Abstract
The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by factoring a well-chosen quadratic polynomial with integral coefficients. When viewed as a general-purpose algorithm, the new algorithm has a high computational complexity. It is shown that the RSA numbern=pq can be easily factored ifp andq have the special form ofp=as+b, q=cs+d, wherea, b, c, d are relatively small numbers. Such prime pairs (p, q) are the weak keys of RSA, so when we generate RSA modulus, we should avoid using such prime pairs (p, q).
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