Multi-user Security of Elephant v2 Sample Clauses

Multi-user Security of Elephant v2. In this work, we prove security of Elephant v2 [11]. The proof differs from the one of v1 [9] in that the new authenticator is considered. In addition, our result shows that Elephant v2 indeed achieves authenticity under nonce-misuse. Finally, our new proof is in the multi-user setting.
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Multi-user Security of Elephant v2. ‌ We prove security of Elephant v2 of Sect. 4.1 for any 2−α-proper tweak space. Theorem 2. Let k, m, n, t, μ N with k, m, t n. Let ϕ1, ϕ2 : 0, 1 n $ 0, 1 n be LFSRs, and let be a 2−α-proper tweak space with respect to (ϕ1, ϕ2). Consider Elephant-v2 = (enc, dec) of Sect. 4.1 based on random permutation P ←− perm(n). For any multi-user adversary A making at most qe ≤ 2n−1 con- struction encryption queries (in total to all μ construction oracles) for unique nonces whenever the same oracle is queried, qd construction decryption queries (in total to all μ construction oracles), each query at most l padded nonce and associated data and message blocks, and in total at most σ padded nonce and associated data and message blocks, and p primitive queries, Advμ-ae (A) ≤ l qe /2n + 3 qe + qd /2n + q /2t + Advμ-tprp(A′), Elephant-v2 SiM for some multi-user adversary ′ that makes 2σ construction queries and p The proof of Theorem 2 is given in Sect. 5 and is significantly different from that of Elephant v1 [9]. In a nutshell, the first change is that the new proof is in the multi-user setting, where the adversary has access to multiple instances, all
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