This vulnerability indicates that the server uses widely-shared Diffie-Hellman prime numbers that enable efficient precomputed attacks, allowing nation-state adversaries to passively decrypt large amounts of internet traffic.

LOGJAM-common_primes occurs when servers use the same standard DH parameters (prime numbers) that are shared across millions of installations. While using shared primes was considered safe, the number field sieve algorithm allows attackers to precompute expensive cryptographic tables once per prime, then quickly break any connection using that prime.

### How It Works:
1. Attacker identifies widely-used DH primes (e.g., default Apache/OpenSSL parameters)
2. Performs expensive precomputation (weeks of compute time) for target prime
3. Passively captures DH key exchanges from any server using that prime
4. Uses precomputed tables to break individual connections in minutes
5. Scales attack across millions of servers sharing the same prime

### Requirements:
- Server uses common/default DH prime numbers (1024-bit or smaller)
- Significant computational resources for initial precomputation (~$100M for 1024-bit)
- Ability to capture network traffic from target connections
- No man-in-the-middle capability needed - purely passive attack

**Example Scenario:**
A major cloud provider uses default 1024-bit DH parameters across thousands of servers. A nation-state actor spends months precomputing cryptographic tables for this specific prime. Once complete, they can passively monitor internet traffic and decrypt any TLS connection to these servers in real-time, affecting millions of users without any active interference or detection.

Breaking the single most common 1024-bit prime would allow passive eavesdropping on 18% of top HTTPS domains, while breaking the two most common primes would compromise 66% of VPN servers and 26% of SSH servers globally.