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The general complex case of the Bernstein-Nachbin approximation problem

S. MachadoJoao Bosco Prolla — 1978

Annales de l'institut Fourier

We present a solution to the (strict) Bernstein-Nachbin approximation problem in the general complex case. As a corollary, we get proofs of the analytic, the quasi-analytic, and the bounded criteria for localizability in the general complex case. This generalizes the known results of the real or self-adjoint complex cases, in the same way that Bishop’s Theorem generalizes the Weierstrass-Stone Theorem. However, even in the real or self-adjoint complex cases, the results that we obtain are stronger...

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

Vinícius G. P. de SÁDavidson R. BoccardoLuiz Fernando RustRaphael C. S. Machado — 2013

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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...

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