Boing Boing just released a classified GCHQ document that was meant to act as the Sept 2011 guide to open research problems in Data Mining. The intended audience, Heilbronn Institute for Mathematical Research (HIMR), is part of the University of Bristol and composed of mathematicians working for half their time on classified problems with GCHQ.

First off, a quick perusal of the actual publication record of the HIMR makes a sad reading for GCHQ: it seems that very little research on data mining was actually performed post-2011-2014 despite this pitch. I guess this is what you get trying to make pure mathematicians solve core computer science problems.

However, the document presents one of the clearest explanations of GCHQ’s operations and their scale at the time; as well as a very interesting list of open problems, along with salient examples.

Overall, reading this document very much resembles reading the needs of any other organization with big-data, struggling to process it to get any value. The constrains under which they operate (see below), and in particular the limitations to O(n log n) storage per vertex and O(1) per edge event, is a serious threat — but of course this is only for un-selected traffic. So the 5000 or so Tor nodes probably would have a little more space and processing allocated to them, and so would known botnets — I presume.

Secondly, there is clear evidence that timing information is both recognized as being key to correlating events and streams; and it is being recorded and stored at an increasing granularity. There is no smoking gun as of 2011 to say they casually de-anonymize Tor circuits, but the writing is on the wall for the onion routing system. GCHQ at 2011 had all ingredients needed to trace Tor circuits. It would take extra-ordinary incompetence to not have refined their traffic analysis techniques in the past 5 years. The Tor project should do well to not underestimate GCHQ’s capabilities to this point.

Thirdly, one should wonder why we have been waiting for 3 years until such clear documents are finally being published from the Snowden revelations. If those had been the first published, instead of the obscure, misleading and very non-informative slides, it would have saved a lot of time — and may even have engaged the public a bit more than bad powerpoint.

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(This is an extract from my contribution to Harper, Richard. “Introduction and Overview”, Trust, Computing, and Society. Ed. Richard H. R. Harper. 1st ed. New York: Cambridge University Press, 2014. pp. 3-14. Cambridge Books Online. Web. 03 February 2016.

Cryptography has been used for centuries to secure military, diplomatic, and commercial communications that may fall into the hands of enemies and competitors (Kahn 1996). Traditional cryptography concerns itself with a simple problem: Alice wants to send a message to Bob over some communication channel that may be observed by Eve, but without Eve being able to read the content of the message. To do this, Alice and Bob share a short key, say a passphrase or a poem. Alice then uses this key to scramble (or encrypt) the message, using a cipher, and sends the message to Bob. Bob is able to use the shared key to invert the scrambling (or “decrypt”) and recover the message. The hope is that Eve, without the knowledge of the key, will not be able to unscramble the message, thus preserving its confidentiality.

It is important to note that in this traditional setting we have not removed the need for a secure channel. The shared key needs to be exchanged securely, because its compromise would allow Eve to read messages. Yet, the hope is that the key is much shorter than the messages subsequently exchanged, and thus easier to transport securely once (by memorizing it or by better physical security). What about the cipher? Should the method by which the key and the message are combined not be kept secret? In “La Cryptographie Militaire” in 1883, Auguste Kerckhoffs stated a number of principles, including that only the key should be considered secret, not the cipher method itself (Kerckhoffs 1883). Both the reliance on a small key and the fact that other aspects of the system are public is an application of the minimization principle we have already seen in secure system engineering. It is by minimizing what has to be trusted for the security policy to hold that one can build and verify secure systems – in the context of traditional cryptography, in principle, this is just a short key.

Kerckhoffs argues that only the key, not the secrecy of the cipher is in the trusted computing base. But a key property of the cipher is relied on: Eve must not be able to use an encrypted message and knowledge of the cipher to recover the message without access to the secret key. This is very different from previous security assumptions or components of the TCB. It is not about the physical restrictions on Eve, and it is not about the logical operations of the computer software and hardware that could be verified by careful inspection. It comes down to an assumption that Eve cannot solve a somehow difficult mathematical problem. Thus, how can you trust a cipher? How can you trust that the adversary cannot solve a mathematical problem?

To speak the truth, this was not a major concern until relatively recently, compared with the long history of cryptography. Before computers, encoding and decoding had to be performed by hand or using electromechanical machines. Concerns such as usability, speed, cost of the equipment, and lack of decoding errors were the main concerns in choosing a cipher. When it comes to security, it was assumed that if a “clever person” proposes a cipher, then it would take someone much cleverer than them to decode it. It was even sometimes assumed that ciphers were of such complexity that there was “no way” to decode messages without the key. The assumption that other nations may not have a supply of “clever” people may have to do with a colonial ideology of nineteenth and early twentieth centuries. Events leading to the 1950s clearly contradict this: ciphers used by major military powers were often broken by their opponents.

In 1949, Claude Shannon set out to define what a perfect cipher would be. He wanted it to be “impossible” to solve the mathematical problem underlying the cipher (Shannon 1949). The results of this seminal work are mixed. On the positive side, there is a perfect cipher that, no matter how clever an adversary is, cannot be solved – the one-time pad. On the down side, the key of the cipher is as long as the message, must be absolutely random, and can only be used once. Therefore the advantage of short keys, in terms of minimizing their exposure, is lost and the cost of generating keys is high (avoiding bias in generating random keys is harder than expected). Furthermore, Shannon proves that any cipher with smaller keys cannot be perfectly secure. Because the one-time pad is not practical in many cases, how can one trust a cipher with short keys, knowing that its security depends on the complexity of finding a solution? For about thirty years, the United States and the UK followed a very pragmatic approach to this: they kept the cryptological advances of World War II under wraps; they limited the export of cryptographic equipment and know-how through export regulations; and their signal intelligence agencies – the NSA and GCHQ, respectively – became the largest worldwide employers of mathematicians and the largest customers of supercomputers. Additionally, in their roles in eavesdropping on their enemies’ communications, they evaluated the security of the systems used to protect government communications. The assurance in cryptography came at the cost of being the largest organizations that know about cryptography in the world.

The problem with this arrangement is that it relies on a monopoly of knowledge around cryptology. Yet, as we have seen with the advent of commercial telecommunications, cryptography becomes important for nongovernment uses. Even the simplest secure remote authentication mechanism requires some cryptography if it is to be used over insecure channels. Therefore, keeping cryptography under wraps is not an option: in 1977, the NSA approved the IBM design for a public cipher, the Data Encryption Standard (DES), for public use. It was standardized in 1979 by the US National Institute for Standards and Technology (NIST).

The publication of DES launched a wide interest in cryptography in the public academic community. Many people wanted to understand how it works and why it is secure. Yet, the fact that the NSA tweaked its design, for undisclosed reasons, created widespread suspicion in the cipher. The fear was that a subtle flaw was introduced to make decryption easy for intelligence agencies. It is fair to say that many academic cryptographers did not trust DES!

Another important innovation in 1976 was presented by Whitfield Diffie and Martin Hellman in their work “New Directions in Cryptography” (Diffie & Hellman 1976). They show that it is possible to preserve the confidentiality of a conversation over a public channel, without sharing a secret key! This is today known as “Public Key Cryptography,” because it relies on Alice knowing a public key for Bob, shared with anyone in the world, and using it to encrypt a message. Bob has the corresponding private part of the key, and is the only one that can decode messages used with the public key. In 1977, Ron Rivest, Adi Shamir, and Leonard Adleman proposed a further system, the RSA, that also allowed for the equivalent of “digital signatures” (Rivest et al. 1978).

What is different in terms of trusting public key cryptography versus traditional ciphers? Both the Diffie-Hellman system and the RSA system base their security on number theoretic problems. For example, RSA relies on the difficulty of factoring integers with two very large factors (hundreds of digits). Unlike traditional ciphers – such as DES – that rely on many layers of complex problems, public key algorithms base their security on a handful of elegant number theoretic problems.

Number theory, a discipline that G.H. Hardy argued at the beginning of the twentieth century was very pure in terms of its lack of any practical application (Hardy & Snow 1967), quickly became the deciding factor on whether one can trust the most significant innovation in the history of cryptology! As a result, a lot of interest and funding directed academic mathematicians to study whether the mathematical problems underpinning public key cryptography were in fact difficult and how difficult the problems were.

Interestingly, public key cryptography does not eliminate the need to totally trust the keys. Unlike traditional cryptography, there is no need for Bob to share a secret key with Alice to receive confidential communications. Instead, Bob needs to keep the private key secret and not share it with anyone else. Maintaining the confidentiality of private keys is simpler than sharing secret keys safely, but it is far from trivial given their long-term nature. What needs to be shared is Bob’s public key. Furthermore, Alice need to be sure she is using the public key associated with the Bob’s private key; if Eve convinces Alice to use an arbitrary public key to encrypt a message to Bob, then Eve could decrypt all messages.

The need to securely associate public keys with entities has been recognized early on. Diffie and Hellman proposed to publish a book, a bit like the phone register, associating public keys with people. In practice, a public key infrastructure is used to do this: trusted authorities, like Verisign, issue digital certificates to attest that a particular key corresponds to a particular Internet address. These authorities are in charge of ensuring that the identity, the keys, and their association are correct. The digital certificates are “signed” using the signature key of the authorities that anyone can verify.

The use of certificate authorities is not a natural architecture in many cases. If Alice and Bob know each other, they can presumably use another way to ensure Alice knows the correct public key for Bob. Similarly, if a software vendor wants to sign updates for their own software, they can presumably embed the correct public key into it, instead of relying on public key authorities to link their own key with their own identity.

The use of public key infrastructures (PKI) is necessary in case Alice wants to communicate with Bob without them having any previous relationship. In that case Alice, given only a valid name for Bob, can establish a private channel to Bob (as long as it trusts the PKI). This is often confused: the PKI ensures that Alice talks to Bob, but not that Bob is “trustworthy” in any other way. For example, a Web browser can establish a secure channel to a Web service that is compromised or simply belong to the mafia. The secrecy provided by the channel does not, in that case, provide any guarantees as to the operation of the Web service. Recently, PKI services and browsers have tried to augment their services by only issuing certificates to entities that are verified as somehow legitimate.

Deferring the link between identities and public keys to trusted third parties places this third party in a system’s TCB. Can certification authorities be trusted to support your security policy? In some ways, no. As implemented in current browsers, any certification authority (CA) can sign a digital certificate for any site on the Internet (Ellison & Schneier 2000). This means that a rogue national CA (say, from Turkey) can sign certificates for the U.S. State Department, that browsers will believe. In 2011, the Dutch certificate authority Diginotar was hacked, and their secret signature key was stolen (Fox-IT 2012). As a result, fake certificates were issued for a number of sensitive sites. Do CAs have incentives to protect their key? Do they have enough incentives to check the identity of the people or entities behind the certificates they sign?

Cryptographic primitives like ciphers and digital signatures have been combined in a variety of protocols. One of the most famous is the Secure Socket Layer SSL or TLS, which provides encryption to access encrypted Web sites on the Internet (all sites following the https://  protocol). Interestingly, once secure primitives are combined into larger protocols, their composition is not guaranteed to be secure. For example a number of problems have been identified against SSL and TLS that are not related to the weaknesses of the basic ciphers used (Vaudenay 2002).

The observation that cryptographic schemes are brittle and could be insecure even if they rely on secure primitives (as did many deployed protocols) led to a crisis within cryptologic research circles. The school of “provable security” proposes that rigorous proofs of security should accompany any cryptographic protocol to ensure it is secure. In fact “provable security” is a bit of a misnomer: the basic building blocks of cryptography, namely public key schemes and ciphers cannot be proved secure, as Shannon argued. So a security proof is merely a reduction proof: it shows that any weakness in the complex cryptographic scheme can be reduced to a weakness in one of the primitives, or a well-recognized cryptographic hardness assumption. It effectively proves that a complex cryptographic scheme reduces to the security of a small set of cryptographic components, not unlike arguments about a small Trusted Computing Base. Yet, even those proofs of security often work at a certain level of abstraction and often do not include all details of the protocol. Furthermore, not all properties can be described in the logic used to perform the proofs. As a result, even provably secure protocols have been found to have weaknesses (Pfitzmann & Waidner 1992).

So, the question of “How much can you trust cryptography?” has in part itself been reduced to “How much can you trust the correctness of a mathematical proof on a model of the world?” and “How much can one trust that a correct proof in a model applies to the real world?” These are deep epistemological questions, and it is somehow ironic that national, corporate, and personal security depends on them. In addition to these, one may have to trust certificate authorities and assumptions on the hardness of deep mathematical problems. Therefore, it is fair to say that trust in cryptographic mechanisms is an extremely complex social process.