Fully homomorphic encryption method and device and computer readable storage medium

A fully homomorphic encryption method, comprising:

• Step S1:
• generating a prime modulus qj=qj (λ, L), according to an input security parameter λ and a number of encryption layers L, wherein qj mod n≡1, n is an integer power of 2, j=0, 1, . . . , L−1, and q0<q1< . . . <qL-1;
• Step S2:
• generating a private key sk and a public key pk according to the prime modulus qj;
• Step S3:
• encrypting plaintext m according to the public key pk;
• and
• Step S4:
• performing a homomorphic operation on two ciphertexts associated with the same private key, the homomorphic operation includes a homomorphic addition operation FHE.Add (c′, c″) and a homomorphic multiplication operation FHE.Mul(c′, c″), wherein the process of the homomorphic multiplication operation FHE.Mul(c′, c″) is as follows:
• calculating a result ciphertext cmul=(cmul,0, cmul,1, cmul,2) according to the following processes, for two ciphertexts c′=(c′0, c′1) and c″=(c″0,c″1) associated with the same given private key:
• cmul,0=[c′0·c″0]qj, cmul,1=[c′0·c″1+c′1·c″0]qj, cmul,2=[c′1·c″1]qj
• outputting cmul directly, if cmul undergoes addition homomorphism in a next operation or no operation;
• if cmul undergoes multiplication homomorphism in a next operation, reducing the size of the ciphertext of cmul from three ring elements to two ring elements by using the aforementioned key exchange technology, to obtain a new ciphertext c*mul=(c*mul,0,c*mul,1),
• wherein c*mul,1=[p·cmul,1+cmul,2·wL-1,1]p·qj, and j∈[0, L−1].