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).
Published Version
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