Translating INT Sample Clauses

Translating INT. CTXT into our notation means we arrive at an integrity definition which is nearly identical to Definition 5, with the only modification being the restriction that former outputs by the encryption oracle cannot be used for decryption. × → { } GCM uses a block cipher E : K X X, where X = 0, 1 128, however, using standard arguments, we can focus on GCM using a URP π over X instead. GCM[π] consists of an encryption enc and a decryption algorithm dec where enc : N × H × M → C , (50) dec : N × H × C → M ∪ {⊥} , (51) ⊥ with N the nonce space, H the associated data, M the plaintexts, C the cipher- texts, and an error symbol. × → On input of (n, a, m), enc generates unique inputs to π, n0, n1,..., nA. The values ni for i > 0 are used to run CTR mode [42] in order to encrypt the plaintext m. The resulting ciphertext c is then used together with the associated data a, and run through a polynomial hash function h : A C X, also called GHASH. XXXXX’s output is then XORed together with the output of π under n0 to create a Xxxxxx-Xxxxxx-style authenticator. The polynomial hash h uses L := π(0128) as a key. GCM with 96 bit nonces ensures that every time π is called by the encryption oracle, π receives a different input.