Fixed Argument Pairing Inversion on Elliptic Curves

Let $E$ be an elliptic curve over a finite field ${\mathbb F}_q$ with a power of prime $q$, $r$ a prime dividing $\#E({\mathbb F}_q)$, and $k$ the smallest positive integer satisfying $r | \Phi_k(p)$, called embedding degree. Then a bilinear map $t: E({\mathbb F}_q)[r] \times E({\mathbb F}_{q^k})/rE({\mathbb F}_{q^k}) \rightarrow {\mathbb F}_{q^k}^*$ is defined, called the Tate pairing. And the Ate pairing and other variants are obtained by reducing the domain for each argument and raising it to some power. In this paper we consider the {\em Fixed Argument Pairing Inversion (FAPI)} problem for the Tate pairing and its variants. In 2012, considering FAPI for the Ate$_i$ pairing, Kanayama and Okamoto formulated the {\em Exponentiation Inversion (EI)} problem. However the definition gives a somewhat vague description of the hardness of EI. We point out that the described EI can be easily solved, and hence clarify the description so that the problem does contain the actual hardness connection with the prescribed domain for given pairings. Next we show that inverting the Ate pairing (including other variants of the Tate pairing) defined on the smaller domain is neither easier nor harder than inverting the Tate pairing defined on the lager domain. This is very interesting because it is commonly believed that the structure of the Ate pairing is so simple and good (that is, the Miller length is short, the solution domain is small and has an algebraic structure induced from the Frobenius map) that it may leak some information, thus there would be a chance for attackers to find further approach to solve FAPI for the Ate pairing, differently from the Tate pairing

Accelerating the Final Exponentiation in the Computation of the Tate Pairings

Tate pairing computation consists of two parts: Miller step and final exponentiation step. In this paper, we investigate how to accelerate the final exponentiation step. Consider an order $r$ subgroup of an elliptic curve defined over \Fq with embedding degree $k$. The final exponentiation in the Tate pairing is an exponentiation of an element in \Fqk by $(q^k-1)/r$. The hardest part of this computation is to raise to the power \lam:=\varphi_k(q)/r. Write it as \lam=\lam_0+\lam_1q+\cdots+\lam_{d-1}q^{d-1} in the $q$-ary representation. When using multi-exponentiation techniques with precomputation, the final exponentiation cost mostly depends on $\kappa(\lambda)$, the size of the maximum of $|\lambda_i|$. In many parametrized pairing-friendly curves, the value $\kappa$ is about $\left(1-\frac{1}{\rho\varphi(k)}\right)\log q$ where $\rho=\log q/\log r$, while random curves will have $\kappa \approx \log q$. We analyze how this small $\kappa$ is obtained for parametrized elliptic curves, and show that $\left(1-\frac{1}{\rho\varphi(k)}\right)\log q$ is almost optimal in the sense that for all known construction methods of parametrized pairing-friendly curves it is the lower bound. This method is useful, but has a limitation that it can only be applied to only parametrized curves and excludes many of elliptic curves. In the second part of our paper, we propose a method to obtain a modified Tate pairing with smaller $\kappa$ for {\em any elliptic curves}. More precisely, our method finds an integer $m$ such that $\kappa(m\lambda)=\left(1-\frac{1}{\rho\varphi(k)}\right)\log q$ efficiently using lattice reduction. Using this modified Tate pairing, we can reduce the number of squarings in the final exponentiation by about $\left(1-\frac{1}{\rho\varphi(k)}\right)$ times from the usual Tate pairing. We apply our method to several known pairing friendly curves to verify the expected speedup

Facile fabrication of two-dimensional inorganic nanostructures and their conjugation to nanocrystals

Nanocomposites of two-dimensional (2D) inorganic nanosheets and inorganic nanocrystals are fabricated. Freestanding atomically flat gamma-AlOOH nanosheets (thickness <1 nm) are synthesized from a one-pot hydrothermal reaction. The freestanding and binder-free film composed of the gamma-AlOOH nanosheets is fabricated by sedimentation. Because they have positive zeta potentials in the pH range below ca. 9.3, the gamma-AlOOH nanosheets can function as positively charged 2D inorganic matrices in a broad pH range. By solution phase (pH 7.0) mixing of the gamma-AlOOH nanosheets (zeta potential: 30.7 +/- 0.8 mV) and inorganic nanocrystals with negative surface charge, including Au nanoparticles, Au nanorods, CdSe quantum dots, CdSe/CdS/ZnS quantum dots and CdSe nanorods, the nanocomposites are self-assembled via electrostatic interactions. Negatively charged inorganic nanostructures with a wide range of chemical compositions, shapes, sizes, surface ligands and adsorbates can be used as building blocks for gamma-AlOOH nanocomposites. Adsorption densities of inorganic nanocrystals on the nanocomposites can be controlled by varying concentrations of nanocrystal solutions. Nanocomposite films containing alternating layers of gamma-AlOOH and nanocrystals are obtained by a simple drop casting method.close3

Nanodelivery of Mycophenolate Mofetil to the Organ Improves Transplant Vasculopathy.

Inflammation occurring within the transplanted organ from the time of harvest is an important stimulus of early alloimmune reactivity and promotes chronic allograft rejection. Chronic immune-mediated injury remains the primary obstacle to the long-term success of organ transplantation. However, organ transplantation represents a rare clinical setting in which the organ is accessible ex vivo, providing an opportunity to use nanotechnology to deliver therapeutics directly to the graft. This approach facilitates the directed delivery of immunosuppressive agents (ISA) to target local pathogenic immune responses prior to the transplantation. Here, we have developed a system of direct delivery and sustained release of mycophenolate mofetil (MMF) to treat the donor organ prior to transplantation. Perfusion of a donor mouse heart with MMF-loaded PEG-PLGA nanoparticles (MMF-NPs) prior to transplantation abrogated cardiac transplant vasculopathy by suppressing intragraft pro-inflammatory cytokines and chemokines. Our findings demonstrate that ex vivo delivery of an ISA to donor organs using a nanocarrier can serve as a clinically feasible approach to reduce transplant immunity

The ID1-CULLIN3 Axis Regulates Intracellular SHH and WNT Signaling in Glioblastoma Stem Cells

SummaryInhibitor of differentiation 1 (ID1) is highly expressed in glioblastoma stem cells (GSCs). However, the regulatory mechanism responsible for its role in GSCs is poorly understood. Here, we report that ID1 activates GSC proliferation, self-renewal, and tumorigenicity by suppressing CULLIN3 ubiquitin ligase. ID1 induces cell proliferation through increase of CYCLIN E, a target molecule of CULLIN3. ID1 overexpression or CULLIN3 knockdown confers GSC features and tumorigenicity to murine Ink4a/Arf-deficient astrocytes. Proteomics analysis revealed that CULLIN3 interacts with GLI2 and DVL2 and induces their degradation via ubiquitination. Consistent with ID1 knockdown or CULLIN3 overexpression in human GSCs, pharmacologically combined control of GLI2 and β-CATENIN effectively diminishes GSC properties. A ID1-high/CULLIN3-low expression signature correlates with a poor patient prognosis, supporting the clinical relevance of this signaling axis. Taken together, a loss of CULLIN3 represents a common signaling node for controlling the activity of intracellular WNT and SHH signaling pathways mediated by ID1

Cytoprotective Effect of Phloroglucinol on Oxidative Stress Induced Cell Damage via Catalase Activation

Abstract We investigated the cytoprotective effect of phloroglucinol, which was isolated from Ecklonia cava (brown alga), against oxidative stress induced cell damage in Chinese hamster lung fibroblast (V79-4) cells. Phloroglucinol was found to scavenge 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical, hydrogen peroxide (H 2 O 2 ), hydroxy radical, intracellular reactive oxygen species (ROS), and thus prevented lipid peroxidation. As a result, phloroglucinol reduced H 2 O 2 induced apoptotic cells formation in V79-4 cells. In addition, phloroglucinol inhibited cell damage induced by serum starvation and radiation through scavenging ROS. Phloroglucinol increased the catalase activity and its protein expression. In addition, catalase inhibitor abolished the protective effect of phloroglucinol from H 2 O 2 induced cell damage. Furthermore, phloroglucinol increased phosphorylation of extracellular signal regulated kinase (ERK). Taken together, the results suggest that phloroglucinol protects V79-4 cells against oxidative damage by enhancing the cellular catalase activity and modulating ERK signal pathway

Delivery of costimulatory blockade to lymph nodes promotes transplant acceptance in mice

The lymph node (LN) is the primary site of alloimmunity activation and regulation during transplantation. Here, we investigated how fibroblastic reticular cells (FRCs) facilitate the tolerance induced by anti-CD40L in a murine model of heart transplantation. We found that both the absence of LNs and FRC depletion abrogated the effect of anti-CD40L in prolonging murine heart allograft survival. Depletion of FRCs impaired homing of T cells across the high endothelial venules (HEVs) and promoted formation of alloreactive T cells in the LNs in heart-transplanted mice treated with anti-CD40L. Single-cell RNA sequencing of the LNs showed that anti-CD40L promotes a Madcam1+ FRC subset. FRCs also promoted the formation of regulatory T cells (Tregs) in vitro. Nanoparticles (NPs) containing anti-CD40L were selectively delivered to the LNs by coating them with MECA-79, which binds to peripheral node addressin (PNAd) glycoproteins expressed exclusively by HEVs. Treatment with these MECA-79-anti-CD40L-NPs markedly delayed the onset of heart allograft rejection and increased the presence of Tregs. Finally, combined MECA-79-anti-CD40L-NPs and rapamycin treatment resulted in markedly longer allograft survival than soluble anti-CD40L and rapamycin. These data demonstrate that FRCs are critical to facilitating costimulatory blockade. LN-targeted nanodelivery of anti-CD40L could effectively promote heart allograft acceptance