Fully Homomorphic Public-Key Encryption with Three Ciphertexts

The book "Fully Homomorphic Public-Key Encryption with Three Ciphertexts" by Masahiro Yagisawa offers a comprehensive analysis and introduction to fully homomorphic encryption, an advanced cryptosystem that supports both addition and multiplication. This technology has the potential to significantly change the way private computations, especially in the field of cloud computing, are conducted. The author presents a novel scheme of fully homomorphic public-key encryption (FHPKE) based on the discrete logarithm assumption and the computational Diffie-Hellman assumption. By utilizing multidimensional polynomials over the octonion ring on the finite ring Z/rZ, a system is developed that generates three ciphertexts for a plaintext and is resistant to specific attacks, such as the 'm and -m attack'. Furthermore, the security of the system against attacks from quantum computers is emphasized, making it a significant contribution to the field of modern cryptography.