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In this paper we are interested in algebraic immunity of several well known highly-nonlinear vectorial Boolean functions (or S-boxes), designed for block and stream ciphers. Unfortunately, ciphers that use such S-boxes may still be vulnerable to so called " algebraic attacks " proposed recently by Courtois, Pieprzyk, Meier, Armknecht, et al. These attacks(More)
We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest 0+ and 1+ resonances in 12C populated in beta decays. These states are dominated by sequential, through the 8Be ground state, and direct decays, respectively.(More)
The complex energies of the three-body resonances for one infinitely heavy particle and two non-interacting light particles are the sum of the two contributing two-body complex resonance energies. The bound state of a Borromean system originates from a resonance when the third interaction is introduced, a finite mass is allowed and proper angular momentum(More)
We describe a reaction mechanism which is consistent with all available experimental information of high energy three-body breakup processes. The dominating channels are removal of one of the three halo particles leaving the other two either undisturbed or absorbed. We compare with the commonly used deceptive assumption of a decay through two-body resonance(More)
– The different kinds of behaviour of three-body systems in the weak binding limit are classified with specific attention to the transition from a true three-body system to an effective two-body system. For weakly bound Borromean systems approaching the limit of binding we show that the size-binding energy relation is an almost universal function of the(More)
We compare the properties of three-body systems obtained with two-body potentials with Pauli forbidden states and with the corresponding phase equivalent two-body potentials. In the first case the forbidden states are explicitly excluded in the calculation. Differences arise due to the off-shell properties of these on-shell equivalent potentials. We use the(More)
We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complex-energy wave-function of the resonance. We use the hyperspherical adiabatic expansion method where all lengths are(More)
The neutron– 9 Li interaction and the corresponding low-energy 10 Li spectrum are decisive for the properties of 11 Li described as a three-body system (n+n+ 9 Li). We compute structure and breakup properties of 11 Li as function of this interaction. The hyperfine structure due to the spin 3/2 of both 9 Li and 11 Li is needed and treated with special care.(More)
The continuum resonance spectrum of 5 H (3 H+n+n) is investigated by use of the complex scaled hyperspherical adiabatic expansion method. The crucial 3 H-neutron potential is obtained by switching off the Coulomb part from successful fits to 3 He-proton experimental data. These two-body potentials must be expressed exclusively by operators conserving the(More)