BFV algorithm is one type of fully homomorphic encryption algorithms, how can I encoding integer to polynomial ring by using batch encoder based on Rt:=Zt[X]/⟨(X^n)+1⟩, the plaintext space (R mod t) is Rt:=R/tR for some integers t and Encryption of the element m(X)∈ Rt. Please help me, because I need a lot to know this conversion with mathematical example, because the algorithm’s work depends on it, and I did not reach an explanation, (I need an answer quickly). Thank you for helping me.
brief overview of encoding integers to polynomial rings using a batch encoder in the context of the BFV (Brakerski-Vaikuntanathan-Vaikuntanathan) fully homomorphic encryption algorithm.
In BFV, the plaintext space is defined as Rt=RtRRt=tRR, where RR is the ring of integers and tt is a parameter. To encode an integer mm into the polynomial ring Rt[X]/⟨Xn+1⟩Rt[X]/⟨Xn+1⟩, you typically follow these steps:
The batch encoding process typically involves representing the integer as a polynomial with coefficients in RtRt and then extending it to a polynomial in Rt[X]/⟨Xn+1⟩Rt[X]/⟨Xn+1⟩ by adding zeroes for higher-degree terms.
Ensure to refer to the specific parameters and conventions used in the BFV algorithm documentation or literature you are following. If you have access to any libraries or implementations of BFV, they might have functions to handle this encoding automatically.
thank you for your answer, but how represent number by batch encoding .
All researchers mentioned the same formula without explaining how the representation is done using batch encoding. Sorry, I began to doubt the veracity of what the researchers said and considered it to be talk on paper without any basis or realistic implementation
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