Cryptography Questions Long
Homomorphic encryption is a cryptographic technique that allows computations to be performed on encrypted data without the need for decryption. In other words, it enables the manipulation and processing of encrypted data while preserving its confidentiality.
The concept of homomorphic encryption revolves around three main properties: additive homomorphism, multiplicative homomorphism, and fully homomorphic encryption.
Additive homomorphism refers to the ability to perform addition operations on encrypted data. This means that if we have two encrypted values, say A and B, we can perform an addition operation on their ciphertexts, resulting in a new ciphertext that, when decrypted, yields the sum of the original plaintexts.
Multiplicative homomorphism extends this concept to multiplication operations. With this property, we can multiply two encrypted values, A and B, and obtain a new ciphertext that, when decrypted, gives us the product of the original plaintexts.
Fully homomorphic encryption takes it a step further by allowing arbitrary computations to be performed on encrypted data. This means that we can perform any sequence of operations on encrypted values, such as addition, multiplication, and even more complex operations like comparisons and logical operations. The result is a ciphertext that, when decrypted, yields the desired output of the computation.
To enable computations on encrypted data, homomorphic encryption schemes utilize mathematical techniques such as lattice-based cryptography or the use of special mathematical structures like the RSA cryptosystem. These techniques ensure that the encryption and decryption operations can be performed in a way that preserves the homomorphic properties.
However, it is important to note that fully homomorphic encryption is still an active area of research, and practical implementations are currently limited in terms of efficiency and scalability. The computational overhead of performing operations on encrypted data is significantly higher compared to traditional encryption schemes. Nonetheless, homomorphic encryption holds great promise for applications where privacy and security are paramount, such as secure cloud computing, privacy-preserving data analysis, and secure outsourcing of computations.