TY  - BOOK
AU  - Rybar, Michal
TI  - (The exact security of) Message Authentication Codes
PY  - 2017///
PB  - IST Austria
N1  - Thesis; Abstract
; About the author; List of publications; List of abbreviations; 1 Introduction; 2 Preliminaries; 3 Message Authentication Codes; 4 Exact Security of HMAC; 5 Exact Security of PMAC; 6 Paper 1; 7 Paper 2; Bibliography
N2  - 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 ith 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 > 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
UR  - https://doi.org/10.15479/at:ista:th_828
ER  -