The efficiency of attacking methods on secure RSA modulus was investigated.It was pointed out by analysis that since the success probability of some attack methods was neglectable

these methods could not be regarded as the reason for choosing strongly secure RSA modulus.In consideration of the analysis of attack methods

the signification of secure RSA modulus was summarized

which enhanced the efficiency of selecting secure parameters in practice.The result that the difference between two RSA primes d=|p-q| must not be too small was further investigated

and the d might be seen as a special case when dl

m=ql-pm（l

m∈Z+） was small.From the analysis

it could be figured out that the randomness of the relation between the two primes should not be neglected during selecting RSA modulus.To improve the security

it should be avoided to have some specially functional relations between the two primes when choosing a