computer science

NTRUSign

NTRUSign 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 NTRUSign rather than just read about it. In short: NTRUSign, also known as the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of NTRUSign was Polynomial Authentication and Signature Scheme (PASS), and was published at CrypTEC'99.

Key takeaways

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

Reference excerpt

NTRUSign, also known as the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of NTRUSign was Polynomial Authentication and Signature Scheme (PASS), and was published at CrypTEC'99. The improved version of PASS was named as NTRUSign, and was presented at the rump session of Asiacrypt 2001 and published in peer-reviewed form at the RSA Conference 2003. The 2003 publication included parameter recommendations for 80-bit security. A subsequent 2005 publication revised the parameter recommendations for 80-bit security, presented parameters that gave claimed security levels of 112, 128, 160, 192 and 256 bits, and described an algorithm to derive parameter sets at any desired security level. NTRU Cryptosystems, Inc. patented the algorithm, but all those patents have since expired. NTRUSign involves mapping a message to a random point in 2N-dimensional space, where N is one of the NTRUSign parameters, and solving the closest vector problem in a lattice closely related to the NTRUEncrypt lattice. NTRUSign is claimed to be faster than those algorithms at low security levels, and considerably faster at high security levels. However, analysis had shown that original scheme is insecure and would leak knowledge of private key. A redesigned pqNTRUSign had been submitted to the NIST Post-Quantum Cryptography Standardization competition. It is based on "hash-and-sign" (contrasting Fiat–Shamir transformation) methodology, and claims to achieve smaller signature size. NTRUSign is under consideration for standardization by the IEEE P1363 working group.

Security It was demonstrated in 2000 by Wu, Bao, Ye and Deng that the signature of PASS, the original version of NTRUSign, can be forged easily without knowing the private key. NTRUSign is not a zero-knowledge signature scheme and a transcript of signatures leaks information about the private key, as first observed by Gentry and Szydlo. Nguyen and Regev demonstrated in 2006 that for the original unperturbed NTRUSign parameter sets an attacker can recover the private key with as few as 400 signatures. The current proposals use perturbations to increase the transcript length required to recover the private key: the signer displaces the point representing the message by a small secret amount before the signature itself is calculated. NTRU claimed that at least 230 signatures are needed, and probably considerably more, before a transcript of perturbed signatures enabled any useful attack. In 2012 an attack on the scheme with perturbations was presented that required a few thousand signatures for standard security parameters. The pqNTRUSign claims a 128-bit classical and quantum security for their given parameter set.

References

External links Most recent NTRUSign paper, including parameter sets for multiple security levels A Java implementation of NTRUSign

Worked examples

Example 1 — a first encounter with NTRUSign

Start with the simplest possible case. Write down what NTRUSign 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 NTRUSign 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 NTRUSign 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 NTRUSign

In research: NTRUSign 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 NTRUSign 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: NTRUSign is common in secondary-school and first-year university syllabi. It links to neighbouring topics Digital signature schemes, Lattice-based cryptography, Post-quantum cryptography, so understanding it makes those chapters shorter.
In everyday life: Look for NTRUSign 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 NTRUSign in 20 minutes

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

Frequently asked questions

What is NTRUSign in simple terms?

Why does NTRUSign 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 NTRUSign?

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 NTRUSign.