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I'm familiar with the concept of batching in the context of (Fully) Homomorphic Encryption - whereby many values can be encrypted as a single ciphertext and operated on simultaneously in an SIMD/vector-processing like manner.

Is it possible to utilise batching with any of the Partial Homomorphic Encryption schemes (such as Pailler, ElGamal, etc.)? I have only seen batching discussed in the context of Levelled and Fully Homomorphic Cryptosystems previously (from Generation 2 onwards, e.g. BFV, TFHE, CKKS).

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No. The batching technique depends on the underlying algebra used for BFV/BGV/CKKS schemes where you can represent one large ciphertext/plaintext as many small ciphertexts/plaintexts in those schemes. But this property does not exist for Paillier or ElGamal.

Note that TFHE usually does not use batching.

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