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Binary neural network (BNN) delivers increased compute intensity and reduces memory/data requirements for computation. Scalable BNN enables inference in a limited time due to different constraints. This paper explores the application of Scalable BNN in oblivious inference, a service provided by a server to mistrusting clients. Using this service, a client can obtain the inference result on his/her data by a trained model held by the server without disclosing the data or learning the model parameters. Two contributions of this paper are: 1) we devise lightweight cryptographic protocols explicitly designed to exploit the unique characteristics of BNNs. 2) we present an advanced dynamic exploration of the runtime-accuracy tradeoff of scalable BNNs in a single-shot training process. While previous works trained multiple BNNs with different computational complexities (which is cumbersome due to the slow convergence of BNNs), we train a single BNN that can perform inference under various computational budgets. Compared to CryptFlow2, the state-of-the-art technique in the oblivious inference of non-binary DNNs, our approach reaches 3 × faster inference while keeping the same accuracy. Compared to XONN, the state-of-the-art technique in the oblivious inference of binary networks, we achieve 2 × to 12 × faster inference while obtaining higher accuracy.