Cryptographic boolean functions via group Hadamard matrices

Authors

Jennifer Seberry, University of WollongongFollow
Xian-Mo Zhang, University of WollongongFollow
Yuliang Zheng, University of WollongongFollow

Publication Details

Jennifer Seberry, Xian-Mo Zhang and Yuliang Zheng, Cryptographic boolean functions via group Hadamard matrices , Australasian Journal of Combinatorics, 10, (1994), 131-145.

Abstract

For any integers n,m, 2n > m > n we construct a set of boolean functions on Vm, say {f₁(z),...,f_n(z)}, which has the following important cryptographic properties:

(i) any nonzero linear combination of the functions is balanced;

(ii) the nonlinearity of any nonzero linear combination of the functions is at least 2^m-1 - 2^n-1;

(iii) any nonzero linear combination of the functions satisfies the strict avalanche criterion;

(iv) the algebraic degree of any nonzero linear combination of the functions is m - n + 1;

(v) F(z) = (f₁(z),...,f_n(z))runs through each vector in Vn precisely 2^m-n times while z runs through V_m.