Improved Security Bound of (E/D)WCDM

In CRYPTO’16, Cogliati and Seurin proposed a block cipher based nonce based MAC, called Encrypted Wegman-Carter with Davies-Meyer (EWCDM), that gives 2n/3 bit MAC security in the nonce respecting setting and n/2 bit security in the nonce misuse setting, where n is the block size of the underlying b...

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Autores principales:	Nilanjan Datta, Avijit Dutta, Kushankur Dutta
Formato:	article
Lenguaje:	EN
Publicado:	Ruhr-Universität Bochum 2021
Materias:	Wegman Carter Extended Mirror Theory Nonce Based MAC EWCDM DWCDM Computer engineering. Computer hardware TK7885-7895
Acceso en línea:	https://doaj.org/article/f72e42b4173c42ecb7412ac4ef65fc1a
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spelling	oai:doaj.org-article:f72e42b4173c42ecb7412ac4ef65fc1a2021-12-03T14:38:29ZImproved Security Bound of (E/D)WCDM10.46586/tosc.v2021.i4.138-1762519-173Xhttps://doaj.org/article/f72e42b4173c42ecb7412ac4ef65fc1a2021-12-01T00:00:00Zhttps://tosc.iacr.org/index.php/ToSC/article/view/9332https://doaj.org/toc/2519-173X In CRYPTO’16, Cogliati and Seurin proposed a block cipher based nonce based MAC, called Encrypted Wegman-Carter with Davies-Meyer (EWCDM), that gives 2n/3 bit MAC security in the nonce respecting setting and n/2 bit security in the nonce misuse setting, where n is the block size of the underlying block cipher. However, this construction requires two independent block cipher keys. In CRYPTO’18, Datta et al. came up with a single-keyed block cipher based nonce based MAC, called Decrypted Wegman-Carter with Davies-Meyer (DWCDM), that also provides 2n/3 bit MAC security in the nonce respecting setting and n/2 bit security in the nonce misuse setting. However, the drawback of DWCDM is that it takes only 2n/3 bit nonce. In fact, authors have shown that DWCDM cannot achieve beyond the birthday bound security with n bit nonces. In this paper, we prove that DWCDM with 3n/4 bit nonces provides MAC security up to O(23n/4) MAC queries against all nonce respecting adversaries. We also improve the MAC bound of EWCDM from 2n/3 bit to 3n/4 bit. The backbone of these two results is a refined treatment of extended mirror theory that systematically estimates the number of solutions to a system of bivariate affine equations and non-equations, which we apply on the security proofs of the constructions to achieve 3n/4 bit security. Nilanjan DattaAvijit DuttaKushankur DuttaRuhr-Universität BochumarticleWegman CarterExtended Mirror TheoryNonce Based MACEWCDMDWCDMComputer engineering. Computer hardwareTK7885-7895ENIACR Transactions on Symmetric Cryptology, Vol 2021, Iss 4 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Wegman Carter Extended Mirror Theory Nonce Based MAC EWCDM DWCDM Computer engineering. Computer hardware TK7885-7895
spellingShingle	Wegman Carter Extended Mirror Theory Nonce Based MAC EWCDM DWCDM Computer engineering. Computer hardware TK7885-7895 Nilanjan Datta Avijit Dutta Kushankur Dutta Improved Security Bound of (E/D)WCDM
description	In CRYPTO’16, Cogliati and Seurin proposed a block cipher based nonce based MAC, called Encrypted Wegman-Carter with Davies-Meyer (EWCDM), that gives 2n/3 bit MAC security in the nonce respecting setting and n/2 bit security in the nonce misuse setting, where n is the block size of the underlying block cipher. However, this construction requires two independent block cipher keys. In CRYPTO’18, Datta et al. came up with a single-keyed block cipher based nonce based MAC, called Decrypted Wegman-Carter with Davies-Meyer (DWCDM), that also provides 2n/3 bit MAC security in the nonce respecting setting and n/2 bit security in the nonce misuse setting. However, the drawback of DWCDM is that it takes only 2n/3 bit nonce. In fact, authors have shown that DWCDM cannot achieve beyond the birthday bound security with n bit nonces. In this paper, we prove that DWCDM with 3n/4 bit nonces provides MAC security up to O(23n/4) MAC queries against all nonce respecting adversaries. We also improve the MAC bound of EWCDM from 2n/3 bit to 3n/4 bit. The backbone of these two results is a refined treatment of extended mirror theory that systematically estimates the number of solutions to a system of bivariate affine equations and non-equations, which we apply on the security proofs of the constructions to achieve 3n/4 bit security.
format	article
author	Nilanjan Datta Avijit Dutta Kushankur Dutta
author_facet	Nilanjan Datta Avijit Dutta Kushankur Dutta
author_sort	Nilanjan Datta
title	Improved Security Bound of (E/D)WCDM
title_short	Improved Security Bound of (E/D)WCDM
title_full	Improved Security Bound of (E/D)WCDM
title_fullStr	Improved Security Bound of (E/D)WCDM
title_full_unstemmed	Improved Security Bound of (E/D)WCDM
title_sort	improved security bound of (e/d)wcdm
publisher	Ruhr-Universität Bochum
publishDate	2021
url	https://doaj.org/article/f72e42b4173c42ecb7412ac4ef65fc1a
work_keys_str_mv	AT nilanjandatta improvedsecurityboundofedwcdm AT avijitdutta improvedsecurityboundofedwcdm AT kushankurdutta improvedsecurityboundofedwcdm
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Improved Security Bound of (E/D)WCDM

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