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Android is an operating system that has been used in a majority of mobile devices. Each application in Android runs in an instance of the Dalvik virtual machine, which is a register-based virtual machine (VM). Most applications for Android are developed using Java, compiled to Java bytecode and then translated to DEX bytecode using the dx tool in the Android SDK. In this work, we aim to develop a type-based method for certifying non-interference properties of DEX bytecode, following a methodology that has been developed for Java bytecode certification by Barthe et al. To this end, we develop a formal operational semantics of the Dalvik VM, a type system for DEX bytecode, and prove the soundness of the type system with respect to a notion of non-interference. We then study the translation process from Java bytecode to DEX bytecode, as implemented in the dx tool in the Android SDK. We show that an abstracted version of the translation from Java bytecode to DEX bytecode preserves the non-interference property. More precisely, we show that if the Java bytecode is typable in Barthe et al's type system (which guarantees non-interference) then its translation is typable in our type system. This result opens up the possibility to leverage existing bytecode verifiers for Java to certify non-interference properties of Android bytecode.