Twisted Edwards curves revisited

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use . It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to . This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.

Faster pairings on special Weierstrass curves

This paper presents efficient formulas for computing cryptographic pairings on the curve y 2 = c x 3 + 1 over fields of large characteristic. We provide examples of pairing-friendly elliptic curves of this form which are of interest for efficient pairing implementations.

Raman spectroscopic study of the uranyl mineral natrouranospinite (Na2,Ca)[(UO2)(AsO4)]2•5H2O

Raman spectra of natrouranospinite complemented with infrared spectra were studied and related to the structure of the mineral. Observed bands were assigned to the stretching and bending vibrations of (UO2)2+ and (AsO4)3- units and of water molecules. U-O bond lengths in uranyl and O-H…O hydrogen bond lengths were calculated from the Raman and infrared spectra.

Raman spectroscopic study of the uranyl sulphate mineral jáchymovite (UO2)8(SO4)(OH)14•13H2O

Raman spectra of jáchymovite, (UO2)8(SO4)(OH)14•13H2O, were studied, complemented with infrared spectra, and compared with published Raman and infrared spectra of uranopilite, [(UO2)6(SO4)O2(OH)6(H2O)6] •6H2O. Bands related to the stretching and bending vibrations of (UO2)2+, (SO4)2-, (OH)- and water molecules were assigned. U-O bond lengths in uranyl and O-H…O hydrogen bond lengths were calculated from the Raman and infrared spectra.

Constructing quality : the Hong Kong Housing Department journey

This paper explores the ‘journey’ along the ‘never ending quality road’ undertaken by the Hong Kong Housing Department over the last 15 years. It briefly covers the early history of public housing in Hong Kong, the catalytic effect brought about by the discovery of the infamous 26 sub-standard blocks in the mid-80s leading to the subsequent major improvements to process control and structural quality in the period 1985-1990. It then moves onto a discussion of initiatives taken since 1991, including the formation of the List of Building Contractors and the implementation of the Performance Assessment Scoring System (PASS). The paper ends with a discussion of the current status of quality issues within the Department and touches on future initiatives being developed to further enhance the quality of public housing in Hong Kong.

Raman spectroscopic study of the antimonate mineral brandholzite Mg[Sb(OH)12].6H2O

Raman spectra of brandholzite Mg[Sb(OH)6].6H2O were studied, complemented with infrared spectra, and related to the structure of the mineral. An intense Raman sharp band at 618 cm-1 is attributed to the SbO symmetric stretching mode. The low intensity band at 730 cm-1 is ascribed to the SbO antisymmetric stretching vibration. Low intensity Raman bands were found at 503, 526 and 578 cm-1. Corresponding infrared bands were observed at 527, 600, 637, 693, 741 and 788 cm-1. Four Raman bands observed at 1043, 1092, 1160 and 1189 cm-1 and eight infrared bands at 963, 1027, 1055, 1075, 1108, 1128, 1156 and 1196 cm-1 are assigned to δ SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and hydroxyl units is observed. Raman bands are observed at 3240, 3383, 3466, 3483 and 3552 cm-1, infrared bands at 3248, 3434 and 3565 cm-1. The first two Raman bands and the first infrared band are assigned to water stretching vibrations. The two higher wavenumber Raman bands observed at 3466 and 3552 cm-1 and two infrared bands at 3434 and 3565 cm-1 are assigned to the stretching vibrations of the hydroxyl units. Observed Raman and infrared bands are connected with O-H…O hydrogen bonds and their lengths 2.72, 2.79, 2.86, 2.88 and 3.0 Å (Raman) and 2.73, 2.83 and 3.07 Å (infrared).

Raman spectroscopic study of the uranyl mineral pseudojohannite Cu6.5[(UO2)4O4(SO4)2]2(OH)5.25H2O

Raman spectra of pseudojohannite were studied and related to the structure of the mineral. Observed bands were assigned to the stretching and bending vibrations of (UO2)2+ and (SO4)2- units and of water molecules. The published formula of pseudojohannite is Cu6.5(UO2)8\[O8](OH)5\[(SO4)4].25H2O; however Raman spectroscopy does not detect any hydroxyl units. Raman bands at 805 and 810 cm-1 are assigned to (UO2)2+ stretching modes. The Raman bands at 1017 and 1100 cm-1 are assigned to the (SO4)2- symmetric and antisymmetric stretching vibrations. The three Raman bands at 423, 465 and 496 cm-1 are assigned to the (SO4)2- ν2 bending modes. The bands at 210 and 279 cm-1 are assigned to the doubly degenerate ν2 bending vibration of the (UO2)2+ units. U-O bond lengths in uranyl and O-H…O hydrogen bond lengths were calculated from the Raman and infrared spectra.

Raman spectroscopic study of the uranyl mineral metauranospinite Ca[(UO2)(AsO4)]2.8H2O

Raman spectra of metauranospinite Ca[(UO2)(AsO4)]2.8H2O complemented with infrared spectra were studied. Observed bands were assigned to the stretching and bending vibrations of (UO2)2+ and (AsO4)3- units and of water molecules. U-O bond lengths in uranyl and O-H…O hydrogen bond lengths were calculated from the Raman and infrared spectra.

The evaluation of a biphasic osteochondral implant coupled with an electrospun membrane in a large animal model

Conventional clinical therapies are unable to resolve osteochondral defects adequately, hence tissue engineering solutions are sought to address the challenge. A biphasic implant which was seeded with Mesenchymal Stem Cells (MSC) and coupled with an electrospun membrane was evaluated as an alternative. This dual phase construct comprised of a Polycaprolactone (PCL) cartilage scaffold and a Polycaprolactone - Tri Calcium Phosphate (PCL - TCP) osseous matrix. Autologous MSC was seeded into the entire implant via fibrin and the construct was inserted into critically sized osteochondral defects located at the medial condyle and patellar groove of pigs. The defect was resurfaced with a PCL - collagen electrospun mesh that served as a substitute for periosteal flap in preventing cell leakage. Controls either without implanted MSC or resurfacing membrane were included. After 6 months, cartilaginous repair was observed with a low occurrence of fibrocartilage at the medial condyle. Osteochondral repair was promoted and host cartilage degeneration was arrested as shown by the superior Glycosaminoglycan (GAG) maintenance. This positive morphological outcome was supported by a higher relative Young's modulus which indicated functional cartilage restoration. Bone in growth and remodeling occurred in all groups with a higher degree of mineralization in the experimental group. Tissue repair was compromised in the absence of the implanted cells or the resurfacing membrane. Moreover healing was inferior at the patellar groove as compared to the medial condyle and this was attributed to the native biomechanical features.

Three-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of L-tartaric acid with the associative-group monosubstituted pyridines 3-minopyridine, 3-carboxypyridine (nicotinic acid) and 2-carboxypyridine (picolinic acid).

The 1:1 proton-transfer compounds of L-tartaric acid with 3-aminopyridine [3-aminopyridinium hydrogen (2R,3R)-tartrate dihydrate, C5H7N2+·C4H5O6-·2H2O, (I)], pyridine-3-carboxylic acid (nicotinic acid) [anhydrous 3-carboxypyridinium hydrogen (2R,3R)-tartrate, C6H6NO2+·C4H5O6-, (II)] and pyridine-2-carboxylic acid [2-carboxypyridinium hydrogen (2R,3R)-tartrate monohydrate, C6H6NO2+·C4H5O6-·H2O, (III)] have been determined. In (I) and (II), there is a direct pyridinium-carboxyl N+-HO hydrogen-bonding interaction, four-centred in (II), giving conjoint cyclic R12(5) associations. In contrast, the N-HO association in (III) is with a water O-atom acceptor, which provides links to separate tartrate anions through Ohydroxy acceptors. All three compounds have the head-to-tail C(7) hydrogen-bonded chain substructures commonly associated with 1:1 proton-transfer hydrogen tartrate salts. These chains are extended into two-dimensional sheets which, in hydrates (I) and (III) additionally involve the solvent water molecules. Three-dimensional hydrogen-bonded structures are generated via crosslinking through the associative functional groups of the substituted pyridinium cations. In the sheet struture of (I), both water molecules act as donors and acceptors in interactions with separate carboxyl and hydroxy O-atom acceptors of the primary tartrate chains, closing conjoint cyclic R44(8), R34(11) and R33(12) associations. Also, in (II) and (III) there are strong cation carboxyl-carboxyl O-HO hydrogen bonds [OO = 2.5387 (17) Å in (II) and 2.441 (3) Å in (III)], which in (II) form part of a cyclic R22(6) inter-sheet association. This series of heteroaromatic Lewis base-hydrogen L-tartrate salts provides further examples of molecular assembly facilitated by the presence of the classical two-dimensional hydrogen-bonded hydrogen tartrate or hydrogen tartrate-water sheet substructures which are expanded into three-dimensional frameworks via peripheral cation bifunctional substituent-group crosslinking interactions.

4-(4-Nitrobenzyl)pyridinium 5-nitrosalicylate

In the title salt, C12H11N2O2+·C7H4NO5-, the cations and anions interact through asymmetric cyclic pyridinium-carboxylate N-HO,O' hydrogen-bonding associations [graph set R12(4)], giving discrete heterodimers having weak cation-anion - aromatic ring interactions [minimum ring centroid separation = 3.7116 (9) Å]

Combined marrow stromal cell-sheet techniques and high-strength biodegradable composite scaffolds for engineered functional bone grafts

In this study, cell sheets comprising multilayered porcine bone marrow stromal cells (BMSC) were assembled with fully interconnected scaffolds made from medical-grade polycaprolactone–calcium phosphate (mPCL–CaP), for the engineering of structural and functional bone grafts. The BMSC sheets were harvested from culture flasks and wrapped around pre-seeded composite scaffolds. The layered cell sheets integrated well with the scaffold/cell construct and remained viable, with mineralized nodules visible both inside and outside the scaffold for up to 8 weeks culture. Cells within the constructs underwent classical in vitro osteogenic differentiation with the associated elevation of alkaline phosphatase activity and bone-related protein expression. In vivo, two sets of cell-sheet-scaffold/cell constructs were transplanted under the skin of nude rats. The first set of constructs (554mm3) were assembled with BMSC sheets and cultured for 8 weeks before implantation. The second set of constructs (10104mm3) was implanted immediately after assembly with BMSC sheets, with no further in vitro culture. For both groups, neo cortical and well-vascularised cancellous bone were formed within the constructs with up to 40% bone volume. Histological and immunohistochemical examination revealed that neo bone tissue formed from the pool of seeded BMSC and the bone formation followed predominantly an endochondral pathway, with woven bone matrix subsequently maturing into fully mineralized compact bone; exhibiting the histological markers of native bone. These findings demonstrate that large bone tissues similar to native bone can be regenerated utilizing BMSC sheet techniques in conjunction with composite scaffolds whose structures are optimized from a mechanical, nutrient transport and vascularization perspective.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.