Dual EC or the NSA's Backdoor: Explanations

Summary

In this video, David Wong explains the controversial history of the Dual EC pseudo-random number generator (PRNG) and its backdoor, which was discovered in 2007. The backdoor, traced to the NSA, raised major security concerns. Wong discusses the mechanics of how the PRNG works, its vulnerabilities, and the implications for cryptographic systems. He also highlights the efforts to address the backdoor in later versions, including the 2007 update to Dual EC, and the role of government entities in the development and exploitation of these algorithms.

Takeaways

• 😀 The Dual EC (Elliptic Curve) algorithm has a controversial history, with a backdoor discovered in 2007 that traced back to the NSA.
• 😀 A Pseudo-Random Number Generator (PRNG) is essential for generating secure random numbers in cryptographic systems, and a backdoor at the PRNG level can compromise the entire system's security.
• 😀 PRNGs use an initial seed, entropy sources like mouse movements or CPU cycles, and one-way functions to generate random numbers. A predictable or reversible PRNG can be exploited by attackers.
• 😀 Dual EC, as part of NIST's standard, included hardcoded elliptic curve points without clear explanations of their origins, raising suspicions about a potential backdoor.
• 😀 The Dual EC algorithm involves multiplying an internal state by specific elliptic curve points to generate random numbers, but this process could be exploited if attackers know the curve's private parameters.
• 😀 In the early versions of Dual EC (2006), an attacker could exploit the system by reverse engineering the random number output to predict future states, using knowledge of the curve parameters.
• 😀 A more secure variant of Dual EC (2007) introduced forward secrecy, ensuring that the internal state couldn't be used to recover earlier states. However, the backdoor remained exploitable in some scenarios.
• 😀 The addition of backward secrecy in the 2007 Dual EC update aimed to prevent attacks where an attacker could guess the next internal state, but it still left the system vulnerable to specific attacks when larger outputs were generated.
• 😀 The NSA's involvement in promoting the Dual EC standard raised suspicions about intentional backdoors, with reports of them paying for implementation in widely-used tools like RSA.
• 😀 In the end, the Dual EC algorithm was heavily criticized for being slow and impractical, but the NSA managed to implement it in a way that allowed them to exploit its weaknesses while discouraging others from using it.

Q & A

What is a PRNG and why is it important in cryptography?

A PRNG, or Pseudo-Random Number Generator, produces sequences of numbers that appear random. In cryptography, PRNGs are crucial because they generate random values for keys, initialization vectors, and tokens, which are fundamental for maintaining security.

What is the difference between public and private random numbers?

Public random numbers are used in processes visible to others, like the IV in CBC mode or client hello in TLS. Private random numbers are used internally, such as for generating recovery tokens or private keys, and must remain secret to ensure security.

What are forward secrecy and backward secrecy in the context of PRNGs?

Forward secrecy ensures that knowing the current internal state of a PRNG does not allow an attacker to recover previous states. Backward secrecy ensures that knowing the current state does not allow an attacker to predict future states.

How does Dual EC use elliptic curves in its PRNG?

Dual EC uses elliptic curves by multiplying the internal state with a point P to generate a new state and then multiplying that new state with a point Q to produce the random output. This relies on the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP) to secure the PRNG.

Why were the points P and Q in Dual EC considered suspicious?

P and Q were hardcoded without a clear explanation or verifiable origin, unlike 'nothing-up-my-sleeve' numbers. This lack of transparency raised concerns that they could be deliberately chosen to allow a backdoor.

How could the NSA exploit Dual EC's PRNG?

If the NSA chose P and Q using a secret scalar D, they could potentially reverse-engineer the internal state from a single output, allowing them to predict future random numbers and compromise cryptographic security.

What was the main vulnerability in Dual EC 2006?

The main vulnerability was that an attacker with knowledge of the secret scalar D could compute the next internal state from the random output R1, effectively creating a backdoor into systems using the PRNG.

How did the 2007 update of Dual EC attempt to fix the backdoor?

The 2007 update added backward secrecy using an intermediate value combined with additional input (like entropy). This made it harder for attackers to predict the next state from a single output, though the backdoor could still be exploited under certain conditions.

What is the role of one-way functions in PRNG security?

One-way functions are used to transform the internal state into the output random number. They prevent an attacker from recovering the internal state from the output, thus ensuring forward secrecy and overall security of the PRNG.

Why is Dual EC considered a controversial PRNG?

Dual EC is controversial because it contains a potential backdoor that could allow the NSA to predict random numbers, compromising cryptographic security. Its design choices, including unexplained hardcoded points and inefficiency, contributed to distrust in its use.

What did the former NSA technical director say about Dual EC?

He said that by embedding Dual EC into a standard, it would likely not be used by others due to its inefficiency and awkward design, but the NSA could exploit it secretly. This highlights the intentional backdoor nature of the algorithm.

Why is using the same PRNG for both public and private random numbers risky?

If an attacker can recover the internal state from public random numbers, they could also predict private random numbers, compromising sensitive operations such as key generation, password recovery, and cryptographic signatures.