How to obtain a RSA private key from a public key

Abstract

Quantum computers (QC) will likely break RSA encryption in the future. This is because QC have the capability to efficiently factorize the two prime numbers that form the foundation of RSA key material.

RSA encryption is widely used to secure web traffic, particularly in protocols up to TLS 1.2. In today's environment, web servers rely on certificates to protect traffic between the server and the client. These certificates contain a 2048 or 4096-bit public key, digitally signed by a Certification Authority. However, what happens when the key material of the certificate is not generated correctly? Can organizations still be confident that their traffic remains secure and uncompromised?

The randomness of prime numbers is crucial, as their uniqueness is required to ensure a secure connection. If compromised, encrypted traffic can be intercepted now and decrypted later.

In this session, Johan Loos demonstrates one of the various methods by which private keys of certificates can be 'recovered' when two web servers share a common prime number. The session is based on his own RSA research and is presented with a live demonstration using virtual machines.

This session is designed for individuals interested in understanding RSA attacks and learning how to enhance security measures to protect against them.

Session Overview:

1. A brief introduction to how the RSA algorithm works

2. An explanation of the RSA attack used in the demonstration

3. A step-by-step approach to recovering private keys from two web servers and using the recovered key to decrypt TLS v1.2 traffic

4. Key takeaways and conclusions