Вычисление случайных пар простых чисел, произведение которых лежит в заданном коротком интервале

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).