Known Plaintext Attacks on the Omar and abed Homomorphic Encryption Scheme

Abstract

In 2020, Omar and abed proposed a new noise-free fully homomorphic encryption scheme that allows arbitrary computations on encrypted data without decryption. However, they did not provide a sufficient security analysis of the proposed scheme and just stated that it is secure under the integer factorization assumption. In this paper, we present known plaintext attacks on their scheme and illustrate them with toy examples. Our attack algorithms are quite simple: They require several times of greatest common divisor (GCD) computations using only a few pair of message and ciphertext.