Self-adaptive large integer modular multiplication operation method and device based on homomorphic encryption

The invention discloses a self-adaptive large integer modular multiplication operation method and device based on homomorphic encryption, and belongs to the field of lattice passwords. The method comprises the following steps: pre-calculating according to modulus and bit width parameters to obtain a cycle indication number; obtaining a decomposition substrate by using the modulus, and decomposing the multiplicand according to the decomposition substrate; substitution reduction is carried out according to the cycle indication number and the bit width parameter, and reduction is carried out by replacing the square term of the substrate with the difference between the square of the decomposition substrate and the modulus in a congruence environment; and then shifting reduction is carried out on the obtained result, and the result is compared with a modulus to obtain a final modular multiplication result. According to the method, the problems that large integer modular multiplication needs a relatively high bit w