Homomorphism attack ($E(m_1{m}_2)=E(m_1)E(m_2)$)

An attack exploiting preservation of an algebraic operation by encryption or signing. The textbook RSA cryptosystem has $E(m_1{m}_2)=E(m_1)E(m_2)(\mathrm{mod}N)$, so unprotected ciphertexts can be modified multiplicatively. Authentication must be verified before accepting a modified message.