Cryptology ePrint Archive: Report 2018/804

Double-block Hash-then-Sum: A Paradigm for Constructing BBB Secure PRF

Nilanjan Datta and Avijit Dutta and Mridul Nandi and Goutam Paul

Abstract: SUM-ECBC (Yasuda, CT-RSA 2010) is the first beyond birthday bound (BBB) secure block cipher based deterministic MAC. After this work, some more BBB secure deterministic MACs have been proposed, namely PMAC_Plus (Yasuda, CRYPTO 2011), 3kf9 (Zhang et al., ASIACRYPT 2012) and LightMAC_Plus (Naito, ASIACRYPT 2017). In this paper, we have abstracted out the inherent design principle of all these BBB secure MACs and present a generic design paradigm to construct a BBB secure pseudo random function, namely Double-block Hash-then-Sum or in short (DbHtS). A DbHtS construction, as the name implies, computes a double block hash on the message and then sum the encrypted output of the two hash blocks. Our result renders that if the underlying hash function meets certain security requirements (namely cover-free and block-wise universal advantage is low), DbHtS construction provides $2n/3$-bit security. We demonstrate the applicability of our result by instantiating all the existing beyond birthday secure deterministic MACs (e.g., SUM-ECBC, PMAC_Plus, 3kf9, LightMAC_Plus) as well as a simple two-keyed variant for each of them and some algebraic hash based constructions.

Category / Keywords: secret-key cryptography / DbHtS, Beyond Birthday, Cover-free, Block-wise Universal, PRF, Sum of PRP

Original Publication (in the same form): IACR-FSE-2019

Date: received 30 Aug 2018, last revised 10 Sep 2018

Contact author: nilanjan_isi_jrf at yahoo com, avirocks dutta13@gmail com, mridul nandi@gmail com, goutam k paul@gmail com

Available format(s): PDF | BibTeX Citation

Note: A Minor change in the constant of the 2K-ECBC Security Bound.

Version: 20180910:110108 (All versions of this report)

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