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A symmetric key cryptosystem based on logarithmic signatures for finite permutation groups was described by the first author in [6], and its algebraic properties were studied in [7]. In this paper we describe two possible approaches to the construction of new public key cryptosystems with message space a large finite group G, using logarithmic signatures and their generalizations. The first approach relies on the fact that permutations of the message space G induced by transversal logarithmic signatures almost always generate the full symmetric group S G on the message space. The second approach could potentially lead to new ElGamal-like systems based on trapdoor, oneway functions induced by logarithmic signature-like objects we call meshes, which are uniform covers for G.

In this report, we present the research results on using the conventional method and microwave technology to extract curcuminoid from turmeric roots originated in different regions of Northern Vietnam. This method is simple, yet economical, non-toxic and still able to achieve high extraction performance to get curcuminoid from turmeric roots. The detailed results on the Raman vibration spectra combined with X-ray powder diffraction and high-performance liquid chromatography/mass spectrometry allowed the evaluation of each batch of curcumin crystalline powder sample received, under the conditions of applied fabrication technology. Also, the absorption and fluorescence spectroscopies of the samples are presented in the paper. The information to be presented in this paper: absorption and fluorescence spectroscopies of the samples; new experimental study results on applied technology to mass-produce curcumin from turmeric rhizomes; comparative study results between fabricated samples and marketing curcumin products—to state the complexity of co-existing crystalline phase in curcumin powder samples. We noticed that, it is possible to use the vibration line at ~959 cm−1—characteristic of the ν C=O vibration, and the ~1625 cm−1 line—characteristic of the ν C=O and ν C=C vibration in curcumin molecules, for preliminary quality assessment of naturally originated curcumin crystalline powder samples. Data on these new optical spectra will contribute to the bringing of detailed information on natural curcumin in Vietnam, serving research purposes and applications of natural curcumin powder and nanocurcumin in Vietnam, as well as being initial materials for the pharmaceutical, cosmetics or functional food industries.

A covering array CA(N; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. Recursive constructions for covering arrays of strengths 3 and 4 are developed, generalizing many "Roux-type" constructions. A numerical comparison with current construction techniques is given through existence tables for covering arrays.

This paper aims to present new upper bounds on the size of separating hash families. These bounds improve previously known bounds for separating hash families.