¹We often get sloppy with notation when discussing asymmetric cryptosystems. Let k = (e,d) be a key pair. We sometimes write k_e and k_d for the first and second keys, respectively, so we might use the rather cumbersome notation E_ke(m) and D_kd(c). But then we might simplify this by dropping the second-level subscripts to get the same notation we use for symmetric cryptosystems, namely E_k(m) and D_k(c). Nevertheless, it should still be understood that the “k” in E_k refers to the first element of the key pair, whereas the “k” in D_k refers to the second. In practice, it isn’t generally as confusing as all this. but the potential for misunderstanding is there.