Research on Homomorphic Encryption for Arithmetic of Approximate Numbers

Homomorphic Encryption for Arithmetic of Approximate Numbers [HEAAN] is an advanced version of Homomorphic Encryption [HE] that supports encryption, computation and decryption on plain text, yielding results corresponding to plaintext computations. The computations include addition and multiplication. HEAAN ensures data security, preserves privacy, and prevents security breaches [5]. HEAAN offers a precision of 32-bit. Traditional Fully Homomorphic Encryption [FHE] schemes facilitate computation on the encrypted integer data, namely, addition and multiplication, yielding results similar to computations on plain text. However, the scope of such FHE is limited to integers, leaving behind floating point numbers. In real time implementation of computations, the scope ranges over real numbers, covering floating point numbers as well. Thus, to overcome the limitations of traditional FHE schemes, HEAAN Encryption scheme is implemented. Scaling, homomorphic addition and multiplication, encryption, and decryption are the components of HEAAN. No matter how big the computed result is, HEAAN retains the initial significant digits. It's accomplished using the Python package Pi-HEAAN.