Using Simon's Algorithm to Attack Symmetric-Key Cryptographic Primitives

We present new connections between quantum information and the field of classical cryptography. In particular, we provide examples where Simon's algorithm can be used to show insecurity of commonly used cryptographic symmetric-key primitives. Specifically, these examples consist of a quantum distinguisher for the 3-round Feistel network and a forgery attack on CBC-MAC which forges a tag for a chosen-prefix message querying only other messages (of the same length). We assume that an adversary has quantum-oracle access to the respective classical primitives. Similar results have been achieved recently in independent work by Kaplan et al. Our findings shed new light on the post-quantum security of cryptographic schemes and underline that classical security proofs of cryptographic constructions need to be revisited in light of quantum attackers.Comment: 14 pages, 2 figures. v3: final polished version, more formal definitions adde

Resonant charging of Xe clusters in Helium nanodroplets under intense laser fields

We theoretically investigate the impact of multiple plasmon resonances on the charging of Xe clusters embedded in He nanodroplets under intense pump-probe laser excitation. Our molecular dynamics simulations on Xe309He10000$and comparison to results for free Xe309$ give clear evidence for selective resonance heating in the He shell and the Xe cluster, but no corresponding double hump feature in the final Xe charge spectra is found. Though the presence of the He shell substantially increases the maximum charge states, the pump-probe dynamics of the Xe spectra from embedded system is similar to that of the free species. In strong contrast to that, the predicted electron spectra do show well-separated and pronounced features from highly efficient plasmon assisted electron acceleration for both resonances in the embedded clusters. A detailed analysis of the underlying ionization and recombination dynamics is presented and explains the apparent disaccord between the resonance features in the ion and electron spectra.Comment: revised manuscrip

Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules

We describe mirror symmetry for weak toric Fano manifolds as an equivalence of D-modules equipped with certain filtrations. We discuss in particular the logarithmic degeneration behavior at the large radius limit point, and express the mirror correspondence as an isomorphism of Frobenius manifolds with logarithmic poles. The main tool is an identification of the Gauss-Manin system of the mirror Landau-Ginzburg model with a hypergeometric D-module, and a detailed study of a natural filtration defined on this differential system. We obtain a solution of the Birkhoff problem for lattices defined by this filtration and show the existence of a primitive form, which yields the construction of Frobenius structures with logarithmic poles associated to the mirror Laurent polynomial. As a final application, we show the existence of a pure polarized non-commutative Hodge structure on a Zariski open subset of the complexified Kaehler moduli space of the variety