BrakerskiVaikuntanathan

BrakerskiVaikuntanathan is a cryptographic algorithm that combines the Brakerski and Vaikuntanathan techniques to achieve fully homomorphic encryption (FHE). Fully homomorphic encryption allows computations to be carried out on ciphertexts, generating an encrypted result which, when decrypted, matches the result of operations performed on the plaintext. This property is particularly useful in scenarios where data privacy is paramount, such as in cloud computing and secure multi-party computations.

The Brakerski technique, introduced by Zvika Brakerski, is a significant advancement in the field of homomorphic encryption. It enables the evaluation of arbitrary functions on encrypted data without the need for bootstrapping, a process that was previously required to refresh ciphertexts and prevent noise growth. Brakerski's approach leverages the "squashing" technique, which allows for the evaluation of multiplications in a more efficient manner.

Vaikuntanathan, on the other hand, introduced a new approach to constructing homomorphic encryption schemes that are both efficient and secure. His technique, known as the "leveled" homomorphic encryption, allows for a limited number of multiplications to be performed on ciphertexts before the noise becomes too large to be corrected. This limitation is addressed by the Brakerski technique, which enables the evaluation of an unlimited number of multiplications.

The BrakerskiVaikuntanathan algorithm combines these two techniques to create a fully homomorphic encryption scheme that is both efficient and secure. It has been shown to be secure under the Learning With Errors (LWE) assumption, a widely accepted assumption in the field of cryptography. The algorithm has been implemented and tested in various settings, demonstrating its practicality and efficiency.