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Oprateur de signature sur les varits avec une strate singulire conique

In this paper, we attack the recent NIST submission Giophantus, a public key encryption scheme. We find that the complicated structure of Giophantus's ciphertexts leaks information via a correspondence from a low dimensional lattice. This allows us to distinguish encrypted data from random data by the LLL algorithm. This is a more efficient attack than previous proposed attacks.

Inspired by the work of Z. Lu and G. Tian (Duke Math. J. 125:351–387,2004) in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan–Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan–Hartogs domain can be viewed as an “iterated” disk bundle over its base and the ideas given in (Arezzo, Loi and Zuddas in Math. Z. 275:1207–1216,2013) for the computation of the Szegö kernel of the disk bundle over an Hermitian symmetric space of compact type.

In this paper, we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0 < p,q ⩽ ∞. Furthermore, we establish Rényi entropic uncertainty principles for subfactor planar algebras.