ANOTHER PROOF OF WIENER'S SHORT SECRET EXPONENT - Asbullah, Muhammad Asyraf; Kamel Ariffin, Muhammad Rezal (Malaysian Journal of Science, 2019)
Wiener’s short secret exponent attack is a well-known crypt-analytical result upon the RSA cryptosystem using a Diophantine’s method called continued fractions. We recall that Wiener’s attack works efficiently on RSA with the condition that the secret exponent <a href="https://www.codecogs.com/eqnedit.php?latex=d<&space;\frac{1}{3}N^{\frac{1}{4}}" target="_blank"><img title="d< \frac{1}{3}N^{\frac{1}{4}}" src="https://latex.codecogs.com/gif.latex?d<&space;\frac{1}{3}N^{\frac{1}{4}}" alt=""> . Later, the upper bound was improved satisfying <a href="https://www.codecogs.com/eqnedit.php?latex=d<\frac{\sqrt{6\sqrt{2}}}{6}N^{\frac{1}{4}}" target="_blank"><img title="d<\frac{\sqrt{6\sqrt{2}}}{6}N^{\frac{1}{4}}" src="https://latex.codecogs.com/gif.latex?d<\frac{\sqrt{6\sqrt{2}}}{6}N^{\frac{1}{4}}" alt=""> . In this work, we present another proof to Wiener’s short secret exponent satisfying <a href="https://www.codecogs.com/eqnedit.php?latex=d<\frac{1}{2}&space;N^{\frac{1}{4}}" target="_blank"><img title="d<\frac{1}{2} N^{\frac{1}{4}}" src="https://latex.codecogs.com/gif.latex?d<\frac{1}{2}&space;N^{\frac{1}{4}}" alt="">. We remark that our result is slightly better than the previously mentioned attacks.