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Many lattice IBE scheme follow the scheme outlined in ABB10.

In ABB10, the ciphertext is

$c_0 = u^\top s + x$, where $u$ is a public parameter. (No consider message here.)

I want to ask:

Is it possible to make sure the ciphertext is generated following the scheme?

That is, can the sender provide a zero-knowledge proof that $c_1$ is generated from $us+x$, instead of $u's+x$?

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