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A new form of nanosized SrTiO 3 semiconducting oxide material with an average crystal grain size of 27 nm has been synthesized using the physical high-energy ball milling technique. The unique presence of the singly charged "O -" ions in the lattice oxygen sites of the nano-range crystal grain material has been observed in the XPS study. This unprecedented and interesting discovery has expounded on the new oxygen sensing mechanism for the near 1 / 2 slope gradient (the best value ever reported) in the logarithmic relationship of the electrical conductance with the oxygen partial pressure. The derived SrTiO 3 oxygen gas sensors were found to operate at 40 °C (the lowest temperature ever reported for an SrTiO 3 -based sensor) that is near to the human body temperature.

In this correspondence, it is given a correction to

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To design an efficient post-quantum linearly homomorphic signature scheme, using the pre-image sampling function, a lattice-based linearly homomorphic signature scheme over a binary field is proposed in this paper. Linear homomorphism is achieved through the homomorphism of the lattice-based hash function used in the proposed signature scheme. It is shown that the proposed scheme satisfies the privacy property. Based on the hardness of the short integer solution problem, the proposed scheme is unforgeable against the type 1 and type 2 adversaries in the random oracle model. Moreover, compared with a presented linearly homomorphic signature scheme in 2011, the proposed scheme has some advantages with respect to the public key size, signature length and computational cost.

An identity‐based signature scheme from lattices is constructed. The scheme is obtained from a modification of Agrawal, Boneh, and Boyen's lattice identity‐based encryption scheme. In this construction, we use two distinct trapdoors for finding short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Furthermore, the generating short bases are used to sample short vectors as signatures. Our scheme is computationally efficient. The scheme's strong unforgeability is proven in the standard model and rests on the hardness of the small integer solution problem. Finally, we extend the basic construction to obtain a hierarchical identity‐based signature scheme. Copyright © 2012 John Wiley & Sons, Ltd.

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