Cryptanalysis of 'less short' RSA secret exponents

In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a ‘short’ secret exponent. Let n=p¿·¿q be the modulus of the system. In the typical case that G=gcd(p-1,¿q-1) is small. Wiener’s method will give the secret exponent d when d does not exceed (approximately) n 1/4. Here, we describe a general method to compute the CF-convergents of the continued fraction expansion of the same number as in Wiener (which has denominator d¿·¿G) up to the point where the denominator of the CF-convergent exceeds approximately n 1/4. When