Abstract: The present application is directed towards a new system for performing FHE and includes a method, system, program and storage medium configured for generating keys for fully homomorphic encryption, wherein generating the keys comprises: obtaining a first set of numbers, wherein the first set of numbers is a set of pairwise coprime numbers P1, . . . , Pk+1; obtaining a second set of prime numbers r1, r2, . . . , rk+1; obtaining a third set of numbers, wherein the third set of numbers is a set of random or pseudo random numbers s1, . . . , sn; calculating a secret key, sk, based on the first set of numbers, the second set of numbers, and third set of numbers; and calculating a public parameter, q, based on the first set of numbers and the second set of numbers.