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As far as we know, the most efficient attack against well-implemented Paillier encryption is to factor the public modulus $n$ part of the public key. That's also the best known attack against RSA, thus is well-studied. For history of factorization open records, see this. In 2020, CADO-NFS has factored a 828-bit $n$ with "roughly 2700 core-years, using ...


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