SECRET EXPONENT

Title: SECRET EXPONENT

Research Question: Can we find a more efficient way to break the RSA cryptosystem with a small secret exponent?

Methodology: The researchers used continued fractions and Legendre's theorem on Diophantine approximations to find a more efficient variant of Wiener's attack on RSA cryptosystems with small secret exponents.

Results: They found that if the secret exponent is small enough, it can be found by looking at the convergents of the continued fraction expansion of the public key. This leads to a more efficient variant of Wiener's attack, which allows the RSA cryptosystem to be broken by an exhaustive search when the secret exponent is a few bits longer than n0.25.

Implications: This research has implications for the security of RSA cryptosystems with small secret exponents. It shows that these systems can be broken more efficiently than previously thought, which could potentially impact the security of these cryptosystems in practice.

Link to Article: https://arxiv.org/abs/0402052v1 Authors: arXiv ID: 0402052v1