mRSA Key Setup.

Recall that, in RSA, each user generates its own modulus n_i and a public/secret key-pair. In mRSA, a trusted party (most likely, a CA) takes care of all key setup. In particular, it generates a distinct set: $\{p_i,\;q_i,\;e_i,\;\mbox{and}\;d_i,d_i^{sem}\}$ for each user. The first four are generated in the same manner as in standard RSA. The fifth value, d_i^sem, is a random integer in the interval [1,n_i]. The last value is set as: d_i^u=d_i-d_i^sem.

After CA computes the above values, d_i^sem is securely communicated to a SEM and d_i^u - to the user U_i. The details of this step are elaborated in Section 5.