A computing device implemented for high-precision rational number arithmetic in homomorphic encryption, the computing device comprising: a memory configured to store homomorphic encrypted data as a dataset; a processor system configured to execute an encryption application that is implemented to: encode integers into plaintext polynomials, the integers representative of initial data received for encryption; encrypt the plaintext polynomials into ciphertexts of the homomorphic encrypted data; perform homomorphic operations as rational number arithmetic on the ciphertexts, generating updated ciphertexts while the homomorphic encrypted data remains encrypted; decrypt the updated ciphertexts to modified plaintext polynomials that can be resolved back to the plaintext polynomials effective to recover the integers that represent the initial data; and decode the modified plaintext polynomials back to the integers effective to recover the initial data in an unencrypted form, wherein the homomorphic encrypted data is encrypted based on a Fan-Vercauteren homomorphic encryption scheme with the plaintext polynomials defined as Z/(b^n+1)Z in an FVb encryption scheme, in which coefficients reduced integer modulo t of the plaintext polynomials Z_t [x]/(x^n+1) in the FV plaintext space are replaced by (x-b), and wherein the encryption application is implemented to replace the t modulus of the plaintext polynomials Z t x / x n + 1 in the FV plaintext space with ( x-b) effective to minimize t and allow homomorphic evaluation of large ciphertext polynomials on encrypted rational numbers, n being a power of 2 and b a positive integer. a memory configured to store homomorphic encrypted data as a dataset; a processor system configured to execute an encryption application that is implemented to: encode integers into plaintext polynomials, the integers representative of initial data received for encryption; encrypt the plaintext polynomials into ciphertexts of the homomorphic encrypted data; perform homomorphic operations as rational number arithmetic on the ciphertexts, generating updated ciphertexts while the homomorphic encrypted data remains encrypted; decrypt the updated ciphertexts to modified plaintext polynomials that can be resolved back to the plaintext polynomials effective to recover the integers that represent the initial data; and decode the modified plaintext polynomials back to the integers effective to recover the initial data in an unencrypted form, wherein the homomorphic encrypted data is encrypted based on a Fan-Vercauteren homomorphic encryption scheme with the plaintext polynomials defined as Z/(b^n+1)Z in an FVb encryption scheme, in which coefficients reduced integer modulo t of the plaintext polynomials Z_t [x]/(x^n+1) in the FV plaintext space are replaced by (x-b), and wherein the encryption application is implemented to replace the t modulus of the plaintext polynomials Z t x / x n + 1 in the FV plaintext space with ( x-b) effective to minimize t and allow homomorphic evaluation of large ciphertext encode integers into plaintext polynomials, the integers representative of initial data received for encryption; encrypt the plaintext polynomials into ciphertexts of the homomorphic encrypted data; perform homomorphic operations as rational number arithmetic on the ciphertexts, generating updated ciphertexts while the homomorphic encrypted data remains encrypted; decrypt the updated ciphertexts to modified plaintext polynomials that can be resolved back to the plaintext polynomials effective to recover the integers that represent the initial data; and decode the modified plaintext polynomials back to the integers effective to recover the initial data in an unencrypted form, wherein the homomorphic encrypted data is encrypted based on a Fan-Vercauteren homomorphic encryption scheme with the plaintext polynomials defined as Z/(b^n+1)Z in an FVb encryption scheme, in which coefficients reduced integer modulo t of the plaintext polynomials Z_t [x]/(x^n+1) in the FV plaintext space are replaced by (x-b), and wherein the encryption application is implemented to replace the t modulus of the plaintext polynomials Z t x / x n + 1 in the FV plaintext space with ( x-b) effective to minimize t and allow homomorphic evaluation of large ciphertext polynomials on encrypted rational numbers, n being a power of 2 and b a positive integer.