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Although information sharing in supply chain management dramatically reduces costs, parties are reluctant to do so, mainly due to fear of information leakage. Solutions based on secure multi-party computation guarantee privacy and correctness, at an extra communication and computation cost. Efficiency is a major concern for practical solutions. The best known solution with public indexes selection is due to Li and Atallah. It has the drawback of requiring a secure permutation on every round of the protocol, which turns to be very expensive. We therefore, propose a probability-based technique to reduce the number of secure permutations required by such solution, improving overall practical performance.