Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multivariate discrete logarithm assumption. This encryption scheme is thought to withstand to quantum computer attacks. Though I can construct this scheme over many non-commutative rings, I will adopt th...

The photoinduced ring-closure/ring-opening reactions of a series of bis-dithienylethene derivatives, as free ligands and Zn(II)-complexes, are investigated by resorting to theoretical (time-dependent density functional theory) and kinetic analyses in solution. The originality of the system stems from the tunability of the photoreaction quantum yields and conversion yields as a function of the e...

We report on the confinement of a Bose-Einstein condensate in an annular trap with widely tunable parameters. The relies combination magnetic, optical and radio-frequency fields. loading procedure is discussed. present traps radii adjusted between 20 150 micrometers. demonstrate preparation persistent flows both rotating laser stirrer global quadrupole deformation ring.Our setup well adapted fo...

The persistent progress of quantum computing with algorithms of Shor and Proos and Zalka has put our present RSA and ECC based public key cryptosystems at peril. There is a flurry of activity in cryptographic research community to replace classical cryptography schemes with their post-quantum counterparts. The learning with errors problem introduced by Oded Regev offers a way to design secure c...

0.1. Overview. The aim of these notes is to describe an exciting chapter in the recent development of quantum cohomology. Guided by ideas from physics (see [W]), a remarkable structure on the solutions of certain rational enumerative geometry problems has been found: the solutions are coefficients in the multiplication table of a quantum cohomology ring. Associativity of the ring yields non-tri...

We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the quantum setting over a field of arbitrary characteristic. We give necessary and sufficient conditions for such algebras to satisfy a Poincaré-Birkhoff-Witt proper...