Speeding up Exponentiation using an Untrusted Computational Resource

We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of over the square-and-multiply algorithm, where k is the bitlength of the exponent. One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform variable-base variable- exponent exponentiation, which also has this feature. Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller. Our protocols are unconditionally secure.     

Real Hypersurfaces of Type B in Complex Two-Plane Grassmannians

In this paper we give a characterization of real hypersurfaces of type B, that is, a tube over a totally real totally geodesic in complex two-plane Grassmannians with the shape operator A satisfying Aφ + φA = kφ, k is non-zero constant, for the structure tensor φ.     

Synthesis and optical characterization of vertically grown ZnO nanowires in high crystallinity through vapor-liquid-solid growth mechanism

The gas-phase growth and optical characteristics of 1-dimensional ZnO nanostructure have been investigated. The ZnO nanowires (NWs) were grown vertically on Au coated silicon substrates by vapor-liquid-solid (VLS) growth mechanism using chemical vapor deposition (CVD). The ZnO NWs were grown in the crystal direction of [0 0 0 1]. The ZnO NWs exhibit the uniform size of less than 100 nm in diameter and up to 5 μm in length. Photoluminescence (PL) spectrum of ZnO NWs shows the strong band-edge emission at ∼380 nm (∼3.27 eV) without significant deep-level defect emission. The exciton lifetime of ZnO NWs was measured to be approximately 150 ± 10 ps.     

Intrinsic ligament and triangular fibrocartilage complex (TFCC) tears of the wrist: comparison of isovolumetric 3D-THRIVE sequence MR arthrography and conventional MR image at 3 T

Purpose

The purpose of the study was to validate the diagnostic performance of high-resolution isovolumetric magnetic resonance arthrography (MRA) for intrinsic ligament and triangular fibrocartilage complex (TFCC) tears of the wrist as compared to conventional MR imaging (MRI).

Materials and methods

Forty-eight patients with traumatic TFCC tears at arthroscopy were enrolled. All patients had underwent proton-density- and T2-weighted MRI before arthrography and three-dimensional T1 high-resolution isovolumetric examination (3D-THRIVE) MRA on a 3-T MR. We assessed the presence of scapholunate interosseous ligament (SLIL)/lunotriquetral interosseous ligament (LTIL) or TFCC tears using the arthroscopy as a gold standard.

Results

Arthroscopy revealed 37 TFCC central tears, 15 TFCC peripheral tears, 20 SLIL tears and 13 LTIL tears. Sensitivities of MRI and MRA were 70.3% and 94.6% for detection of TFCC central tears, 60.0% and 93.3% for detection of TFCC peripheral tears, 65.0% and 85.0% for SLIL tears, and 61.5% and 84.6% for LTIL tears. The specificity of the MRI was 100% for the detection of ligaments and TFCC tears. The specificities of the MRA for detection of TFCC central tears, TFCC peripheral tears, SLIL tears and LTIL tears were 100%, 97%, 96.4% and 100%, respectively.

Conclusion

Isovolumetric 3D-THRIVE wrist MRA provided better results for depiction of intrinsic ligament and TFCC tears than wrist MRI.     

Real Hypersurfaces in Complex Two-plane Grassmannians with {\mathfrak{D}^{\bot}}-Parallel Shape Operator

In this paper we consider a new notion of ${\mathfrak{D}^{\bot}}$ -parallel shape operator for real hypersurfaces in complex two-plane Grassmannians ${G_2(\mathbb{C}^{m+2})}$ and give a non-existence theorem for a Hopf hypersurface in ${G_2(\mathbb{C}^{m+2})}$ with ${\mathfrak{D}^{\bot}}$ -parallel shape operator.     

Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians

We classify the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians _SU2,m/S(_U2⋅_Um)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$, m?2$m?2$. Each can be described as a tube over a totally geodesic _SU2,m−1/S(_U2⋅_Um−1)${\mathit{SU}}_{2,m-1}/S(U_2\cdot U_{m-1})$ in _SU2,m/S(_U2⋅_Um)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$ or a horosphere whose center at infinity is singular.     

A New Reversible Colorimetric Chemosensor Based on Julolidine Moiety for Detecting F−

Journal of Fluorescence - We synthesized an original reversible colorimetric chemosensor PDJ...