## Cryptology ePrint Archive: Report 2017/198

FHE with Recursive Ciphertext

Masahiro Yagisawa

Abstract: In this paper I propose fully homomorphic public-key encryption (FHPKE) with the recursive ciphertex. A ciphertext consists of three sub-ciphertexts corresponding to one plaintext. When we execute the additional operation or multiplicative operation, a new three sub-ciphertexts are generated from the three sub-ciphertexts recursively without revealing the plaintexts. The scheme is based on the discrete logarithm assumption (DLA) and computational Diffie–Hellman assumption (CDH) of multivariate polynomials on octonion ring with composite number modulus. The scheme is immune from “m and - m attack”.

Category / Keywords: public-key cryptography / fully homomorphic public-key encryption, discrete logarithm assumption, computational Diffie–Hellman assumption, octonion ring, factorization

Original Publication (with minor differences): Masahiro, Y. (2017). Fully Homomorphic Public-Key Encryption with Three Ciphertexts which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany .