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A tight bound for exhaustive key search attacks against Message Authentication Codes

Published online by Cambridge University Press:  06 November 2012

Vinícius G.P. de SÁ ,
Davidson R. Boccardo ,
Luiz Fernando Rust  and
Raphael C.S. Machado
Vinícius G.P. de SÁ
Affiliation:
Depto. de Ciência da Computação, Univ. Federal do Rio de Janeiro, Brazil. vigusmao@dcc.ufrj.br
Davidson R. Boccardo
Affiliation:
Inmetro, National Institute of Metrology, Quality and Technology, Brazil; drboccardo@inmetro.gov.br; lfrust@inmetro.gov.br; rcmachado@inmetro.gov.br
Luiz Fernando Rust
Affiliation:
Inmetro, National Institute of Metrology, Quality and Technology, Brazil; drboccardo@inmetro.gov.br; lfrust@inmetro.gov.br; rcmachado@inmetro.gov.br
Raphael C.S. Machado
Affiliation:
Depto. de Ciência da Computação, Univ. Federal do Rio de Janeiro, Brazil. vigusmao@dcc.ufrj.br Inmetro, National Institute of Metrology, Quality and Technology, Brazil; drboccardo@inmetro.gov.br; lfrust@inmetro.gov.br; rcmachado@inmetro.gov.br
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Abstract

A Message Authentication Code (MAC) is a function that takes a message and a key as parameters and outputs an authentication of the message. MAC are used to guarantee the legitimacy of messages exchanged through a network, since generating a correct authentication requires the knowledge of the key defined secretly by trusted parties. However, an attacker with access to a sufficiently large number of message/authentication pairs may use a brute force algorithm to infer the secret key: from a set containing initially all possible key candidates, subsequently remove those that yield an incorrect authentication, proceeding this way for each intercepted message/authentication pair until a single key remains. In this paper, we determine an exact formula for the expected number of message/authentication pairs that must be used before such form of attack is successful, along with an asymptotical bound that is both simple and tight. We conclude by illustrating a modern application where this bound comes in handy, namely the estimation of security levels in reflection-based verification of software integrity.

Keywords

CryptographyMessage Authentication Codeasymptotic analysis
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 2 , April 2013 , pp. 171 - 180
Copyright
© EDP Sciences 2012

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