Anonymous messaging platforms, such as Secret and Whisper and Yik Yak, have emerged as important social media for sharing one's thoughts without the fear of being judged by friends, family, or the public. Further, such anonymous platforms are crucial in nations with authoritarian governments, where the right to free expression and sometimes the personal safety of the message author depends on anonymity. Whether for fear of judgment or personal endangerment, it is crucial to keep anonymous the identity of the users who initially posted sensitive messages in these platforms.

In this paper, we consider an adversary who has a snapshot of the spread of the messages at a certain time and pose the problem of designing a messaging protocol that spreads the message fast while keeping the identity of the source hidden from the adversary. We present an anonymous messaging protocol, which we call adaptive diffusion, and show that it spreads fast and achieves perfect obfuscation of the source: all users with the message are nearly equally likely to have been the origin of the message.

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