You are given a (CPA-secure) Public-key encryption scheme E=(GenE, Enc, Dec), a (securet) digital signature scheme S=(Gens, Sig, rfys) and a (securet) private-key authentication scheme A=(Gen_A, Auth, Verfy_A). The (private-key) latter is substantially more efficient than the (public-key) formers. Bob has never met Alice before, but through a trusted CA, Bob knows Alice's (encryption) public-key pk_p, and (signature) public-key qkA and Alice knows Bob's (encryption) public-key pka and (signature) public-key qk_a. i) Explain how you may combine (only) these three ingredients (E, S and A) and allow Bob to authenticate an enormous amount of data to Alice, as efficiently as possible. Justify your choices. ii) Give specific systems to instantiate each of E, S and A. iii) Explain why having either only E, A or only S, A is fairly useless for the same task as in i)... You are given a (CPA-secure) Public-key encryption scheme E=(GenE, Enc, Dec), a (securet) digital signature scheme S=(Gens, Sig, rfys) and a (securet) private-key authentication scheme A=(Gen_A, Auth, Verfy_A). The (private-key) latter is substantially more efficient than the (public-key) formers. Bob has never met Alice before, but through a trusted CA, Bob knows Alice's (encryption) public-key pk_p, and (signature) public-key qkA and Alice knows Bob's (encryption) public-key pka and (signature) public-key qk_a. i) Explain how you may combine (only) these three ingredients (E, S and A) and allow Bob to authenticate an enormous amount of data to Alice, as efficiently as possible. Justify your choices. ii) Give specific systems to instantiate each of E, S and A. iii) Explain why having either only E, A or only S, A is fairly useless for the same task as in i)