On RSA Moduli with Almost Half of the Bits Prescribed

2007/09/17 by Sidney W. Graham, Graham, Sidney W., Igor E. Shparlinski +1 · 1 citation
Mathematics · #11A63 #11L40 #11N25 #94A60 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A63 #msc:11L40 #msc:11N25 #msc:94A60

paper · pdf · doi:10.48550/arxiv.0709.2704

arxiv created 2007/09/17 · arxiv updated 2009/12/01

Abstract

We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli M=pl, where p and l are primes, with prescribed bit patterns. We are now able to specify about n bits instead of about n/2 bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional version of a combinatorial result of W. de Launey and D. Gordon that was originally derived under the Extended Riemann Hypothesis.

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