# ciphertext & plaintext multiplication Given $ct$ ciphertext and plaintext $pt$ then $ct\cdot pt$ is a ciphertext contains the component wise multiplication of $ct$ slots with $pt$. It requires a rescale before decryption as the result noise is too big. #### Proof Let $ct=(b,a)$ s.t. $b=as+m+e$. $ct\cdot pt=(b\cdot pt, a\cdot pt)=a\cdot pt\cdot s + m\cdot pt +e\cdot pt, a\cdot pt)$ After rescaling $e\cdot pt$ norm should be small as required. It is clear that the result decrypts to $m\cdot pt$ which is equivalent of multiplying their slots. Reference: see mulPlaintextMul function in evaluator.go of Lattigo lib. ## Created 2023-01-12 12:37