We investigate various questions concerning the reciprocal sum of divisors, or prime Mersenne numbers $2^n-1$. Conditional on Elliott-Halberstam Conjecture and Generalized Riemann Hypothesis, we determine $\max_{n\le x} \sum_{p \mid 2^n-1} 1/p$ to within $o(1)$ \sum_{d\mid 2^n-1}1/d$ a factor $1+o(1)$, as $x\to\infty$. This refines, conditionally, earlier estimates Erd?s Erd?s-Kiss-Pomerance. C...

Article history: Received 18 June 2014 Received in revised form 11 June 2015 Accepted 12 June 2015 Available online 22 June 2015 Communicated by Neal Koblitz MSC: primary 11A41, 11A07 secondary 15B99, 05C90

Aggarwal, Joux, Prakash and Santha recently introduced a new potentially quantum-safe public-key cryptosystem, and suggested that a brute-force attack is essentially optimal against it. They consider but then dismiss both Meet-in-the-Middle attacks and LLL-based attacks. Very soon after their paper appeared, Beunardeau et al. proposed a practical LLL-based technique that seemed to significantly...