Tuesday, August 23, 2016

CRYPTO 2016 – Backdoors, big keys and reverse firewalls on compromised systems

The morning of the second day at CRYPTO’s 2016 started with a track on “Compromised Systems”, consisting of three talks covering different scenarios and attacks usually disregarded in the vast majority of the cryptographic literature. They all shared, as well, a concern about mass surveillance.

Suppose Alice wishes to send a message to Bob privately over an untrusted channel. Cryptographers have worked hard on this scenario, developing a whole range of tools, with different notions of security and setup assumptions, between which one of the most common axioms is that Alice has access to a trusted computer with a proper implementation of the cryptographic protocol she wants to run. The harsh truth is that this is a naïve assumption. The Snowden revelations show us that powerful adversaries can and will corrupt users machines via extraordinary means, such as subverting cryptographic standards, intercepting and tampering with hardware on its way to users or using Tailored Access Operation units.

Nevertheless, the relevance of these talks was not just a matter of a “trending topic”, or distrust on the authoritarian and unaccountable practices of intelligence agencies. More frequently than we would like, presumably accidental vulnerabilities (such as Poodle, Heartbleed, etc.) are found in popular cryptographic software, leaving the final user unprotected even when using honest implementations. In the meantime, as Paul Kocher remembered on his invited talk the day after, for most of our community it passes without notice that, when we design our primitives and protocols, we blindly rely on a mathematical model of reality that sometimes has little to do with it.

In the same way as people from the CHES community has become more aware –mainly also the hard way– that relying on the wrong assumptions leads to a false confidence of the security of the deployed systems and devices, I think those of us not that close to hardware should also try to step back and look at how realistic are our assumptions. This includes, as these talks addressed in different ways, starting to assume that some standards might –and most of the systems will— be compromised at some point, and that we understand what can still be done in those cases.

How would a Cryptography that worries not only about prevention, but also about the whole security cycle look like? How can the cryptography and information security communities come closer?

Message Transmission with Reverse Firewalls— Secure Communication on Corrupted Machines

The reverse firewalls framework was recently introduced by Mironov and Stephens-Davidowitz, with a paper that has already been discussed in our group’s seminars and this same blog. A secure reverse firewall is a third party that “sits between Alice and the outside world” and modifies her sent and received messages so that even if her machine has been corrupted, Alice’s security is still guaranteed.

Their elegant construction does not require the users to place any additional trust on the firewall, and relies on having the underlying cryptographic schemes to be rerandomizable. With this threat model and rerandomization capabilities, they describe impossibility results as well as concrete constructions.

For example, in the context of semantically secure public-key encryption, in order to provide reverse firewalls for Bob, the scheme must allow a third party to rerandomize a public key and map ciphertexts under the rerandomized public key to ciphertexts under the original public key. In the same context, Alice’s reverse firewall must be able to rerandomize the ciphertext she sends to Bob, in such a way that Dec(Rerand(Enc(m)))=m.

Big-Key Symmetric Encryption: Resisting Key Exfiltration

The threat addressed in Bellare’s talk is that of malware that aims to exfiltrate a user's key, likely using her system’s network connection. On their work, they design a schemes that aim to protect against this kind of Advanced Persistent Threats by making secret keys so big that their undetected exfiltration by the adversary is difficult, yet making the user’s overhead almost exclusively in terms of storage instead of speed.

Their main result is a subkey prediction lemma, that gives a nice bound on an adversary’s ability to guess a modest length subkey, derived by randomly selecting bits of a big-key from which partial information has already been leaked. This approach, known as the Bounded Retrieval Model, has been –in the words of the authors—largely a theoretical area of research, whereas they show a fully concrete security analysis with good numerical bounds, constants considered.
Other highlighted aspects of their paper were the concrete improvements over [ADW09] and the key encapsulation technique carefully based in different security assumptions (random oracle, standard model).

Backdoors in Pseudorandom Number Generators: Possibility and Impossibility Results

The last talk of the session focused on the concrete problem of backdoored Pseudorandom Number Generators (PRGs) and PRNGs with input, which are fundamental building blocks in cryptographic protocols that have already been successfully compromised, as we learnt when the DUAL_EC_DRBG scandal came to light.
On their paper, the authors revisit a previous abstraction of backdoored PRGs [DGA+15] which modeled the adversary (Big Brother) with weaker powers than it could actually have. By giving concrete “Backdoored PRG” constructions, they show how that model fails. Moreover, they also study robust PRNGs with input, for which they show that Big Brother is still able to predict the values of the PRNG state backwards, as well as giving bounds on the number of these previous phases that it can compromise, depending on the state-size of the generator.

[ADW09] J. Alwen, Y. Dodis, and D. Wichs. Leakage-resilient public-key cryptography in the bounded-retrieval model. In S. Halevi, editor, CRYPTO 2009, volume 5677 of LNCS, pages 36{54. Springer, Heidelberg, Aug. 2009.

[DGA+15] Yevgeniy Dodis, Chaya Ganesh, Alexander Golovnev, Ari Juels, and Thomas Ristenpart. A formal treatment of backdoored pseudorandom generators. In Elisabeth Oswald and Marc Fischlin, editors, EUROCRYPT 2015, Part I, volume 9056 of LNCS, pages 101–126, Sofia, Bulgaria, April 26–30, 2015. Springer, Heidelberg, Germany.

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