# Papers in pure and applied mathematics

Papers by others. You may also be interested in papers by other authors that cite the following ones.

Papers. Most of the titles are linked to the webpage of their published version. If this does not work but should have, you can try the alternative link "A", or the preprint link "P". Sometimes the preprints (postprints) are more updated than the published versions.

## Main papers

### Pure mathematics

1. Additivity numbers of covering properties, in: Selection Principles and Covering Properties in Topology (L. Kocinac, editor), Quaderni di Matematica 18, Seconda Universita di Napoli, Caserta 2006, 245-282. (A, P)
2. Selection Principles and special sets of reals, in: Open Problems in Topology II (E. Pearl, ed.), Elsevier B.V., 2007, 91-108. (P)
3. Scales, fields, and a problem of Hurewicz (with L. Zdomskyy), Journal of the European Mathematical Society 10 (2008), 837-866. (A, P)
4. The combinatorics of the Baer-Specker group (with M. Machura), Israel Journal of Mathematics 168 (2008), 125-151. (A, P)
5. Superfilters, Ramsey theory, and van der Waerden's Theorem (with N. Samet), Topology and its Applications 156 (2009), 2659-2669. (A, P)
6. Squares of Menger-bounded groups (with M. Machura and S. Shelah), Transactions of the American Mathematical Society 362 (2010), 1751-1764. (A, P)
7. Point-cofinite covers in Laver's model (with A. Miller), Proceedings of the American Mathematical Society 138 (2010), 3313-3321. (A, P)
8. Menger's and Hurewicz's Problems: Solutions from The Book'' and refinements, Contemporary Mathematics 533 (2011), 211-226. (A, P)
9. Linear sigma-additivity and some applications (with T. Orenshtein), Transactions of the American Mathematical Society 363 (2011), 3621-3637. (A, P)
10. Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations (with L. Zdomskyy), Journal of the European Mathematical Society 12 (2012), 353-372. (A, P)
11. Pointwise convergence of partial functions: The Gerlits-Nagy Problem (with T. Orenshtein), Advances in Mathematics 232 (2013), 311-326. (A, P)
12. Selective covering properties of product spaces (with A. Miller and L. Zdomskyy), Annals of Pure and Applied Logic 165 (2014), 1034-1057. (A, P)
13. The character of topological groups, via bounded systems, Pontryagin–van Kampen duality and pcf theory (with C. Chis, M.V. Ferrer, and S. Hernández), Journal of Algebra 420 (2014), 86-119. (A, P, Video)
14. Selective covering properties of product spaces, II: $\gamma$ spaces (with A. Miller, L. Zdomskyy), Transactions of the American Mathematical Society 368 (2016), 2865-2889. (A, P)
15. Products of Menger spaces: A combinatorial approach (with P. Szewczak), Annals of Pure and Applied Logic 168 (2017), 1-18. (A, P)
16. Algebra, selections, and additive Ramsey theory, Fundamenta Mathematicae 240 (2018), 81-104. (A, P)
17. The Haar Measure Problem (with P. Szewczak, A. Prze\'zdziecki), Proceedings of the American Mathematical Society 147 (2019), 1051-1057. (A, P)

### Computational mathematics

1. Guaranteeing the diversity of number generators (with A. Shamir), Information and Computation 171 (2001), 350-363. (A, P)
2. Efficient linear feedback shift registers with maximal period (with U. Vishne), Finite Fields and their Applications 8 (2002), 256-267. (A, P)
3. Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation, Journal of Algorithms 47 (2003), 104-121. (A, P)
4. Probabilistic solutions of equations in the braid group (with D. Garber, S. Kaplan, M. Teicher, and U. Vishne), Advances in Applied Mathematics 35 (2005), 323-334. (A, P)
5. Theoretical cryptanalysis of the Klimov-Shamir number generator TF-1, Journal of Cryptology 20 (2007), 389-392. (A, P) [Klimov-Shamir's handout]
6. Length-based cryptanalysis: The case of Thompson's Group (with D. Ruinskiy and A. Shamir), Journal of Mathematical Cryptology 1 (2007), 359-372. (A, P)
7. Solving random equations in Garside groups using length functions (with M. Hock), in: Combinatorial and Geometric Group Theory (O. Bogopolski, I. Bumagin, O. Kharlampovich, E. Ventura, eds.), Trends in Mathematics, Birkh\"auser 2010, 149-169. (P)
8. Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser (with A. Kalka and M. Teicher), Advances in Applied Mathematics 49 (2012), 57-76. (A, P)
9. Cryptanalysis of SP networks with partial non-linear layers (with A. Bar-On, I. Dinur, O. Dunkelman, N. Keller, V. Lallemand), EUROCRYPT 2015, Lecture Notes in Computer Science 9056 (2015), 315-342. (A, P)
10. Polynomial-time solutions of computational problems in noncommutative algebraic cryptography, Journal of Cryptology 28 (2015), 601-622. (A, P)
11. A practical cryptanalysis of the Algebraic Eraser (with A. Ben Zvi and S. Blackburn), CRYPTO 2016, Lecture Notes in Computer Science 9814 (2016), 179-189. (A, P) Video presentation media coverage
12. Cryptanalysis via algebraic spans (with A. Ben-Zvi, A. Kalka), CRYPTO 2018, Lecture Notes in Computer Science 10991 (2018), 255-274. (A, P) Video presentations: Concise (Crypto '18), Detailed (PSIT '19)
13. Nonabelian Cryptology and Lightweight Hash: TS-Hash, lecture video.

### Pure mathematics

1. A topological interpretation of t, Real Analysis Exchange 25 (1999/2000), 391-404. (A, P)
2. A diagonalization property between Hurewicz and Menger, Real Analysis Exchange 27 (2001/2002), 757-763. (A, P)
3. The combinatorics of Borel covers (with M. Scheepers), Topology and its Applications 121 (2002), 357-382. (A, P)
4. Additivity properties of topological diagonalizations (with T. Bartoszynski and S. Shelah), Journal of Symbolic Logic 68 (2003), 1254-1260. (A, P)
5. Critical cardinalities and additivity properties of combinatorial notions of smallness (with S. Shelah), Journal of Applied Analysis 9 (2003), 149-162. (A, P)
6. Selection principles and the Minimal Tower problem, Note di Matematica 22 (2003), 53-81. (A, P)
7. Topological diagonalizations and Hausdorff dimension (with T. Weiss), Note di Matematica 22 (2003), 83-92. (A, P)
8. Selection principles in mathematics: A milestone of open problems, Note di Matematica 22 (2003), 179-208. (A, P)
9. The minimal cardinality where the Reznichenko property fails, Israel Journal of Mathematics 140 (2004), 367-374. (P)
10. The Hurewicz covering property and slaloms in the Baire space, Fundamenta Mathematicae 181 (2004), 273-280. (A, P)
11. The combinatorics of splittability, Annals of Pure and Applied Logic 129 (2004), 107-130. (A, P)
12. Products of special sets of real numbers (with T. Weiss), Real Analysis Exchange 30 (2004/5), 819-836. (A, P)
13. Strong gamma-sets and other singular spaces, Topology and its Applications 153 (2005), 620-639. (A, P)
14. Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures (with T. Bartoszynski), Proceedings of the American Mathematical Society 134 (2006), 605-615. (A, P)
15. o-bounded groups and other topological groups with strong combinatorial properties, Proceedings of the American Mathematical Society 134 (2006), 881-891. (A, P)
16. Covering the Baire space by families which are not finitely dominating (with H. Mildenberger and S. Shelah), Annals of Pure and Applied Logic 140 (2006), 60-71. (A, P)
17. Menger's covering property and groupwise density (with L. Zdomskyy), Journal of Symbolic Logic 71 (2006), 1053-1056. (A, P)
18. Some new directions in infinite-combinatorial topology, Set Theory J. Bagaria and S. Todorcevic, Trends in Mathematics, Birkhauser, 2006, 225-255. (A, P)
19. The combinatorics of tau-covers (with H. Mildenberger and S. Shelah), Topology and its Applications 154 (2007), 263-276. (A, P)
20. On the Kocinac alpha_i properties, Topology and its Applications 155 (2007), 141-145. (A, P)
21. A new selection principle, Topology Proceedings 31 (2007), 319-329. (P)
22. On the Pytkeev property in spaces of continuous functions (with P. Simon), Proceedings of the American Mathematical Society 136 (2008), 1125-1135. (A, P)
23. Several comments about the combinatorics of tau-covers, Note di Matematica 27 (2007), 47-53. (A, P)
24. Hurewicz sets of reals without perfect subsets (with D. Repovs and L. Zdomskyy), Proceedings of the American Mathematical Society 136 (2008), 2515-2520. (A, P)
25. Continuous selections and sigma-spaces (with D. Repovs and L. Zdomskyy), Topology and its Applications 156 (2008), 104-109. (A, P)
26. Null sets and games in Banach spaces (with J. Duda), Topology and its Applications 156 (2008), 56-60. (A, P)
27. Combinatorial images of sets of reals and semifilter trichotomy (with L. Zdomskyy), Journal of Symbolic Logic 73 (2008), 1278-1288. (A, P)
28. A note on the method of Nyikos of detecting spaces X with non-stratifiable Ck(X) (with L. Zdomskyy), unpublished note.
29. Partition relations for Hurewicz-type selection hypotheses (with N. Samet and M. Scheepers), Topology and its Applications 156 (2009), 616-623. (A, P)
30. On the Pytkeev property in spaces of continuous functions (II) (with L. Zdomskyy), Houston Journal of Mathematics, 35 (2009), 563-571. (A, P)
31. On a problem of Juhasz and van Mill (with Saharon Shelah), Topology Proceedings 36 (2010), 385-392. (A, P)
32. Sequential properties of function spaces with the compact-open topology (with G. Gruenhage and L. Zdomskyy), Topology and its Applications 158 (2011), 387-391. (A, P)
33. On productively Lindelöf spaces (with F. Tall), Topology and its Applications 158 (2011), 1239-1248. (A, P)
34. Monochromatic generating sets in groups and other algebraic structures (with I. Ravia and N. Lifshitz), unpublished note.
35. Hindman's coloring theorem in arbitrary semigroups (with G. Golan), Journal of Algebra 395 (2013), 111-120. (A, P)
36. On the cardinality of the θ-closed hull of sets (with F. Cammaroto, A. Catalioto, B. Pansera), Topology and its Applications 160 (2013), 2371-2378. (A, P)
37. Diagonalizations of dense families (with M. Bonanzinga, F. Cammaroto, B. Pansera), Topology and its Applications 165 (2014) 12-25. (A, P)
38. Additivity of the Gerlits-Nagy property and concentrated sets (with L. Zdomskyy), Proceedings of the American Mathematical Society 142 (2014), 2881-2890. (A, P)
39. Combinatorial aspects of selective star covering properties in $\Psi$-spaces, Topology and its Applications 192 (2015), 198-207. (A, P)
40. Arhangel'skii sheaf amalgamations in topological groups (with L. Zdomskyy), Fundamenta Mathematicae 232 (2016), 281-293. (A, P)
41. The linear refinement number and selection theory (with M. Machura, S. Shelah), Fundamenta Mathematicae 234 (2016), 15-40. (A, P)

### Computational mathematics

1. The conjugacy problem and related problems in lattice-ordered groups (with W. C. Holland), International Journal of Algebra and Computation 15 (2005), 395-404. (A, P)
2. Fast generators for the Diffie-Hellman key agreement protocol and malicious standards, Information Processing Letters 99 (2006), 145-148. (A, P)
3. Length-based conjugacy search in the Braid group (with D. Garber, S. Kaplan, M. Teicher, and U. Vishne), Contemporary Mathematics 418 (2006), 75-87. (P)
4. Decompositions of graphs of functions and fast iterations of lookup tables, Discrete Applied Mathematics 155 (2007), 386-393. (A, P)
5. Cryptanalysis of group-based key agreement protocols using subgroup distance functions (with D. Ruinskiy and A. Shamir), Proceedings of the 10th International Conference on Practice and Theory in Public-Key Cryptography PKC07, Lecture Notes In Computer Science 4450 (2007), 61-75. (A, P)
6. Random strategies with memory for the Robin Hood game, in: Foundations of the Formal Sciences V: Infinite Games (S. Bold, B. Loewe, T. Raesch, J. van Benthem, eds.), Studies in Logic 11, College Publications, London 2007, 271-278. (P)
7. The Discrete Logarithm Problem in Bergman's non-representable ring (with M. Banin), Journal of Mathematical Cryptology 6 (2012), 171-182. (A, P)
8. Cryptanalysis of the MORE symmetric key fully homomorphic encryption scheme (with N. Lifshitz), Journal of Mathematical Cryptology 9 (2015), 75-78. (P)
9. SL$_2$ homomorphic hash functions: Worst case to average case reduction and short collision search (with C. Mullan), Designs Codes and Cryptography 81 (2016), 83-107. (A, P)
10. A reduction of Semigroup DLP to classic DLP (with M. Banin), Designs Codes and Cryptography 81 (2016), 75-82. (A, P)

### Recreational mathematics

1. On the Rabbinical approximation of Pi (with D. Garber), Historia Mathematica 25 (1998), 75-84. (A, P)
2. A mechanical derivation of the area of a sphere (with D. Garber), American Mathematical Monthly 108 (2001), 10-15. (A)
3. Bernoulli numbers and the probability of a birthday surprise, Discrete Applied Mathematics 127 (2003), 657-663. (A, P)
4. The SPM Bulletin: history and future, Note di Matematica 27 (2007), 111-117.
5. The mathematics of Ljubiša D.R. Kočinac, Topology and its Applications 160 (2013), 2234-2242. (A)