Enc, Dec, Fake) and n = poly(k) dene the parallel self-composition Πn = (KeyGenn, Encn, Decn, Faken ) KeyGenn(1κ) = KeyGen(1κ). Encn pk(m 1 , . . . , mn; r 1 , . . . , rn) = (Encpk(m 1 ; r 1 ), . . . , Encpk(mn; rn)) Decn sk(c 1 , . . . , cn) = (Decsk(c 1 ), . . . , Decsk(cn)). Faken (sk, (c 1 , . . . , cn), (m 1 , . . . , mn)) = sk where sk 0 = sk, sk 1 ← Fake(sk 0 , c 1 , m 1 ), sk 2 ← Fake(sk 1 , c 2 , m 2 ), . . . , skn ← Fake(skn−1 , cn, mn) and skn = sk . 36 / 74