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In this work we have examined the problem of consensus information fusion from a novel point of view, challenging the fundamental assumption of mutual trust among the fusion parties. In quest for a method to make information fusion possible while preserving the mutual confidentiality and anonymity of the fused information even in case of collusion of the malicious nodes, we propose the Blind Information Fusion Framework (BIFF). In BIFF, which is a secure information fusion framework, the nodes are not aware of the actual information they are processing, yet converging to the intended result(s). We formulate BIFF according to the anonymization transform and discuss its robustness against collusions for privacy violation. As an example, two secure consensus averaging methods are formulated according to BIFF.