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Non-injective functions and one-way functions aren't the same thing. In laymen's terms, a one way function is one for which finding any element of the preimage of a given image element is difficult. (The word "difficult" is a technical term here). So, for example, SHA-256 seems to be a one-way function... Because if I give you give you a random 256 bits, it is difficult (in the technical sense of the word) for you to find ANY input to SHA-256 that will output the random numbers I gave you. We have several candidates for one-way functions that seem to be one-way. But nobody has been able to present a formal proof. Interesting things: the existence of one-way functions would imply that P does not equal NP. a great deal of modern provable cryptography rests on the underlying assumption that one-way functions exist. f(x)=0 is not one-way because it is trivially easy to find a preimage element for the only element of the image (0). So a function being non-injective, or "lossy" isn't enough.
It seems that the interceptor could piece together the message but would be unable to fend off the coordinated attack even if they knew what time it would occur. The primary problem is coordinating the attack if you don't know if any number of your messengers have been compromised - which is why you can't rely on "majority rules." With proof-of-work, it appears to me that so long as at least one true message gets through, the attack can be coordinated - though I suspect it would take a few messages back and forth if the two armies are of similar proof-of-work power, to get everyone working on the same work chain.
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