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Automated Trust Negotiation (ATN) is an approach to allow two participants to automatically verify whether their policies are consistent with each other or not. During the negotiation process, in order to protect privacy, both participants intend to disclose their credentials and policies as little as possible. A previous work(ATN) successfully negotiates with perfect privacy preservation where post-negotiation, neither credentials nor policies were revealed to each other. Unfortunately, in order to negotiate with policy with ℓ conjunctive "and" conditions, consisting of m credentials it requires a large computation cost which is linear to combination(m, ℓ). In our work, we focus on this problem and establish a new scheme to lower the cost in the conjunctive condition policy so that our protocol require only mℓ which can highly decrease computation and communication costs. The proposed scheme performs in semi-honest model. The new idea is adding a dynamic secret key to verify which credentials match with the requested policies. We also demonstrate that this new approach can improve the efficiency of the previous one by showing a qualitative evaluation using implementation and analysis of computation and communication cost.