We present an exhaustive search method to find all small solutions of a multivariate modular linear equation over the integers on the basis of lattice enumeration technique. Previous methods become ineffective when the bound in the definition of small solutions becomes large. Our algorithm can find all the solutions in a given bound; therefore, it can cope with problems with large bounds. We demonstrate the superiority of our algorithm by applying it to the attack on the RSA-CRT with small secret exponent.