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We examine the impact of small parity-time (PT) symmetric perturbations on nonlinear optical honeycomb lattices in the tight-binding limit. We show for strained lattices that complex dispersion relationships do not form under perturbation, and we find a variety of nonlinear wave equations which describe the effective dynamics in this regime. The existence of semilocalized gap solitons in this case is also shown, though we numerically demonstrate these solitons are likely unstable. We show for unstrained lattices under the effect of a restricted class of PT perturbations, which prevent complex dispersion relationships from appearing, that nontrivial phase dynamics emerge as a result of the PT perturbation. This phase can be understood as momentum imparted to optical beams by the lattice, thus showing PT perturbations offer potentially novel means for the control of light in honeycomb lattices.

No abstract uploaded!

No abstract uploaded!

Sflash is a fast multivariate signature scheme. Though the first version Sflash-v1 was flawed, a second version, Sflash-v2 was selected by the Nessie Consortium and was recommended for implementation of low-end smart cards. Very recently, due to the security concern, the designer of Sflash recommended that Sflash-v2 should not be used, instead a new version Sflash-v3 is proposed, which essentially only increases the length of the signature. The Sflash family of signature schemes is a variant of the Matsumoto and Imai public key cryptosystem. The modification is through the Minus method, namely given a set of polynomial equations, one takes out a few of them to make them much more difficult to solve. In this paper, we attack the Sflash-v3 scheme by combining an idea from the relinearization method by Kipnis and Shamir, which was used to attack the Hidden Field Equation schemes, and the linearization method by Patarin. We show that the attack complexity is less than 2^{80}, the security standard required by the Nessie Consortium.