--- _id: '2082' abstract: - lang: eng text: '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). Security proofs and attacks for NMAC can typically be lifted to HMAC. 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, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto''06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: 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+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto''99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto''05].' alternative_title: - LNCS author: - first_name: Peter full_name: Gazi, Peter id: 3E0BFE38-F248-11E8-B48F-1D18A9856A87 last_name: Gazi - first_name: Krzysztof Z full_name: Pietrzak, Krzysztof Z id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87 last_name: Pietrzak orcid: 0000-0002-9139-1654 - first_name: Michal full_name: Rybar, Michal id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87 last_name: Rybar citation: ama: 'Gazi P, Pietrzak KZ, Rybar M. The exact PRF-security of NMAC and HMAC. In: Garay J, Gennaro R, eds. Vol 8616. Springer; 2014:113-130. doi:10.1007/978-3-662-44371-2_7' apa: 'Gazi, P., Pietrzak, K. Z., & Rybar, M. (2014). The exact PRF-security of NMAC and HMAC. In J. Garay & R. Gennaro (Eds.) (Vol. 8616, pp. 113–130). Presented at the CRYPTO: International Cryptology Conference, Santa Barbara, USA: Springer. https://doi.org/10.1007/978-3-662-44371-2_7' chicago: Gazi, Peter, Krzysztof Z Pietrzak, and Michal Rybar. “The Exact PRF-Security of NMAC and HMAC.” edited by Juan Garay and Rosario Gennaro, 8616:113–30. Springer, 2014. https://doi.org/10.1007/978-3-662-44371-2_7. ieee: 'P. Gazi, K. Z. Pietrzak, and M. Rybar, “The exact PRF-security of NMAC and HMAC,” presented at the CRYPTO: International Cryptology Conference, Santa Barbara, USA, 2014, vol. 8616, no. 1, pp. 113–130.' ista: 'Gazi P, Pietrzak KZ, Rybar M. 2014. The exact PRF-security of NMAC and HMAC. CRYPTO: International Cryptology Conference, LNCS, vol. 8616, 113–130.' mla: Gazi, Peter, et al. The Exact PRF-Security of NMAC and HMAC. Edited by Juan Garay and Rosario Gennaro, vol. 8616, no. 1, Springer, 2014, pp. 113–30, doi:10.1007/978-3-662-44371-2_7. short: P. Gazi, K.Z. Pietrzak, M. Rybar, in:, J. Garay, R. Gennaro (Eds.), Springer, 2014, pp. 113–130. conference: end_date: 2014-08-21 location: Santa Barbara, USA name: 'CRYPTO: International Cryptology Conference' start_date: 2014-08-17 date_created: 2018-12-11T11:55:36Z date_published: 2014-01-01T00:00:00Z date_updated: 2023-09-07T12:02:27Z day: '01' ddc: - '000' - '004' department: - _id: KrPi doi: 10.1007/978-3-662-44371-2_7 ec_funded: 1 editor: - first_name: Juan full_name: Garay, Juan last_name: Garay - first_name: Rosario full_name: Gennaro, Rosario last_name: Gennaro file: - access_level: open_access checksum: dab6ab36a5f6af94f2b597e6404ed11d content_type: application/pdf creator: system date_created: 2018-12-12T10:13:17Z date_updated: 2020-07-14T12:45:28Z file_id: '4999' file_name: IST-2016-682-v1+1_578.pdf file_size: 492310 relation: main_file file_date_updated: 2020-07-14T12:45:28Z has_accepted_license: '1' intvolume: ' 8616' issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 113 - 130 project: - _id: 258C570E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '259668' name: Provable Security for Physical Cryptography publication_status: published publisher: Springer publist_id: '4955' pubrep_id: '682' quality_controlled: '1' related_material: record: - id: '838' relation: dissertation_contains status: public status: public title: The exact PRF-security of NMAC and HMAC type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 8616 year: '2014' ...