computer science

Identity-based cryptography

Identity-based cryptography is a computer 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 Identity-based cryptography rather than just read about it. In short: Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as a public key. The public string could include an email address, domain name, or a physical IP address.

Key takeaways

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

Reference excerpt

Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as a public key. The public string could include an email address, domain name, or a physical IP address.

The first implementation of identity-based signatures and an email-address based public-key infrastructure (PKI) was developed by Adi Shamir in 1984, which allowed users to verify digital signatures using only public information such as the user's identifier. Under Shamir's scheme, a trusted third party would deliver the private key to the user after verification of the user's identity, with verification essentially the same as that required for issuing a certificate in a typical PKI. Shamir similarly proposed identity-based encryption, which appeared particularly attractive since there was no need to acquire an identity's public key prior to encryption. However, he was unable to come up with a concrete solution, and identity-based encryption remained an open problem for many years. The first practical implementations were finally devised by Sakai in 2000, and Boneh and Franklin in 2001. These solutions were based on bilinear pairings. Also in 2001, a solution was developed independently by Clifford Cocks. Closely related to various identity-based encryption schemes are identity based key agreement schemes. One of the first identity based key agreement algorithms was published in 1986, just two years after Shamir's identity based signature. The author was E. Okamoto. Identity based key agreement schemes also allow for "escrow free" identity based cryptography. A notable example of such an escrow free identity based key agreement is the McCullagh-Barreto's "Authenticated Key Agreement without Escrow" found in section 4 of their 2004 paper, "A New Two-Party Identity-Based Authenticated Key Agreement". A variant of this escrow free key exchange is standardized as the identity based key agreement in the Chinese identity based standard SM9.

Usage Identity-based systems allow any party to generate a public key from a known identity value, such as an ASCII string. A trusted third party, called the private key generator (PKG), generates the corresponding private keys. To operate, the PKG first publishes a master public key, and retains the corresponding master private key (referred to as master key). Given the master public key, any party can compute a public key corresponding to the identity ID by combining the master public key with the identity value. To obtain a corresponding private key, the party authorized to use the identity ID contacts the PKG, which uses the master private key to generate the private key for the identity ID.

Limitation Identity-based systems have a characteristic problem in operation. Suppose Alice and Bob are users of such a system. Since the information needed to find Alice's public key is completely determined by Alice's ID and the master public key, it is not possible to revoke Alice's credentials and issue new credentials without either (a) changing Alice's ID (usually a phone number or an email address which will appear in a corporate directory); or (b) changing the master public key and re-issuing private keys to all users, including Bob. This limitation may be overcome by including a time component (e.g. the current month) in the identity.

See also Identity-based encryption Identity-based conditional proxy re-encryption SM9 - Chinese National Identity Based Cryptography Standard Sakai–Kasahara Identity Based Encryption Boneh–Franklin

References

Worked examples

Example 1 — a first encounter with Identity-based cryptography

Start with the simplest possible case. Write down what Identity-based cryptography claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer 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 Identity-based cryptography 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 Identity-based cryptography 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 Identity-based cryptography

In research: Identity-based cryptography appears in computer 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 Identity-based cryptography 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: Identity-based cryptography is common in secondary-school and first-year university syllabi. It links to neighbouring topics Identity-based cryptography, Public-key cryptography, so understanding it makes those chapters shorter.
In everyday life: Look for Identity-based cryptography 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 Identity-based cryptography in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Identity-based cryptography 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 Identity-based cryptography out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Identity-based cryptography in simple terms?

Why does Identity-based cryptography matter?

Because it connects several computer 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 Identity-based cryptography?

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 Identity-based cryptography.