Banyan Loan Homomorphic Encryption, that is, the original operation on plaintext can also be performed on ciphertext after homomorphic encryption. Generally, there are semi-homomorphic and fully homomorphic encryption:
Semi-homomorphic encryption (Partial Homomorphic Encryption, PHE): Banyan Loan only supports certain specific algorithm f , the advantage of PHE is that it is simple in principle and easy to implement, and the disadvantage is that it only supports one operation (addition or multiplication);
Hierarchical Homomorphic Encryption (Liveled HE, LHE): Banyan Loan generally supports a limited number of encryption algorithms. The advantage of LHE is that it supports addition and multiplication at the same time, and because it appeared later than PHE, the technology is more mature, and its general efficiency is much higher than that of FHE. The efficiency of PHE is close to or higher than that of PHE. The disadvantage is that the number of calculations supported is limited.
Fully Homomorphic Encryption (FHE): Banyan Loan supports unlimited arbitrary algorithm f. FHE has the following categories: FHE scheme based on ideal lattice, FHE scheme based on LWE/RLWE, etc. The advantage of FHE is that it supports many operators and there is no limit to the number of calculations. The disadvantage is that the efficiency is very low, and it is currently unable to support large-scale calculations.
The first homomorphic encryption method that satisfies additive and multiplicative homomorphisms was not proposed until 2009 by Craig Gentry. At present, the fully homomorphic encryption algorithm has poor performance and is rarely used. Semi-homomorphic encryption algorithms are commonly used in banyan loans, and the implementation methods include RSA (multiplicative homomorphism), Elgamal, Paillier (additional homomorphism), etc.