Terminal device performing homomorphic encryption, server device processing ciphertext and methods thereof
An encryption method is provided. According to the encryption method, a scaling factor may be reflected in a message and then, a homomorphic ciphertext may be generated using a public key. The generated ciphertext is, when decryption is performed, generated in a form that a result value obtained by adding an error value to a value obtained by reflecting the scaling factor in the message is restored. Accordingly, a homomorphic ciphertext capable of being computed in a ciphertext state can be effectively generated.
1. An encryption method of a terminal device, the encryption method comprising:
setting a ring which is a set including elements between which addition and multiplication are defined, the ring including a plaintext space that is a real number from among sets that are closed to addition and multiplication;
calculating a secret key from the ring;
calculating a public key corresponding to the calculated secret key;
applying the public key to a message and generating a homomorphic ciphertext;
receiving a pre-generated homomorphic ciphertext from another terminal device;
performing at least one computation from among addition or multiplication with respect to the generated homomorphic ciphertext and the received pre-generated homomorphic ciphertext;
transmitting a result of the at least one computation to the other terminal device, wherein performing the at least one computation comprises:
performing a first function process with respect to each of the generated homomorphic ciphertext and the received pre-generated homomorphic ciphertext;
performing a computation between the homomorphic ciphertext for which the first function process is performed; and
performing a second function process, which is an inverse function of the first function, with respect to a homomorphic ciphertext for which the computation is performed.
2. The encryption method as claimed in claim 1 , wherein the ring satisfies the following equation:
a ( X )= a ( X −1 ) where a ( X )∈ R, X −1 :−X n−1
wherein X is a variable, n is a natural number, a(X) is a polynomial corresponding to the ring, and the R is a ring including a real space that is a complex number.
3. The encryption method as claimed in claim 2 , wherein the homomorphic ciphertext has a complexity of o(n log n) with respect to an addition or multiplication computation where n is a natural number.
4. The encryption method as claimed in claim 1 , further comprising:
calculating a first random polynomial from the ring;
extracting an error; and
modulating the error in the first random polynomial and the secret key, and calculating a second random polynomial,
wherein the calculating the public key comprises:
calculating the public key using the first and second random polynomials.
5. The encryption method as claimed in claim 1 , wherein the generating the homomorphic ciphertext comprises:
calculating the message as a polynomial corresponding to the ring, and applying the public key to the calculated polynomial and generating a homomorphic ciphertext.
6. The encryption method as claimed in claim 1 , wherein the first function is a Number Theoretic Transform (NTT) function.
7. The encryption method as claimed in claim 1 , wherein the homomorphic ciphertext is, based on a decryption being performed, in a form that a result value obtained by adding an error value to the message is restored.