computer science

Publicly verifiable secret sharing

Publicly verifiable secret sharing 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 Publicly verifiable secret sharing rather than just read about it. In short: In cryptography, a secret sharing scheme is publicly verifiable (PVSS) if it is a verifiable secret sharing scheme and if any party (not just the participants of the protocol) can verify the validity of the shares distributed by the dealer. In verifiable secret sharing (VSS) the object is to resist malicious players, such as (i) a dealer sending incorrect shares to some or all of the participants, and (ii) participa…

Key takeaways

Publicly verifiable secret sharing 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 Publicly verifiable secret sharing to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Publicly verifiable secret sharing from memory before moving on to harder problems.

Reference excerpt

In cryptography, a secret sharing scheme is publicly verifiable (PVSS) if it is a verifiable secret sharing scheme and if any party (not just the participants of the protocol) can verify the validity of the shares distributed by the dealer.

In verifiable secret sharing (VSS) the object is to resist malicious players, such as (i) a dealer sending incorrect shares to some or all of the participants, and (ii) participants submitting incorrect shares during the reconstruction protocol, cf. [CGMA85]. In publicly verifiable secret sharing (PVSS), as introduced by Stadler [Sta96], it is an explicit goal that not just the participants can verify their own shares, but that anybody can verify that the participants received correct shares. Hence, it is explicitly required that (i) can be verified publicly.

The method introduced here according to the paper by Tang, Pei, Liu, and He is non-interactive and maintains this property throughout the protocol.

Initialization The PVSS scheme dictates an initialization process in which:

All system parameters are generated. Each participant must have a registered public key. Excluding the initialization process, the PVSS consists of two phases:

Distribution Distribution of secret s {\displaystyle s} shares is performed by the dealer D {\displaystyle D} , which does the following: The dealer creates s 1 , s 2 . . . s n {\displaystyle s_{1},s_{2}...s_{n}} for each participant P 1 , P 2 . . . P n {\displaystyle P_{1},P_{2}...P_{n}} respectively. The dealer publishes the encrypted share E i ( s i ) {\displaystyle E_{i}(s_{i})} for each P i {\displaystyle P_{i}} . The dealer also publishes a string p r o o f D {\displaystyle \mathrm {proof} _{D}} to show that each E i {\displaystyle E_{i}} encrypts s i {\displaystyle s_{i}}

(note: p r o o f D {\displaystyle \mathrm {proof} _{D}} guarantees that the reconstruction protocol will result in the same s {\displaystyle s} . Verification of the shares: Anybody knowing the public keys for the encryption methods E i {\displaystyle E_{i}} , can verify the shares. If one or more verifications fails the dealer fails and the protocol is aborted.

Reconstruction Decryption of the shares: The Participants P i {\displaystyle P_{i}} decrypts their share of the secret s i {\displaystyle s_{i}} using E i ( s i ) {\displaystyle E_{i}(s_{i})} . (note: fault-tolerance can be allowed here: it is not required that all participants succeed in decrypting E i ( s i ) {\displaystyle E_{i}(s_{i})} as long as a qualified set of participants are successful to decrypt s i {\displaystyle s_{i}} ). The participant release s i {\displaystyle s_{i}} plus a string p r o o f P i {\displaystyle \mathrm {proof} _{P_{i}}} this shows the released share is correct. Pooling the shares: Using the strings p r o o f P i {\displaystyle \mathrm {proof} _{P_{i}}} to exclude the participants which are dishonest or failed to decrypt E i ( s i ) {\displaystyle E_{i}(s_{i})} . Reconstruction s {\displaystyle s} can be done from the shares of any qualified set of participants.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Publicly verifiable secret sharing

Start with the simplest possible case. Write down what Publicly verifiable secret sharing 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 Publicly verifiable secret sharing 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 Publicly verifiable secret sharing 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 Publicly verifiable secret sharing

In research: Publicly verifiable secret sharing 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 Publicly verifiable secret sharing 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: Publicly verifiable secret sharing is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applications of cryptography, so understanding it makes those chapters shorter.
In everyday life: Look for Publicly verifiable secret sharing 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 Publicly verifiable secret sharing in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Publicly verifiable secret sharing 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 Publicly verifiable secret sharing out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Publicly verifiable secret sharing in simple terms?

Why does Publicly verifiable secret sharing 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 Publicly verifiable secret sharing?

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 Publicly verifiable secret sharing.