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It is a common practice in transform-domain fragile watermarking schemes for authentication purposes to watermark some selected transform coefficients so as to minimise embedding distortion. The author points out that leaving most of the coefficients unmarked results in a wide-open security gap for attacks to be mounted on them. A fragile watermarking scheme is proposed to implicitly watermark all the coefficients by registering the zero-valued coefficients with a key-generated binary sequence to create the watermark and involving the unwatermarkable coefficients during the embedding process of the embeddable ones. Non-deterministic dependence is established by involving some of the unwatermarkable coefficients selected according to the watermark from a nine-neighbourhood system in order to thwart different attacks, such as cover-up, vector quantisation and transplantation. No hashing is needed in establishing the non-deterministic dependence.