Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Variational study of J_(1)-J_(2) Heisenberg model on kagome lattice using projected Schwinger-boson wave functions

Motivated by the unabating interest in the spin-1/2 Heisenberg antiferromagnetic model on the kagome lattice, we investigate the energetics of projected Schwinger-boson (SB) wave functions in the J_(1)-J_(2) model with antiferromagnetic J_(2) coupling. Our variational Monte Carlo results show that Sachdev’s Q_(1)=Q_(2) SB ansatz has a lower energy than the Dirac spin liquid for J_(2) ≳ 0.08J_(1) and the q=0 Jastrow-type magnetically ordered state. This work demonstrates that the projected SB wave functions can be tested on the same footing as their fermionic counterparts

Extended paraconductivity regime in underdoped cuprates

We reconsider transport experiments in strongly anisotropic superconducting cuprates and we find that universal Aslamazov-Larkin (AL) paraconductivity in two dimensions is surprisingly robust even in the underdoped regime below the pseudogap crossover temperature T^*. We also establish that the underlying normal state resistivity in the pseudogap phase is (almost) linear in temperature, with all the deviations being quantitatively accounted by AL paraconductivity. The disappearence of paraconductivity is governed by the disappearence of gaussian pair fluctuations at an energy scale related to T^*.Comment: 5 pages and 2 figure