Gerald Bourgeois

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Let A, B be n × n complex matrices such that C = AB − BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n ≥ 3, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of(More)
We present an algebraic attack on NTRU (restricted to the case where the parameter q is a power of two) using the method of the Witt vectors proposed by Silverman, Smart and Vercauteren [17]; the latter considered only the first two bits of a Witt vector attached to the recovering of the secret key in order to reduce the problem to the resolution of an(More)
on améliore une attaque algébrique de NTRU (où le paramètre q est une puissance de 2), due à Silverman, Smart et Vercauteren ; au lieu de considérer, comme les précédents, les 2 premiers bits d'un vecteur de Witt attaché à la recherche de la clé secrète, on considère ici les 4 premiers bits, ce qui fournit des équations supplémentaires de degrés 4 puis 8.(More)
f, g ∈ L(E) where E is a k vector space of dimension d. We introduce the relation (*): exp(t.f + g) = exp(t.f) • exp(g) for any t ∈ k or N; we study the connections between the relations (*) and f • g = g • f for d = 2 or 3. Let d = 2: if k = R and if (*) is verified for t ∈ N then f • g = g • f ; we obtain all the couples f , g verifying (*) on C and such(More)
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