Abstract: An example embodiment provides a calculating method using a zero-knowledge proof-friendly one-way function, performed by a computing device, the calculating method including: calculating a first intermediate bit stream by inputting an input bit stream of a one-way function to an augmented matrix, calculating a second intermediate bit stream by dividing the first intermediate bit stream into a predetermined number of bit streams and inputting each of the predetermined number of divided bit streams to a substitution-box (S-box), and outputting an output bit stream of the one-way function by inputting the second intermediate bit stream to a reduced matrix.

Abstract: A method for encryption according to an embodiment includes generating a ciphertext for a secret key that is an integer vector by using an integer-based first homomorphic encryption algorithm, generating a key stream that is the integer vector from a nonce and the secret key by using a key stream generator, encoding the key stream by using a message encoding function of the first homomorphic encryption algorithm, encoding a message that is a real vector by using a message encoding function of a real number-based second homomorphic encryption algorithm, generating a ciphertext for the message by using a result of the encoding of the key stream and a result of the encoding of the message, and transmitting the nonce, the ciphertext for the secret key, and the ciphertext for the message to an apparatus for converting a ciphertext.

Abstract: 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.

Abstract: A method for encryption according to an embodiment includes generating a ciphertext for a secret key that is an integer vector by using an integer-based first homomorphic encryption algorithm, generating a key stream that is the integer vector from a nonce and the secret key by using a key stream generator, encoding the key stream by using a message encoding function of the first homomorphic encryption algorithm, encoding a message that is a real vector by using a message encoding function of a real number-based second homomorphic encryption algorithm, generating a ciphertext for the message by using a result of the encoding of the key stream and a result of the encoding of the message, and transmitting the nonce, the ciphertext for the secret key, and the ciphertext for the message to an apparatus for converting a ciphertext.