Printable string encodings are widely used in several applications that cannot deal with binary data, the most known example being the mail system. In this paper, we investigate the potential of some of the proposed encodings to hide and carry extra information. We describe a framework for reversibly embedding data in printable string encodings, like Base45. The method leverages the characteristic of some encodings that are not surjective by using illegal configurations to embed one bit of information. With the assumption of uniformly distributed binary input data, an estimation of the expected payload can be computed easily. Results are reported for Base45 and Base85 encodings.

We present a complete analysis of the integer division of a single unsigned dividend word by a single unsigned divisor word based on double-word multiplication of the dividend by an inverse of the divisor. The well-known advantage of this method yields run-time efficiency, if the inverse of the divisor can be calculated at compile time, since multiplication is much faster than division in arithmetic units. Our analysis leads to the discovery of a limit to the straightforward application of this method in the form of a critical dividend, which fortunately associates with a minority of the possible divisors (20%) and defines only a small upper part of the available dividend space. We present two algorithms for ascertaining whether a critical dividend exists and, if so, its value along with a circumvention of this limit. For completeness, we include an algorithm for integer division of a unsigned double-word dividend by an unsigned single-word divisor in which the quotient is not limited to a single word and the remainder is an intrinsic part of the result.

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a b s t r a c tThe watermarking of digital images has an important role in the protection of digital content with respect to many aspects. In this paper we present a reversible watermarking algorithm for hiding information into medical images having luminance histograms with particular characteristics. Some radiographic images have the property that not all the gray levels are present; this leads to sequences of 0 values (0-runs) in the corresponding histograms. It is possible to use these 0-runs to encode information by modifying pixels having gray levels contiguous to these runs; by encoding also the run information it is possible to restore the original image after extracting the stored data. In this work we present a novel reversible watermarking technique capable of exploiting all the 0-runs in the image histogram to achieve high capacity. We show that an optimization problem arises for those cases in which two or more non-zero frequency gray levels are contiguous to 0-runs. Part of the watermark information may be devoted to a digital signature of the original image, whose authenticity may also be verified by a user.