Tight bounds for unconditional authentication protocols in the manual channel and shared key models

Moni Naor, Gil Segev, Adam Davison Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

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 < ∈ < 1 there exists a log* n-round protocol for authenticating n-bit messages, in which only 2 log(1/∈) + O(1) bits are manually authenticated, and any adversary (even computationally unbounded) has probability of at most ∈ 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/∈) - 6 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. Once again, we apply our proof technique, and prove a lower bound of 2 log(1/∈) - 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 essential (and sufficient) for the existence of protocols breaking the above lower bounds in the computational setting.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - CRYPTO 2006 - 26th Annual International Cryptology Conference, Proceedings
PublisherSpringer Verlag
Pages214-231
Number of pages18
ISBN (Print)3540374329, 9783540374329
StatePublished - Jan 1 2006
Event26th Annual International Cryptology Conference, CRYPTO 2006 - Seattle, WA, United States
Duration: Aug 20 2006Aug 24 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4117 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th Annual International Cryptology Conference, CRYPTO 2006
CountryUnited States
CitySeattle, WA
Period8/20/068/24/06

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Naor, M., Segev, G., & Smith, A. D. (2006). Tight bounds for unconditional authentication protocols in the manual channel and shared key models. In Advances in Cryptology - CRYPTO 2006 - 26th Annual International Cryptology Conference, Proceedings (pp. 214-231). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4117 LNCS). Springer Verlag.