How to pack the inputs using hybrid encoding?

Bob

9/19/23, 3:15 AM

I'm reading Gazelle. This paper proposes a matrix multiplication vector(encrypted) method using the SIMD property of RLWE-based FHE. It proposed a hybrid encoding. For $n_o \times n_i$ matrix, when $n_o < n, n_i <n$ where n is the slot count.

The author said that using the input packing, the number of $\text{SIMDScMult}$ and the hoisted rotation is $\frac{n_o\cdot n_i}{n}$. Without input packing, the number is just $n_o$, I want to know how to pack the inputs using the hybrid method?

For example, suppose the matrix W is $\left[ \begin{matrix} w_{00} & w_{01} & w_{02} & w_{03}\\ w_{10} & w_{11} & w_{12} & w_{13} \end{matrix} \right]$ , and the vector X is $(x_0,x_1,x_2,x_3)^T$, then $n_i = 4, n_o = 2$, let $n = 8$, how to pack?

0 + 0

homomorphic-encryption

matrix-multiplication

Elon Musk

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

EN: How to pack the inputs using hybrid encoding?

TH: จะแพ็คอินพุตโดยใช้การเข้ารหัสแบบไฮบริดได้อย่างไร

RO: Cum se împachetează intrările folosind codificare hibridă?

RU: Как упаковать входные данные с помощью гибридного кодирования?

VI: Làm cách nào để đóng gói đầu vào bằng mã hóa lai?

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