Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

A Practical Cryptanalysis of the Algebraic Eraser

Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.Comment: 15 pages. Updated references, with brief comments added. Minor typos corrected. Final version, accepted for CRYPTO 201

The metabolomic-gut-clinical axis of Mankai plant-derived dietary polyphenols

24openInternationalBothBackground: Polyphenols are secondary metabolites produced by plants to defend themselves from environmental stressors. We explored the effect of Wolffia globosa ‘Mankai’, a novel cultivated strain of a polyphenol-rich aquatic plant, on the metabolomic-gut clinical axis in vitro, in-vivo and in a clinical trial. Methods: We used mass-spectrometry-based metabolomics methods from three laboratories to detect Mankai phenolic metabolites and examined predicted functional pathways in a Mankai artificial-gut bioreactor. Plasma and urine polyphenols were assessed among the 294 DIRECT-PLUS 18-month trial participants, comparing the effect of a polyphenol-rich green-Mediterranean diet (+1240 mg/polyphenols/day, provided by Mankai, green tea and walnuts) to a walnuts-enriched (+440 mg/polyphenols/day) Mediterranean diet and a healthy controlled diet. Results: Approximately 200 different phenolic compounds were specifically detected in the Mankai plant. The Mankai-supplemented bioreactor artificial gut displayed a significantly higher relative-abundance of 16S-rRNA bacterial gene sequences encoding for enzymes involved in phenolic compound degradation. In humans, several Mankai-related plasma and urine polyphenols were differentially elevated in the green Mediterranean group compared with the other groups (p < 0.05) after six and 18 months of intervention (e.g., urine hydroxy-phenyl-acetic-acid and urolithin-A; plasma Naringenin and 2,5-diOH-benzoic-acid). Specific polyphenols, such as urolithin-A and 4-ethylphenol, were directly involved with clinical weight-related changes. Conclusions: The Mankai new plant is rich in various unique potent polyphenols, potentially affecting the metabolomic-gut-clinical axisopenYaskolka Meir, A.; Tuohy, K.; von Bergen, M.; Krajmalnik-Brown, R.; Heinig, U.; Zelicha, H.; Tsaban, G.; Rinott. E.; Kaplan, A.; Aharoni, A.; Zeibich, L.; Chang, D.; Dirks, B.; Diotallevi, C.; Arapitsas, P.; Vrhovsek, U.; Ceglarek, U.; Haange, S.; Rolle-Kampczyk, U.; Engelmann, B.; Lapidot, M.; Colt, M.; Sun, Q.; Shai, I.Yaskolka Meir, A.; Tuohy, K.; von Bergen, M.; Krajmalnik-Brown, R.; Heinig, U.; Zelicha, H.; Tsaban, G.; Rinot, T.E.; Kaplan, A.; Aharoni, A.; Zeibich, L.; Chang, D.; Dirks, B.; Diotallevi, C.; Arapitsas, P.; Vrhovsek, U.; Ceglarek, U.; Haange, S.; Rolle-Kampczyk, U.; Engelmann, B.; Lapidot, M.; Colt, M.; Sun, Q.; Shai, I

Practical Attacks Against the Walnut Digital Signature Scheme

Recently, NIST started the process of standardizing quantum- resistant public-key cryptographic algorithms. WalnutDSA, the subject of this paper, is one of the 20 proposed signature schemes that are being considered for standardization. Walnut relies on a one-way function called E-Multiplication, which has a rich algebraic structure. This paper shows that this structure can be exploited to launch several practical attacks against the Walnut cryptosystem. The attacks work very well in practice; it is possible to forge signatures and compute equivalent secret keys for the 128-bit and 256-bit security parameters submitted to NIST in less than a second and in less than a minute respectively

The effect of high-polyphenol Mediterranean diet on visceral adiposity: the DIRECT PLUS randomized controlled trial

Background Mediterranean (MED) diet is a rich source of polyphenols, which benefit adiposity by several mechanisms. We explored the effect of the green-MED diet, twice fortified in dietary polyphenols and lower in red/processed meat, on visceral adipose tissue (VAT). Methods In the 18-month Dietary Intervention Randomized Controlled Trial PoLyphenols UnproceSsed (DIRECT-PLUS) weight-loss trial, 294 participants were randomized to (A) healthy dietary guidelines (HDG), (B) MED, or (C) green-MED diets, all combined with physical activity. Both isocaloric MED groups consumed 28 g/day of walnuts (+ 440 mg/day polyphenols). The green-MED group further consumed green tea (3–4 cups/day) and Wolffia globosa (duckweed strain) plant green shake (100 g frozen cubes/day) (+ 800mg/day polyphenols) and reduced red meat intake. We used magnetic resonance imaging (MRI) to quantify the abdominal adipose tissues. Results Participants (age = 51 years; 88% men; body mass index = 31.2 kg/m2; 29% VAT) had an 89.8% retention rate and 79.3% completed eligible MRIs. While both MED diets reached similar moderate weight (MED: − 2.7%, green-MED: − 3.9%) and waist circumference (MED: − 4.7%, green-MED: − 5.7%) loss, the green-MED dieters doubled the VAT loss (HDG: − 4.2%, MED: − 6.0%, green-MED: − 14.1%; p < 0.05, independent of age, sex, waist circumference, or weight loss). Higher dietary consumption of green tea, walnuts, and Wolffia globosa; lower red meat intake; higher total plasma polyphenols (mainly hippuric acid), and elevated urine urolithin A polyphenol were significantly related to greater VAT loss (p < 0.05, multivariate models). Conclusions A green-MED diet, enriched with plant-based polyphenols and lower in red/processed meat, may be a potent intervention to promote visceral adiposity regression

Cryptanalysis via algebraic spans

We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic group theory based key exchange protocol that could not be cryptanalyzed by earlier methods