thesis published Michal Rybar author 2B3E3DE8-F248-11E8-B48F-1D18A9856A87 KrPi department In this thesis we discuss the exact security of message authentications codes HMAC , NMAC , and PMAC . NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). PMAC is a block-cipher based mode of operation, which also happens to be the most famous fully parallel MAC. NMAC was introduced by Bellare, Canetti and Krawczyk Crypto’96, who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, under two assumptions. Unfortunately, for many instantiations of HMAC one of them has been found to be wrong. To restore the provable guarantees for NMAC , Bellare [Crypto’06] showed its security without this assumption. PMAC was introduced by Black and Rogaway at Eurocrypt 2002. If instantiated with a pseudorandom permutation over n -bit strings, PMAC constitutes a provably secure variable input-length PRF. For adversaries making q queries, each of length at most ` (in n -bit blocks), and of total length σ ≤ q` , the original paper proves an upper bound on the distinguishing advantage of O ( σ 2 / 2 n ), while the currently best bound is O ( qσ/ 2 n ). In this work we show that this bound is tight by giving an attack with advantage Ω( q 2 `/ 2 n ). In the PMAC construction one initially XORs a mask to every message block, where the mask for the i th block is computed as τ i := γ i · L , where L is a (secret) random value, and γ i is the i -th codeword of the Gray code. Our attack applies more generally to any sequence of γ i ’s which contains a large coset of a subgroup of GF (2 n ). As for NMAC , our first contribution is a simpler and uniform proof: If f is an ε -secure PRF (against q queries) and a δ - non-adaptively secure PRF (against q queries), then NMAC f is an ( ε + `qδ )-secure PRF against q queries of length at most ` blocks each. We also show that this ε + `qδ bound is basically tight by constructing an f for which an attack with advantage `qδ exists. Moreover, we analyze the PRF-security of a modification of NMAC called NI by An and Bellare that avoids the constant rekeying on multi-block messages in NMAC and allows for an information-theoretic analysis. We carry out such an analysis, obtaining a tight `q 2 / 2 c bound for this step, improving over the trivial bound of ` 2 q 2 / 2 c . Finally, we investigate, if the security of PMAC can be further improved by using τ i ’s that are k -wise independent, for k &gt; 1 (the original has k = 1). We observe that the security of PMAC will not increase in general if k = 2, and then prove that the security increases to O ( q 2 / 2 n ), if the k = 4. Due to simple extension attacks, this is the best bound one can hope for, using any distribution on the masks. Whether k = 3 is already sufficient to get this level of security is left as an open problem. Keywords: Message authentication codes, Pseudorandom functions, HMAC, PMAC. https://research-explorer.ista.ac.at/download/838/4799/IST-2017-828-v1+3_2017_Rybar_thesis.pdf application/pdfno https://research-explorer.ista.ac.at/download/838/6202/2017_Thesis_Rybar_source.zip application/zip Institute of Science and Technology Austria2017 eng 2663-337X10.15479/AT:ISTA:th_828 86 https://research-explorer.ista.ac.at/record/2082 https://research-explorer.ista.ac.at/record/6196 Rybar, Michal. <i>(The Exact Security of) Message Authentication Codes</i>. Institute of Science and Technology Austria, 2017, doi:<a href="https://doi.org/10.15479/AT:ISTA:th_828">10.15479/AT:ISTA:th_828</a>. Rybar, Michal. “(The Exact Security of) Message Authentication Codes.” Institute of Science and Technology Austria, 2017. <a href="https://doi.org/10.15479/AT:ISTA:th_828">https://doi.org/10.15479/AT:ISTA:th_828</a>. M. Rybar, “(The exact security of) Message authentication codes,” Institute of Science and Technology Austria, 2017. Rybar, M. (2017). <i>(The exact security of) Message authentication codes</i>. Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/AT:ISTA:th_828">https://doi.org/10.15479/AT:ISTA:th_828</a> Rybar M. 2017. (The exact security of) Message authentication codes. Institute of Science and Technology Austria. Rybar M. (The exact security of) Message authentication codes. 2017. doi:<a href="https://doi.org/10.15479/AT:ISTA:th_828">10.15479/AT:ISTA:th_828</a> M. Rybar, (The Exact Security of) Message Authentication Codes, Institute of Science and Technology Austria, 2017. 8382018-12-11T11:48:46Z2026-04-08T14:18:39Z