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6

At a high-level (ignoring the messier details), recryption that boosts bounded-depth homomorphism to unbounded-depth homomorphism works as follows: Suppose you have a public-key "somewhat-homomorphic" encryption scheme with procedures: $(PK, SK) \leftarrow Gen(1^{secparam}; coins)$: generates encryption/decryption keys $c \leftarrow Enc(PK, m; coins)$: ...

3

The original question seems to assume that the BGN scheme is the state-of-the-art for problems like this (correct me if I'm wrong :)), so for what it's worth: The BGN scheme scheme is a prototypical version of a somewhat homomorphic encryption scheme -- the bilinear map gives you a single multiplication on any ciphertext still in the source group $\mathbb{G}... 2 1)$x_0\$ is (indeed) a plaintext. (Perhaps to guess at where confusion arose from:) the 'more modern' version of homomorphic encryption is fully homomorphic encryption (FHE) fully supporting both additive and multiplicative homomorphisms, whereas the paper you're reading was published about 2.5 years before Gentry's original FHE scheme came out. (Check out ...

1

Well, this is not exact. Clearly there exists an irrational number that contains all patterns - simply concatenate all finite patterns (e.g. in lexicographical order, from shortest and up) However, not every number contains all these patterns. Indeed, you can construct an irrational number by concatenating the binary sequences "000" and "111", which will ...

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