Provided are a method and apparatus for a hardware-based accelerated arithmetic operation on homomorphically encrypted messages. The method of performing hardware-based modular multiplication on homomorphically encrypted messages according to the present invention includes receiving a plurality of homomorphically encrypted messages expressed in a polynomial form and a modulus for modular multiplication, decomposing the modulus into a product of a plurality of disjoint factors through CRT operation, and extracting a divided ciphertext from a plurality of homomorphically encrypted messages based on each of the disjoint factors, performing NTT transformation on each coefficient of the divided ciphertext, performing a pointwise multiplication operation between result values of the NTT transformation, performing INTT transformation on a result value of the pointwise multiplication operation to obtain the divided ciphertext, and merging the divided ciphertext obtained in the performing of the INTT transformation through ICRT operation to generate an output ciphertext.