We construct a signature scheme that is proved secure, without random oracles, under the strong RSA assumption. Unlike other efficient strong-RSA based schemes, the new scheme does not generate large prime numbers during signing. The public key size and signature size are competitive with other strong RSA schemes, but verification is less efficient. The new scheme adapts the prefix signing tech...

Decomposing a divisor over a suitable factor basis in the Jacobian of a hyperelliptic curve is a crucial step in an index calculus algorithm for the discrete log problem in the Jacobian. For small genus curves, in the year 2000, Gaudry had proposed a suitable factor basis and a decomposition method. In this work, we provide a new method for decomposition over the same factor basis. The advantag...

Transposed-letter (TL) nonwords (e.g., jugde) can be easily misperceived as words, a fact that is somewhat inconsistent with the letter-position-coding schemes employed by most current models of visual word recognition. To examine this issue further, we conducted four masked semantic/associative priming experiments, using a lexical decision task. In Experiment 1, the related primes could be wor...

Abstract Let N be a $$\mathbb {Z}$$ Z -nearalgebra; that is, left nearring with identity satisfying $$ k(nn^{\prime })=(kn)n^{\prime }=n(kn^{\prime })$$ k ( n ′ ) =</mml:m...

Dirichlet considered a question very similar to the one which inspired Euler’s introduction of the ζfunction: namely, how the primes are distributed modulo m. The simplest question of this type is whether are there infinitely many primes congruent to a modulo m. Obviously there can only be infinitely many primes of this form if a and m are relatively prime. Unfortunately, this problem turned ou...

Let $\alpha>1$ be irrational and of finite type, $\beta\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection Beatty sequence $\mathcal{B}_{\alpha,\beta}$ $\lfloor n^c\rfloor$, where $c_R$ an explicit constant depending on $R$ herein, $n$ a natural number with at most prime factors, counted multiplicity.

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...