no. 2
A tight bound for exhaustive key search attacks against Message Authentication Codes
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) no. 2, pp. 171-180.

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.

DOI : 10.1051/ita/2012025
Classification : 94A60
Mots clés : cryptography, message authentication code, asymptotic analysis 
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     author = {de S\'A, Vin{\'\i}cius G. P. and Boccardo, Davidson R. and Rust, Luiz Fernando and Machado, Raphael C. S.},
     title = {A tight bound for exhaustive key search attacks against {Message} {Authentication} {Codes}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {171--180},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {2},
     year = {2013},
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     url = {http://archive.numdam.org/articles/10.1051/ita/2012025/}
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de SÁ, Vinícius G. P.; Boccardo, Davidson R.; Rust, Luiz Fernando; Machado, Raphael C. S. A tight bound for exhaustive key search attacks against Message Authentication Codes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) no. 2, pp. 171-180. doi : 10.1051/ita/2012025. http://archive.numdam.org/articles/10.1051/ita/2012025/

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