On Enhancing Security for Division Homomorphism with ElGamal

Abstract

Secure auctions and machine learning in cloud increasingly employs multi-party and homomorphic encryption support.
A modification to Elgamal public key cryptosystem was shown to enable homomorphic division using an encoding of plaintext as fractions with numerator and denominator encrypted separately. However we notice that unlike for other homomorphic cryptography schemes, the obtained division homomorphism allows for the retrieval of the input secrets from the result of the division. Since this cancels the benefit of the encryption, we propose the introduction of a masking operation based on random factors and discuss its success with operations in Z_p and Q.