science

Key selection vector

Key selection vector is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Key selection vector rather than just read about it. In short: A Key Selection Vector (KSV) is a numerical identifier associated with a Device Key Set which is distributed by a Licensor or its designee to Adopters and is used to support authentication of Licensed Products and Revocation as part of the HDCP copy protection system. The KSV is used to generate confidential keys, specifically used in the Restricted Authentication process of HDCP.

Key takeaways

Key selection vector belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Key selection vector to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Key selection vector from memory before moving on to harder problems.

Reference excerpt

A Key Selection Vector (KSV) is a numerical identifier associated with a Device Key Set which is distributed by a Licensor or its designee to Adopters and is used to support authentication of Licensed Products and Revocation as part of the HDCP copy protection system. The KSV is used to generate confidential keys, specifically used in the Restricted Authentication process of HDCP. Restricted Authentication is an AKE method for devices with limited computing resources. This method is used by copying devices of any kind (such as DV recorders or D-VHS recorders) and devices communicating with them for authenticating protected content. The restricted authentication protocol uses asymmetric key management and common key cryptography, and relies on the use of shared secrets and hash functions to respond to a random challenge.

Restricted Authentication Protocol The goal of Restricted Authentication is for a device to prove that it holds a secret shared with other devices. One device authenticates another by issuing a random challenge for which the response is generated by combining the shared secrets and multiple hashes. Formally, a Key Selection Vector is a 40-bit vector containing 20 ones and 20 zeros, and is used to specify the random challenge. The Device Key Set is a collection of 40 56-bit values, and is the set of shared secrets for this protocol During the authentication process, both parties (a transmitter and a receiver) exchange their KSVs. Then each device adds (unsigned addition modulo 2 56 {\displaystyle 2^{56}} ) its own device secret keys according to a KSV received from another device. If a particular bit in the KSV is set to 1, then the corresponding secret key is used in the addition and otherwise it is ignored. For each set of keys a special key called a KSV (Key Selection Vector) is created. Each KSV has exactly 20 bits set to 0 and 20 bits set to 1. Keys and KSVs are generated in such a way that during this process both devices get the same 56 bit number as a result. That number is later used in the encryption process.

Uniqueness and Revocation of KSVs Since valid keys can become compromised (hacked, for instance through reverse engineering hardware), the HDCP scheme includes a mechanism to revoke keys. The KSV values are unique to each key set and, therefore to each device. The HDCP system can then compare these values to a revocation list, and authentication fails if either the transmitter or receiver appears on the revocation list. Updates to the revocation list arrive with new media and are automatically integrated into a device's revocation list. This means that damage can be limited if a key set is exposed or copied. This revocation process does not affect other devices, even if the devices are of the same make and model. KSV values are similar to serial numbers in this sense. As an example of how this system works, if two customers were to buy the same model of television on the same day at the same store, and the first customer hacked their television, the first customer's key could be revoked without affecting the ability of the other customer's television to play content.

Attacks on Restricted Authentication If an attacker can find 40 linearly independent vectors ( A 1 {\displaystyle A_{1}} ) keys ... ( A 40 {\displaystyle A_{40}} )keys (i.e. the vectors generated by adding together a device's Device Key Set based on a KSV,) then they can completely break the HDCP system for all devices using a given Device Key Set. At this point, they can extract the secret key array for any number of KSVs, which allows them to access the shared secrets used in the HDCP authentication protocol. Since the keys generated from the KSVs are produced linearly in the given system (i.e. getting a key from a KSV can be viewed as matrix multiplication), someone could determine the Device Key Set matrix from any 40-50 different systems: A 1 {\displaystyle A_{1}} .... A n {\displaystyle A_{n}} , and the associated KSV (this is public information from the protocol). In other cases where the extracted keys are not linearly independent, it is still possible to create a new XKey for a new Xksv that is within the span of the ( A i {\displaystyle A_{i}} )KSVs (by taking linear combinations) for which the private keys have been found. There will be, however, no guarantee of them satisfying the required property that a KSV must have; 20 ones and 20 zeros.

Setting up the Equations Assuming there are 40 ( A i {\displaystyle A_{i}} ) KSVs that are linearly independent (and naming Xkeys the matrix of the keys in the Device Key Set), this gives a set of n linear equations on 40 unknowns – [Xkeys] * (A1)ksv = = [(A1)keys] * Xksv[Xkeys] * (A2)ksv = = [(A2)keys] * Xksv...[Xkeys] * (A40)ksv = = [(A40)keys] * Xksv By having acknowledgment on all the KSVs, and assuming the secret key vectors ( A i {\displaystyle A_{i}} )keys are known, the above algorithm can be used to find the secret keys to produce a new derived key from arbitrary new KSV. If the space spanned by the ( A i {\displaystyle A_{i}} )KSVs doesn't span the full 40 dimensional space, this may be okay because the KSVs were either not designed to not span the space, or only a small number of extra keys are needed to find a set of vectors spanning the full space. Each additional device has low odds of being linearly dependent with the existing set. (roughly 1/2^[40-dimensionality-of-spanned-space]. This analysis of probabilities of linear dependence is similar to the analysis of Simon's Algorithm).

Worked examples

Example 1 — a first encounter with Key selection vector

Start with the simplest possible case. Write down what Key selection vector claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Key selection vector before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Key selection vector ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Key selection vector

In research: Key selection vector appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Key selection vector in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Key selection vector is common in secondary-school and first-year university syllabi. It links to neighbouring topics Digital rights management standards, so understanding it makes those chapters shorter.
In everyday life: Look for Key selection vector outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Key selection vector in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Key selection vector means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Key selection vector out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Key selection vector in simple terms?

Why does Key selection vector matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Key selection vector?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Key selection vector.