Technical summary: it seems OK against an observer who can see the network traffic but hasn't infiltrated the phone of the source or the computer of the news organization.
Any real message is stored locally on the smartphone by the CoverDrop module and sent as the next CoverDrop message, i.e. replacing the dummy message which would otherwise have been sent. Consequently a network observer cannot determine whether any communication is taking place and CoverDrop therefore provides the potential source with plausible deniability.
The CoverNode and each journalist has their own public-private key pair. These keys are published by the news organization and available to the CoverDrop module directly so the user does not need know about them. When the CoverDrop module is used for the first time, it generates a new, random public-private key pair for the user.
All real CoverDrop messages sent by the CoverDrop module to the CoverNode include the text written by the potential source as well as their own public key. The message is first encrypted using the public key of the journalist who will ultimately receive the message, then encrypted a second time using the public key of the CoverNode. All dummy CoverDrop messages are encrypted using the public key of the CoverNode. All messages, real or dummy, are arranged to be the same, fixed length. Encryption and length constraints ensure that only the CoverNode can distinguish between real and dummy messages.
