Group key management approach based on linear geometry

Abstract

A group key management approach based on linear geometry is disclosed. The approach includes the following steps: step 1: a group controller selects a mapping f and a finite field F; each group member selects a m-dimensional private vector over the finite field F, and sends it to the group controller via secure channel; step 2: the group controller selects a mapping parameter in the finite field F randomly, and maps the private vectors of all the group members into a new set of vectors by using the mapping f according to the mapping parameter; step 3: the group controller selects a random number k in the finite field F as a group key, and constructs a system of linear equations by using the new set of vectors and the group key; the group controller computes the central vector, and sends the central vector and the mapping parameter to all the group members via open channel; step 4: after the group members receive the central vector and the mapping parameter, the private vector of each group member is mapped to a new vector in a vector space according to the mapping parameter, and the group key is obtained by calculating the inner product of the new vector and the central vector. This invention requires small memory and little computation, has high security property, and is effective against brute-force attacks.