A method for generating a key stream according to an embodiment includes generating r round keys that are each N-dimensional integer vectors including elements of an integer set defined based on a prime number t, based on a random bit string, an encryption counter, and a secret key that is an N-dimensional integer vector consisting of elements of the integer set , generating a first round output vector x1 by performing a modular addition operation on an initial vector and a first round key RK1 of the r round keys with the prime number t as a modulus, and generating a key stream that is an N-dimensional integer vector consisting of elements of the integer set from the first round output vector x1 by using a second to r-th round keys of the r round keys, and one or more first round functions and a second round function.