Discussion of Theorem Sample Clauses

Discussion of Theorem. 2 The Elephant v2 submission to the NIST Lightweight Cryptography competi- tion [26] consists of three instances: Dumbo, Jumbo, and Delirium [11]. All three variants process a key of size k = 128 bits and a nonce of size m = 96 bits. Dumbo uses an n = 160-bit permutation and outputs tags of size t = 64 bits, Jumbo uses an n = 176-bit permutation and outputs tags of size t = 64 bits, and Delirium uses an n = 200-bit permutation and outputs tags of size t = 64 bits. For each of the three variants, the authors have developed an LFSR that defines an 2−n-proper mask function [11]. If we model the permutations underlying Dumbo, Jumbo, and Delirium as random permutations, we can conclude from Theorem 2 and Theorem 1 that the three functions are secure authenticated encryption schemes up to bound d l qe /2n +3 qe + qd /2n + q /2t − · · 4σ2 + 4σp + (μ 1)2σ + μ (4σ + p + μ−1 ) + 2n μ (p + μ−1 ) + 2k , against any nonce-respecting adversary that makes at most qe encryption queries and qd decryption queries, all of maximum length l blocks and in total of length at most σ blocks, and that makes at most p evaluations of the random primitive ≤