# HE scalar multiplication Let $ct=(c_0,c_1)=(as+m+e,a)$ encrypting a vector $v$ w.r.t secret key $s$ and modulo $Q$. Let $d$ be a scalar and $\Delta$ the scale. If $d$ is small integer then compute: the ciphertext $(d\cdot c_0, d\cdot c_1)$ which encrypts the vector $d\cdot v$ . Note: As the error of the ciphertext also increases by $d$ - it's value should be small so the error will not be too big. If $d$ is float, we first multiply it by $\Delta$ then multiply by the ciphertext polynomial's and rescale. In case we want to multiply slots with different scalars then we need to apply plaintext ciphertext multiplication by encoding the slots of scales to polynomial and multiply it by the ciphertext. reference: [[@Approximate Homomorphic Encryption with Reduced Approximation Error]], pages 1,12 ## Created 2022-05-17 06:19