About learning with error rings with only constant coefficient

js wang

6/13/24, 9:38 PM

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

1 + 0

homomorphic-encryption

lattice-crypto

ring-lwe

Score:1

Crypto

The Dice Man

6/14/24, 1:58 PM

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.

+ 0

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: About learning with error rings with only constant coefficient

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