# The improvement of the private key exponent in the M.Weiner Attack

I am working on attacks on RSA and came across the M. Weiner attack.

The limit for $d$ in order for the attack to apply is $d <= (\frac{1}{3})N^{0.25}$. The paper states that Boneh and Durfee improved this limit… but to what? What's the limit they reach for the attack to still apply?

## 1 Answer

Quoting the abstract:

Abstract: We show that if the private exponent d used in the RSA system is less than $N^{0.292}$ then the system is insecure. This is the first improvement of an old result of Wiener showing that when $d < N^{0.25}$ RSA is insecure. We hope our approach can be used to eventually improve the bound to $d < N^{0.5}$.

https://crypto.stanford.edu/~dabo/abstracts/lowRSAexp.html