3 min read

Digital Rights Management Protection

Digital Rights Management Protection

In 2004, Intel, Nokia, Panasonic, and Samsung, announced plans for a licensing and compliance framework called Content Management License Administrator (CMLA) (see www.cm-la.com). This body was formed to address necessary business concerns and enable rapid delivery of high-quality digital files to mobile handsets and other devices that deploy Open Mobile Alliance (OMA).CMLA's goal is to provide vendors and service providers with clear processes and guidelines for robust and compliant OMA DRM Version 2.0 implementations making their product development cycles faster and easier. Ultimately, CMLA will assist in bringing consumers greater access to new and emerging digital content such as music, audio files, video clips, games, etc.

CMLA asked Cryptomathic to help improve security without influencing performance. To this end, Cryptomathic made a proposal, which CMLA has now adapted, and it has filed an international patent application with the Cryptomathic cryptographers as inventors.

The approach was to ensure that keys were of maximum entropy, i.e., "as random as possible.” The following is a condensed version of the introduction to a scientific paper submitted for publication.

A key derivation function (KDF) is a function that takes as input a (short) string of random bits and outputs some number of (pseudo-randomly chosen) keys for some cryptosystem, typically keys for a symmetric cipher such as AES. This can be useful, for instance, when we have a truly random seed of limited size, but we need to generate many keys.

Moreover, any secure pseudorandom generator G can be used as a KDF: just split the output from G in a number of consecutive k-bit blocks, where k is the length of keys we want, and output each segment as a key. 

The important question is whether the encryption we get by using the KDF-output as encryption keys is as secure as if we had chosen the keys independently and uniformly. For the simple construction just mentioned, we can say that the answer is yes if G is a good pseudorandom generator this means the adversary cannot distinguish G(R) from a genuinely random string.

New Call-to-actionBut this point of view is overly simplified for several reasons: first, a pseudorandom generator is not simply "good" or "bad"; it has a certain amount of strength, depending on how hard it is to distinguish its output from random. It may be prudent to design our KDF construction so that all security is not lost, even if the generator turns out to be weaker than we had hoped. A second - perhaps more important is that while pseudorandom generators are usually seen as general methods for making bits that are as good as random for any practical purpose, we have a specific application in mind to generate cryptographic keys. Certain properties may be especially important in this application, and we should consider whether we can ensure they are satisfied.


One such property we consider is called local g-uniformity. A locally g-uniform KDF has the property that any subset of g output keys is genuinely uniform.

Why is this a nice property? In the special case where only a single key is generated, it seems reasonable to demand that this key is genuinely random as long as the seed contains enough randomness for this to be possible. Local 1-uniformity ensures this. But local 1-uniformity is also desirable when several keys are generated: As mentioned, the adversary will not be looking directly at the keys; instead, he will have to try to break the encryptions we produce using the keys. Say we use the keys for some block cipher like AES. Now observe that, as long as the adversary tries to break encryptions produced from a single key Ki. Since Ki is uniform, this will be as hard as simply breaking AES, i.e., using this type of attack, the adversary cannot exploit the fact that a KDF derives the keys.

The only way he can do so is by simultaneously attacking encryptions under at least two different output keys, Ki, and Kj, and somehow using the fact that Kj and I are not independent. This can reasonably be expected to be harder than attacking a single key and exploiting that this single key is not uniform, which would be a possibility for the adversary if the KDF was not locally uniform.

Motivated by this, we chose a KDF construction that augments a pseudorandom generator G with universal hashing. This construction guarantees local (almost) 1- uniformity for any desired key length, assuming the seed is sufficiently long, given that G satisfies a condition we call local randomness. This is much weaker than local uniformity and loosely says that if we split the output from G into in consecutive blocks, each block contains at least some (small) amount of randomness. This construction needs only what is needed as input for G as a secret seed. 

Image: "Mobile", courtesy of Jeff Turner, Flickr (CC BY 2.0)


Previously published in Cryptomathic NewsOnInk, 2005