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The number of biologically interesting natural products possessing peroxide structure motifs is substantial and still growing. 1 Many peroxy natural products display antitumor, anticancer and anti parasite activities, which are attributed to the propensity of the peroxide to initiate radical reactions in an ironrich environment. 2 Furthermore, peroxide natural products such as artemisinin are clinically important anti malaria drugs. Despite the potential of chiral peroxides as biologically interesting or even clinically important compounds, synthetic methods for the preparation of chiral peroxides are highly limited. 3,4,5,6 In particular efficient catalytic enantioselective peroxidations with simple achiral precursors are urgently needed, yet none are available. In fact only a single example of a chiral auxiliarydirected peroxidation in high diastereoselectivity could be found in the literature. 7 Herein, we wish to report the development of a highly enantioselective peroxidation of α,β-unsaturated ketones with an easily accessible chiral organic catalyst.The base-promoted reaction of α,β-unsaturated ketones 1 with hydroperoxides 2 represents a classic epoxidation reaction. Asymmetric variants of this epoxidation with both chiral metal and organic catalysts have also been reported. 8-13 It is well-established that the epoxide 3 is formed via a two-step mechanism (Scheme 1); nucleophilic addition of the hydroperoxide 2 to 1 followed by an intramolecular nucleophilic substitution of the resulting enolate (5) that breaks the weak peroxide bond. In principle this epoxidation pathway (1 to 3) could be converted into a peroxidation pathway (1 to 6) if 5 could be trapped by protonation, although the overwhelming preference of 5 for the intramolecular nucleophilic substitution is evident from the lack of reported peroxidation of α,β-unsatrated carbonyl compounds.Although chiral amine-catalyzed nucleophilic epoxidations of α,β-unsaturated carbonyl compounds have already been reported, 13 we suspected that a cinchona alkaloid derivative such as 8 14 could not only render the nucleophilic addition of the hydroperoxide 2 to the iminium intermediate 9 enantioselective, but also strongly influence the partitioning of the peroxyenamine intermediate 10 between the epoxidation (10 to 11) and the peroxidation (10 to 12) pathways (Scheme 2). Presumably, due to steric crash and multipoint binding interactions between the peroxyenamine intermediate and the covalently linked cinchona alkaloid, the bond-rotational freedom of the peroxyenamine should be hampered, compared to that of the enolate 5 in Scheme 1. We expected that this conformational rigidity imposed by 8 on the peroxyenamine would diminish its ability to adopt the active conformation by which the nucleophilic enamine moiety is optimally aligned relative to the O-O bond for the nucleophilic attack. This in turn would decelerate the epoxidation. In contrast, with the NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript protonated quinuclidine as a prot...

In EUROCRYPT 2018, Cid et al. [16] introduced a new concept on the cryptographic property of S-boxes: Boomerang Connectivity Table (BCT for short) for evaluating the subtleties of boomerang-style attacks. Very recently, BCT and the boomerang uniformity, the maximum value in BCT, were further studied by Boura and Canteaut [4]. Aiming at providing new insights, we show some new results about BCT and the boomerang uniformity of permutations in terms of theory and experiment in this paper. Firstly, we present an equivalent technique to compute BCT and the boomerang uniformity, which seems to be much simpler than the original definition from [16].

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