result is a generalization of what is obtained for Boolean functions.Let f23) 64 Cryptography and Security in Computing www.intechopen.com