Cryptology ePrint Archive: Report 2006/175

Tight Bounds for Unconditional Authentication Protocols in the Manual Channel and Shared Key Models

Moni Naor and Gil Segev and Adam Smith

Abstract: We address the message authentication problem in two seemingly different communication models. In the first model, the sender and receiver are connected by an insecure channel and by a low-bandwidth auxiliary channel, that enables the sender to ``manually'' authenticate one short message to the receiver (for example, by typing a short string or comparing two short strings). We consider this model in a setting where no computational assumptions are made, and prove that for any $0 < \epsilon < 1$ there exists a $\log^* n$-round protocol for authenticating $n$-bit messages, in which only $2 \log(1 / \epsilon) + O(1)$ bits are manually authenticated, and any adversary (even computationally unbounded) has probability of at most $\epsilon$ to cheat the receiver into accepting a fraudulent message. Moreover, we develop a proof technique showing that our protocol is essentially optimal by providing a lower bound of $2 \log(1 / \epsilon) - O(1)$ on the required length of the manually authenticated string.

The second model we consider is the traditional message authentication model. In this model the sender and the receiver share a short secret key; however, they are connected only by an insecure channel. We apply the proof technique above to obtain a lower bound of $2 \log(1 / \epsilon) - 2$ on the required Shannon entropy of the shared key. This settles an open question posed by Gemmell and Naor (CRYPTO '93).

Finally, we prove that one-way functions are {\em necessary} (and sufficient) for the existence of protocols breaking the above lower bounds in the computational setting.

Category / Keywords: cryptographic protocols / authentication, lower bounds, one-way functions, unconditional security

Publication Info: Preliminary version in CRYPTO '06. Full version in IEEE Transactions on Information Theory (special issue on Information-Theoretic Security).

Date: received 18 May 2006, last revised 3 Jul 2008

Contact author: gil segev at weizmann ac il

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Version: 20080703:225533 (All versions of this report)

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