Selective screenability in topological groups

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which the properties are preserved by products. Among metrizable groups we characterize the ones of countable covering dimension by a natural game.Comment: 12 pages. Improved Theorem 5. Added remarks. Fixed typographical error

Selection principles and countable dimension

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.Comment: 10 page

Weakly infinite dimensional subsets of R^N

The Continuum Hypothesis implies an Erd\"os-Sierpi\'nski like duality between the ideal of first category subsets of \reals^{\naturals}, and the ideal of countable dimensional subsets of \reals^{\naturals}. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of \reals^{\naturals} with any compactly countable dimensional subset of \reals^{\naturals} has first category.Comment: 16 pages, corrected Statements of Theorem 6 and Lemma 8, Inserted Problem 1, Inserted remarks by R. Pol, solving Problem 3, in "Added in Proof" sectio

Elliptic Pairs of Primes in Cryptography and Their Effects on RSA Security

Cryptography is a constantly evolving field – elliptic curve groups have been a major part of this field since 1987 when Koblitz and Miller separately proposed their use in cryptosystems such as RSA. Elliptic Curve: A curve defined by the equation: where A and B are less than a prime p, and where the discriminant is not equal to zero. We are concerned with the curves where A = 0. Elliptic Curve Group (ECG): A group whose elements are defined by the elliptic curve and the operation in question. Elliptic curves naturally qualify as groups due simply to their nature. Elliptic Pair of Primes: Two primes (p,q) such that an ECG defined by the following equation has an order q, and the ECG defined by a different equation mod q has the order p. These pairs are the main topic of our study, and learning more about them and their effects on RSA security is our primary goal. Discrete Log Problem (DLP): Solving for x in the equation: NOTE: Operations such as addition and multiplication are defined differently when used in terms of an ECG operation. An example can be found below

Weakly Infinite Dimensional Subsets of R\u3csup\u3eN\u3c/sup\u3e

The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝℕ, and the ideal of countable dimensional subsets of ℝℕ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝℕ with any compactly countable dimensional subset of ℝℕ has first category