The exact security of PMAC
Gazi, Peter
Pietrzak, Krzysztof Z
Rybar, Michal
ddc:000
PMAC is a simple and parallel block-cipher mode of operation, which was introduced by Black and Rogaway at Eurocrypt 2002. If instantiated with a (pseudo)random permutation over n-bit strings, PMAC constitutes a provably secure variable input-length (pseudo)random function. For adversaries making q queries, each of length at most l (in n-bit blocks), and of total length σ ≤ ql, the original paper proves an upper bound on the distinguishing advantage of Ο(σ2/2n), while the currently best bound is Ο (qσ/2n).In this work we show that this bound is tight by giving an attack with advantage Ω (q2l/2n). In the PMAC construction one initially XORs a mask to every message block, where the mask for the ith block is computed as τi := γi·L, where L is a (secret) random value, and γi is the i-th codeword of the Gray code. Our attack applies more generally to any sequence of γi’s which contains a large coset of a subgroup of GF(2n). We then investigate if the security of PMAC can be further improved by using τi’s that are k-wise independent, for k > 1 (the original distribution is only 1-wise independent). We observe that the security of PMAC will not increase in general, even if the masks are chosen from a 2-wise independent distribution, and then prove that the security increases to O(q<2/2n), if the τi are 4-wise independent. Due to simple extension attacks, this is the best bound one can hope for, using any distribution on the masks. Whether 3-wise independence is already sufficient to get this level of security is left as an open problem.
Ruhr University Bochum
2017
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/6196
https://research-explorer.app.ist.ac.at/download/6196/6197
Gazi P, Pietrzak KZ, Rybar M. The exact security of PMAC. <i>IACR Transactions on Symmetric Cryptology</i>. 2017;2016(2):145-161. doi:<a href="https://doi.org/10.13154/TOSC.V2016.I2.145-161">10.13154/TOSC.V2016.I2.145-161</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.13154/TOSC.V2016.I2.145-161
info:eu-repo/semantics/altIdentifier/issn/2519-173X
info:eu-repo/grantAgreement/EC/H2020/682815
https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess