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Security and Communication Networks
Volume 2018, Article ID 9715947, 12 pages
Research Article

Close to Optimally Secure Variants of GCM

1Key Laboratory of Electromagnetic Space Information, CAS, University of Science and Technology of China, Hefei 230027, China
2School of Economics and Management, Southeast University, Nanjing 211189, China

Correspondence should be addressed to Ping Zhang; nc.ude.ctsu.liam@pgz

Received 21 August 2017; Revised 5 December 2017; Accepted 16 January 2018; Published 6 March 2018

Academic Editor: Kamal D. Singh

Copyright © 2018 Ping Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Galois/Counter Mode of operation (GCM) is a widely used nonce-based authenticated encryption with associated data mode which provides the birthday-bound security in the nonce-respecting scenario; that is, it is secure up to about adversarial queries if all nonces used in the encryption oracle are never repeated, where is the block size. It is an open problem to analyze whether GCM security can be improved by using some simple operations. This paper presents a positive response for this problem. Firstly, we introduce two close to optimally secure pseudorandom functions and derive their security bound by the hybrid technique. Then, we utilize these pseudorandom functions that we design and a universal hash function to construct two improved versions of GCM, called OGCM-1 and OGCM-2. OGCM-1 and OGCM-2 are, respectively, provably secure up to approximately and adversarial queries in the nonce-respecting scenario if the underlying block cipher is a secure pseudorandom permutation. Finally, we discuss the properties of OGCM-1 and OGCM-2 and describe the future works.