(a) An Authenticated Encryption (AE) scheme consists of a triple of algorithms,(KGen, Enc, Dec). Describe the function of each of these algorithms and explain what is meant by the correctness of an AE scheme.[4 marks] (b) Security for AE schemes is defined in terms of the combination of two security notions: indistinguish ability under chosen plain text attacks (IND-CPA security), and integrity of cipher texts (INT-CTXT security). Give informal descriptions of these two notions, using diagrams to illustrate your answer if you wish. For both notions, state what it means for an AE scheme to be[8 marks]secure. (c) AE schemes can be built using generic composition of symmetric encryption schemes and MAC schemes. There are three principal methods for doing so, known as EtM,MtE and E&M. Briefly describe each of these three methods, and comment on their AE security when instantiated using an IND-CPA secure encryption scheme and a strongly unforgeable MAC scheme. In each case, justify your answer.[12 marks] (d) In applications, we are often interested in simultaneously providing confidentiality and integrity for some data but only integrity for other, associated data. An Authenticated Encryption with Associated Data (AEAD) scheme meets this goal. Define the syntax of an AEAD scheme and show how to extend the generic EtM construction of an AE scheme to obtain an AEAD scheme. Use a diagram to illustrate the second part of your answer.[6 marks] (e) Nonce-based AEAD is a further extension of the AEAD paradigm. Explain what is meant by nonce-based AEAD and why it is a good primitive to offer to software developers.[4 marks]