computer science

LCS35

LCS35 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 LCS35 rather than just read about it. In short: LCS35 is a cryptographic challenge and a time-lock puzzle set by Ron Rivest in 1999. The challenge is to calculate the value w = 2 2 t ( mod n ) {\displaystyle w=2^{2^{t}}{\pmod {n}}} where t is a specific 14-digit (or 47-bit) integer, namely 79685186856218, and n is a specific 616-digit (or 2048-bit) integer that is the product of two large primes (which are not given).

Key takeaways

LCS35 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 LCS35 to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of LCS35 from memory before moving on to harder problems.

Reference excerpt

LCS35 is a cryptographic challenge and a time-lock puzzle set by Ron Rivest in 1999. The challenge is to calculate the value

w = 2 2 t ( mod n ) {\displaystyle w=2^{2^{t}}{\pmod {n}}}

where t is a specific 14-digit (or 47-bit) integer, namely 79685186856218, and n is a specific 616-digit (or 2048-bit) integer that is the product of two large primes (which are not given). The value of w can then be used to decrypt the ciphertext z, another 616-digit integer. The plaintext provides the concealed information about the factorisation of n, allowing the solution to be easily verified. The idea behind the challenge is that the only known way to find the value of w without knowing the factorisation of n is by t successive squarings. The value of t was chosen so that this brute-force calculation would require about 35 years using 1999 chip speeds as a starting point, taking into account Moore's law. Rivest notes that "just as a failure of Moore's Law could make the puzzle harder than intended, a breakthrough in the art of factoring would make the puzzle easier than intended." The challenge was set at (and takes its name from) the 35th anniversary celebrations of the MIT Laboratory for Computer Science, now part of MIT Computer Science and Artificial Intelligence Laboratory. The LCS35 challenge was solved on April 15, 2019, twenty years later, by programmer Bernard Fabrot. The plaintext begins with "!!! Happy Birthday LCS !!!". On May 14, 2019, Ronald L. Rivest published a new version of LCS35 (named CSAIL2019) to extend the puzzle out to the year 2034.

References

External links Description of the LCS35 Time Capsule Crypto-Puzzle, Ronald L. Rivest Time capsule opening ceremony

Worked examples

Example 1 — a first encounter with LCS35

Start with the simplest possible case. Write down what LCS35 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 LCS35 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 LCS35 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 LCS35

In research: LCS35 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 LCS35 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: LCS35 is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cryptography contests, so understanding it makes those chapters shorter.
In everyday life: Look for LCS35 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 LCS35 in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what LCS35 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 LCS35 out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is LCS35 in simple terms?

LCS35 is a cryptographic challenge and a time-lock puzzle set by Ron Rivest in 1999. The challenge is to calculate the value w = 2 2 t ( mod n ) {\displaystyle w=2^{2^{t}}{\pmod {n}}} where t is a specific 14-digit (or 47-bit) integer, namely 79685186856218, and n is a specific 616-digit (or 2048-b…

Why does LCS35 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 LCS35?

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 LCS35.