Timeline for Homomorphic Encryption - Integer modulus in HEAAN and key sampling
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2023 at 14:47 | vote | accept | Alexander Magyari | ||
| Jun 21, 2023 at 11:55 | history | edited | The Dice Man | CC BY-SA 4.0 |
deleted 17 characters in body
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| Jun 21, 2023 at 11:54 | comment | added | The Dice Man | As you decrypt the $-a*s$ part gets removed first. Then you perform a rounded integer division by $\Delta^{-1}$ and if $round(\Delta^{-1} e) = 0$, because $e$ is small enough, you retrieve $m$ correctly. | |
| Jun 21, 2023 at 11:46 | comment | added | The Dice Man | Yes, it's mandatory. Maybe I was a bit imprecise, but you don't have to protect $m$ from the overflow, but rather from the errors. The overflow is just part of the system. Say, you work modulo $Q$ and encode $m \in {0,...,T-1}$ with $\Delta m$, and $\Delta = Q/T$. Then you add error(s) $e$ due to computations. That means, you have a ciphertext like $(a,-a*s+\Delta m +e)$. Meanwhile, you work mod $Q$ and overflow. | |
| Jun 21, 2023 at 3:21 | comment | added | Alexander Magyari | Is it the right interpretation that not only can the public key overflow a+m, but that it is expected? Could you please elaborate on how delta affects protecting the message from overflow? I understand how it can be used to maintain precision, but I still don't see the how the plaintext message could be preserved after the encryption process, given that the addition of a results in a modular overflow . | |
| Jun 20, 2023 at 10:09 | history | answered | The Dice Man | CC BY-SA 4.0 |