Systems and methods for enabling constant plaintext space in bootstrapping in fully homomorphic encryption (FHE) are disclosed. A computer-implemented method for producing an encrypted representation of data includes accessing a set of encoded digits. The method includes applying an inverse linear transformation to the set of encoded digits to obtain a first encoded polynomial. The method includes applying a modulus switching and dot product with bootstrapping key to add an error term to each of the encoded digits in the first polynomial to obtain a second encoded polynomial. The method includes applying a linear transformation to the second encoded polynomial to obtain a first batch encryption. The method includes applying digit extraction to the first batch encryption to obtain a second batch encryption, the second batch encryption corresponding to the set of encoded digits without the error term.