I am new to RLWE, would like to ask whether what I am thinking make sense
Suppose I have a message e.g.: x=5
And I have a lattice based encryption scheme, e.g.: BGV
could I encrypt x with BGV by treating x as a polynomial ring with constant coefficient=5, and other coefficient =0?
Thanks
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1 Answer
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Yes, you could encrypt the message $5$ as a polynomial $f = 5$ in the polynomial ring, which is usually something like $R := \mathbb Z [X] / \langle x^N + 1 \rangle$ with $N$ being quite large $>2^{10}$ in practice. All the homomorphic algorithms, e.g., addition, multiplication, and others, will work fine with this message.
However, encrypting only constant messages is a huge waste of both computation time and storage space, since RLWE supports SIMD (single instruction multiple data) operations. I.e. in such a polynomial $f$ one can encrypt more than one constant message, details omitted here.
