computer science

Texas Instruments signing key controversy

Texas Instruments signing key controversy 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 Texas Instruments signing key controversy rather than just read about it. In short: The Texas Instruments signing key controversy resulted from Texas Instruments' (TI) response to a project to factorize the 512-bit RSA cryptographic keys needed to write custom firmware to TI devices. Project In July 2009, Benjamin Moody, a United-TI forum user, published the factors of a 512-bit RSA key used to sign the TI-83+ series graphing calculator.

Key takeaways

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

Reference excerpt

Project In July 2009, Benjamin Moody, a United-TI forum user, published the factors of a 512-bit RSA key used to sign the TI-83+ series graphing calculator. The discovery of the private key would allow end users to flash their own operating systems onto the device without having to use any special hardware. Moody used two free software implementations of the general number field sieve, msieve and ggnfs; the computation took 73 days on a 1.9 GHz dual-core processor. This demonstrates the progress of hardware development: the factorization of the similar 512-bit RSA-155 in 1999 using the same algorithm required a large dedicated research group, 8000 MIPS-years of computing time, and a Cray C916 supercomputer. In response, members of the wider TI graphing calculators community (at yAronet) set up a BOINC-based distributed computing project, RSA Lattice Siever (RSALS for short), that quickly factored the other keys. RSA Lattice Siever remained active for nearly three years after outliving its initial purpose, by factoring other integers for the mathematical community. After factoring over 400 integers, RSALS moved to RSALS-inspired NFS@home at the end of August 2012.

Legal response Texas Instruments began by sending out two initial Digital Millennium Copyright Act (DMCA) take-down requests to the hackers, referring to sites or forum posts that they controlled. The hackers responded by removing the keys, without consulting an attorney. TI then sent further DMCA notices to a variety of websites displaying the keys, including United-TI, Reddit, and Wikipedia. Texas Instruments' efforts then became subject to the Streisand effect, and the keys were mirrored on a number of sites, including WikiLeaks. In September 2009, Dan Goodin from The Register alerted the Electronic Frontier Foundation (EFF) to TI's actions, and the EFF agreed to take on the case pro bono, representing three people who had received DMCA notices. On October 13, 2009, the EFF sent a letter to TI warning them that the posting of the keys did not violate the DMCA, and that it might be liable for misrepresentation. Despite the letter by the EFF, TI continued to send DMCA notices to websites that posted the keys, but stopped doing so after late 2009. The EFF filed a DMCA Section 512 counter-notice on behalf of three of the bloggers who received DMCA notices. When the EFF did not receive a response by the deadline, the bloggers reposted the content that had been taken down.

Cryptographic keys The public (or verifying) RSA parameters of the original TI-83+ / TI-83+ Silver Edition OS signing key factored by Benjamin Moody are the following 512-bit modulus n and exponent e (specified in hexadecimal):

n = 82EF4009ED7CAC2A5EE12B5F8E8AD9A0AB9CC9F4F3E44B7E8BF2D57A2F2BEACE83424E1CFF0D2A5A7E2E53CB926D61F347DFAA4B35B205B5881CEB40B328E58F e = 11

By factoring n, Moody obtained the factors p (252 bits) and q (260 bits), which can be used in turn to quickly compute the 512-bit private (or signing) key d = e − 1 mod ( p − 1 ) ( q − 1 ) {\displaystyle d=e^{-1}{\bmod {(}}p-1)(q-1)} :

p = B709D3A0CD2FEC08EAFCCF540D8A100BB38E5E091D646ADB7B14D021096FFCD q = B7207BD184E0B5A0B89832AA68849B29EDFB03FBA2E8917B176504F08A96246CB d = 4D0534BA8BB2BFA0740BFB6562E843C7EC7A58AE351CE11D43438CA239DD99276CD125FEBAEE5D2696579FA3A3958FF4FC54C685EAA91723BC8888F292947BA1

The value d can then be used to sign arbitrary OS software. The keys factored by RSA Lattice Siever (the TI-92+, TI-73, TI-89, Voyage 200, TI-89 Titanium, TI-84+ / TI-84 Silver Edition OS signing and date-stamp signing keys) are similar but with different values of n, p, q, and d. A single date-stamp signing key is shared by all models.

See also AACS encryption key controversy DeCSS Illegal number

References

External links Suppressed Texas Instruments cryptographic signing keys, 28 Aug 2009 at the Wayback Machine (archived June 6, 2010) at the Internet Archive. The file at the Wayback Machine (archived June 6, 2010).

Illustrations

Texas Instruments signing key controversy: A TI-83+ graphing calculator displaying a sine wave — A TI-83+ graphing calculator displaying a sine wave

Worked examples

Example 1 — a first encounter with Texas Instruments signing key controversy

Start with the simplest possible case. Write down what Texas Instruments signing key controversy 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 Texas Instruments signing key controversy 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 Texas Instruments signing key controversy 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 Texas Instruments signing key controversy

In research: Texas Instruments signing key controversy 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 Texas Instruments signing key controversy 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: Texas Instruments signing key controversy is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2009 controversies in the United States, 2009 in American law, Cryptography law, so understanding it makes those chapters shorter.
In everyday life: Look for Texas Instruments signing key controversy 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 Texas Instruments signing key controversy in 20 minutes

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Frequently asked questions

What is Texas Instruments signing key controversy in simple terms?

The Texas Instruments signing key controversy resulted from Texas Instruments' (TI) response to a project to factorize the 512-bit RSA cryptographic keys needed to write custom firmware to TI devices. Project In July 2009, Benjamin Moody, a United-TI forum user, published the factors of a 512-bit R…

Why does Texas Instruments signing key controversy 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 Texas Instruments signing key controversy?

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 Texas Instruments signing key controversy.