Digital signatures

To send you a message that can only have come from me, I encrypt it first with my secret key, and then with your public key:

         S(me) P(you)
     {{M}     }       = C

To decrypt, you first apply your secret key (which only you can do):

        S(you)      S(me)
     {C}       = {M}

Then you apply my public key:

         S(me) P(me)
     {{M}     }      = M