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Formal security of recycled random blinding in a Paillier scheme

This question is a follow-up/variant on a previous question. Supposing that we are trying to generate a large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the ...
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Updating the secret key used for HMAC

I am designing a distributed system, composed by a set of physically distributed embedded devices (8 bit cores with less than 1 KB of RAM). The devices need to be able to authenticate the originator ...
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CBC with a fixed or random IV

I have two probably quite naive questions: 1) Why, exactly, is it so bad to have a fixed (or predictable) IV in CBC mode? An example would be great! 2) Given 1), why is a random IV better? And if ...
Let $e: \mathbb G_1 \times \mathbb G_1 \rightarrow \mathbb G_T$ be an efficient bilinear pairing. Note that the pairing is symmetric (i.e., Type 1). The problem is, given $g \in \mathbb G_1$ and ...