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In this paper, we propose a novel and efficient protocol for proving the correctness of a shuffle, without leaking how the shuffle was performed. Using this protocol, we can prove the correctness of a shuffle of n data with roughly 18n exponentiations, where as the protocol of Sako-Kilian[SK95] required 642n and that of Abe[Ab99] required 22n log n. The(More)
Soluble ionic aluminum (Al) inhibits root growth and reduces crop production on acid soils. Al-resistant cultivars of barley (Hordeum vulgare L.) detoxify Al by secreting citrate from the roots, but the responsible gene has not been identified yet. Here, we identified a gene (HvAACT1) responsible for the Al-activated citrate secretion by fine mapping(More)
In this paper, we propose a scheme to simultaneously prove the correctness of both shuffling and decryption. Our scheme is the most efficient of all previous schemes, as a total, in proving the correctness of both shuffling and decryption of ElGamal ciphertexts. We also propose a formal definition for the core requirement of unlinkability in verifiable(More)
SUMMARY In this paper, we propose an efficient protocol for proving the correctness of shuffling and an efficient protocol for simultaneously proving the correctness of both shuffling and decryption. The former protocol is the most efficient in computational and communication complexity among 3-move honest verifier perfect zero-knowledge protocols for(More)
Aluminum (Al) is highly toxic to plant growth. The toxicity is characterized by rapid inhibition of root elongation. However, some plant species and cultivars have evolved some mechanisms for detoxifying Al both internally and externally. In this review, the recent progress made in the research of external detoxification of Al is described. Accumulating(More)
Aluminium (Al) toxicity is an important limitation to barley (Hordeum vulgare L.) on acid soil. Al-resistant cultivars of barley detoxify Al externally by secreting citrate from the roots. To link the genetics and physiology of Al resistance in barley, genes controlling Al resistance and Al-activated secretion of citrate were mapped. An analysis of(More)
High salinity is an environmental factor that inhibits plant growth and development, leading to large losses in crop yields. We report here that mutations in SIZ1 or PHO2, which cause more accumulation of phosphate compared with the wild type, enhance tolerance to salt stress. The siz1 and pho2 mutations reduce the uptake and accumulation of Na(+). These(More)
We propose an authentication scheme in which users can be authenticated anonymously so long as times that they are authenticated is within an allowable number. The proposed scheme has two features that allow 1) no one, not even an authority, identify users who have been authenticated within the allowable number, and that allow 2) anyone to trace, without(More)