### Far Eastern Mathematical Journal

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Calculation of random pairs of primes whose product lies in a given short interval

Bykovskii V.A.

2020, issue 2, Ñ. 150–154
DOI: https://doi.org/10.47910/FEMJ202016

Abstract
The paper proposes heuristic algorithms for constructing pairs of random primes, the product of which lies in a given interval $\left (\Delta, \, \Delta + \delta \right).$ One algorithm refers to the case $\delta = \sqrt {\Delta },$ and the second to $\delta = 30 \Delta^{1/3}.$ They allow in the well-known RSA cryptosystem to choose shorter public keys (twice for the first algorithm and three times for the second).

Keywords:
Number theory, cryptography, RSA cryptosystem