Optimal threshold padlock systems

In 1968, Liu described the problem of securing documents in a shared secret project. In an example, at least six out of eleven participating scientists need to be present to open the lock securing the secret documents. Shamir proposed a mathematical solution to this physical problem in 1979, by designing an efficient k-out-of-n secret sharing scheme based on Lagrange’s interpolation. Liu and Shamir also claimed that the minimal solution using physical locks is clearly impractical and exponential in the number of participants. In this paper we relax some implicit assumptions in their claim and propose an optimal physical solution to the problem of Liu that uses physical padlocks, but the number of padlocks is not greater than the number of participants. Then, we show that no device can do better for k-out-of-n threshold padlock systems as soon as k ⩾ 2 n , which holds true in particular for Liu’s example. More generally, we derive bounds required to implement any threshold system and prove a lower bound of O ( log ( n ) ) padlocks for any threshold larger than 2. For instance we propose an optimal scheme reaching that bound for 2-out-of-n threshold systems and requiring less than 2 log 2 ( n ) padlocks. We also discuss more complex access structures, a wrapping technique, and other sublinear realizations like an algorithm to generate 3-out-of-n systems with 2.5 n padlocks. Finally we give an algorithm building k-out-of-n threshold padlock systems with only O ( log ( n ) k − 1 ) padlocks. Apart from the physical world, our results also show that it is possible to implement secret sharing over small fields.

Elaboration by Wrapping Process and Multiscale Characterisation of Thermoplastic Bio-Composite Based on Hemp/PA11 Constituents

The present work investigates the potential of developing bio-composites based on thermoplastic polymers reinforced with natural fibres by using hybrid yarns. The hybrid yarns were produced by the wrapping technique, in which a multifilament of polyamide 11 (PA11) was wrapped around an untreated low-twisted hemp roving to produce a yarn with sufficient tenacity and stiffness for the next step of weaving. The tensile behaviour of the wrapped yarns was identified both in the dry- and thermo-state. Then, two different fabrics were woven and tested to study the influence of yarn densities and weave diagrams on the tensile and flexural properties. At this fabric scale, properties of fabrics made from hybrid yarns were compared with those of fabrics from a previous study made from 100% hemp roving. Composites made from these fabrics, with stacking of two cross-plies, were produced by thermocompression and characterised regarding mechanical strength.

Strengthening Full-Scale Damaged Precast/Prestressed Concrete Double-Tee Girders Using CFRP Sheets

Canada is facing a major crisis with the deterioration of its infrastructure (bridges, harbours, buildings, water structures, sewers, parking garages, etc.). Many of these structures were build using precast prestressed concrete members. These members may be under-strength because of deficiencies in design, increase in applied loads, loss of prestress, or damage due to the effects of corrosion, collision or military operations. Epoxy-bonding composite materials to the tension side of prestressed concrete girders is an effective technique for shear/flexural rehabilitation and strengthening of such members. To ensure successful and cost-effective applications of such materials, engineers need to improve their knowledge with respect to the actual behavior of full-size girders so that they can gain confidence on using these materials on structural strengthening and rehabilitation. This can be achieved by providing more data on testing-to-collapse and on field conditions full-scale prestressed girders strengthened using FRP materials. This study details the use of Carbon Fiber Reinforced Polymer (CFRP) Sheets to repair and strengthen precast presetressed concrete Double-Tee (DT) girders in flexure and shear. Three actual-size partially-damaged DT precast pretensioned girders were obtained from the manufacturer. All three of the girders were repaired and strengthened, and then tested to failure to determine flexural and shear capacities. The stems of two of these girders were strengthened in flexures using U-shape un-directional carbon fiber reinforced polymer sheets (CFRP), extending from the mid-span to the quarter points of the girders. Two girders were strengthened in shear the dapped ends using 0° wrapping technique around the stem, while the dapped ends of the third girder were strengthened using 0°/90° wrapping technique. Each girder was loaded incrementally up to failure using Jersey Barriers. This project summarizes the loading history and reports test results that can be further used to demonstrate the practicality of girder strengthening with CFRP sheets in field conditions.

Strengthening Full-Scale Damaged Precast/Prestressed Concrete Double-Tee Girders Using CFRP Sheets

Canada is facing a major crisis with the deterioration of its infrastructure (bridges, harbours, buildings, water structures, sewers, parking garages, etc.). Many of these structures were build using precast prestressed concrete members. These members may be under-strength because of deficiencies in design, increase in applied loads, loss of prestress, or damage due to the effects of corrosion, collision or military operations. Epoxy-bonding composite materials to the tension side of prestressed concrete girders is an effective technique for shear/flexural rehabilitation and strengthening of such members. To ensure successful and cost-effective applications of such materials, engineers need to improve their knowledge with respect to the actual behavior of full-size girders so that they can gain confidence on using these materials on structural strengthening and rehabilitation. This can be achieved by providing more data on testing-to-collapse and on field conditions full-scale prestressed girders strengthened using FRP materials. This study details the use of Carbon Fiber Reinforced Polymer (CFRP) Sheets to repair and strengthen precast presetressed concrete Double-Tee (DT) girders in flexure and shear. Three actual-size partially-damaged DT precast pretensioned girders were obtained from the manufacturer. All three of the girders were repaired and strengthened, and then tested to failure to determine flexural and shear capacities. The stems of two of these girders were strengthened in flexures using U-shape un-directional carbon fiber reinforced polymer sheets (CFRP), extending from the mid-span to the quarter points of the girders. Two girders were strengthened in shear the dapped ends using 0° wrapping technique around the stem, while the dapped ends of the third girder were strengthened using 0°/90° wrapping technique. Each girder was loaded incrementally up to failure using Jersey Barriers. This project summarizes the loading history and reports test results that can be further used to demonstrate the practicality of girder strengthening with CFRP sheets in field conditions.

Toughness of Timber Beams Strengthened with Jute Fibers

This research involves investigating the toughness behavior of timber beams strengthened by jute fibers with various forms of strengthening. Ten timber specimens with dimensions (70×100×1000) mm are divided into four groups and loaded under a third point loading. The experimental program was carried out to investigate shear and flexural strengthening effects on toughness, toughness indices, ultimate loads, and the mid-span deflection of the tested beams. One beam as a control beam (un-strengthened beam), four specimens are wrapped in U technique in single and double layers along the whole length of the beam in full and strips wrapping technique, three specimens are wrapped in full technique along the whole length of the beam in full and strips wrapping technique, three timber specimens wrapped in flexural strengthening technique with two, four, and six layers of jute fibers. The results show that jute fibers strengthening increases the toughness ratios of timber beams by about (175%-320%), (190%-401%), and (106%-240%) for U, full, and flexural strengthening techniques, respectively, at the ultimate loads compared with the control beam. Furthermore, it is found that the highest toughness ratio is when the beam is wrapped in full strengthening technique.