Optimal matrix embedding for Voice-over-IP steganography

• We present an optimal embedding scheme for Voice over IP.
• A novel adjustable matrix encoding (AME) is proposed to suit the limited cover.
• The optimal embedding using AME is modeled as a combinatorial optimization problem.
• An algorithm to search the optimal solution is provided.
• Our scheme can provide consistently optimal embedding performances in any case.

Divide-and-rule strategy is popularly adopted in steganography based on Voice-over-IP (VoIP), which often divides a cover into many small parts and performs embedding operation on each one to maintain the real-time requirement of VoIP services. No existing study, however, notices that the cover length of the parts may seriously affect the embedding performance. The goal of this paper is to fill in the gap and present a novel steganographic scheme to achieve the optimal embedding. To attain the goal, we first present an adjustable matrix encoding (AME) approach, which can adaptively generate a guide matrix to accommodate to the given cover length and provide the best performance while guaranteeing the desired embedding capacity. Further, the optimal embedding is modeled as a typical combinatorial optimization problem, of which the optimal solution is an AME or a combination of multiple AMEs. We evaluate the proposed scheme with ITU-T G. 711 (A-law) as the codec of the cover speech and compare it with previous methods. The experimental results demonstrate that the proposed scheme is really feasible in both theory and practice, and can provide consistently optimal embedding performance in any case.