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I have referenced some documents stating that "To implement bootstrapping, the plaintext modulus 𝑡 needs to be chosen as a prime power." Meanwhile, the SEAL library documentation on Batch Encoding mentions that "Batching only works when the plaintext modulus 𝑡 is chosen to be a prime number and congruent to 1 (mod 2n).".However, in this paper https://eprint.iacr.org/2018/462.pdf, I noticed that the author used both Batch Encoding and Bootstrapping, while choosing 𝑡 as a prime power. Can someone help me clarify this?

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A prime power is just a positive integer that has only 1 unique factors other than 1. For example:

$27 = 3^3, 125=5^3$ etc.

The requirement from the SEAL library means the exponent must be 1.

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  • $\begingroup$ Ah, I see. But in my attached paper, the author chooses parameter t as 127^3, which does not meet the requirement of SEAL. He uses both bootstrapping that requires t is p^r is a prime power with r > 1 (specifically, in this case, p is 127 and r is 3) and batch encode that requires t is a prime number in SEAL. Because this paper was published a long time ago and I couldn't find any public code, so I'm not very clear about this issue $\endgroup$
    – Huy Vu
    Commented Jun 11 at 5:33

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