Twofish

Key takeaways

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

Reference excerpt

In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization. Twofish is related to the earlier block cipher Blowfish. Twofish's distinctive features are the use of pre-computed key-dependent S-boxes, and a relatively complex key schedule. One half of an n-bit key is used as the actual encryption key and the other half of the n-bit key is used to modify the encryption algorithm (key-dependent S-boxes). Twofish borrows some elements from other designs; for example, the pseudo-Hadamard transform (PHT) from the SAFER family of ciphers. Twofish has a Feistel structure like DES. Twofish also employs a Maximum Distance Separable matrix. When it was introduced in 1998, Twofish was slightly slower than Rijndael (the chosen algorithm for Advanced Encryption Standard) for 128-bit keys, but somewhat faster for 256-bit keys. Since 2008, virtually all AMD and Intel processors have included hardware acceleration of the Rijndael algorithm via the AES instruction set; Rijndael implementations that use the instruction set are now orders of magnitude faster than (software) Twofish implementations. Twofish was designed by Bruce Schneier, John Kelsey, Doug Whiting, David Wagner, Chris Hall, and Niels Ferguson: the "extended Twofish team" met to perform further cryptanalysis of Twofish. Other AES contest entrants included Stefan Lucks, Tadayoshi Kohno, and Mike Stay. The Twofish cipher has not been patented, and the reference implementation has been placed in the public domain. As a result, the Twofish algorithm is free for anyone to use without any restrictions whatsoever. It is one of a few ciphers included in the OpenPGP standard (RFC 9580). However, Twofish has seen less widespread usage than Blowfish, which has been available longer.

Performance During the design of Twofish, performance was always an important factor. It was designed to allow for several layers of performance trade offs, depending on the importance of encryption speed, memory usage, hardware gate count, key setup and other parameters. This allows a highly flexible algorithm, which can be implemented in a variety of applications. There are multiple space-time tradeoffs that can be made, in software as well as in hardware for Twofish. An example of such a tradeoff would be the precomputation of round subkeys or s-boxes, which can lead to speed increases of a factor of two or more. These come, however, at the cost of more RAM needed to store them. The estimates in the table below are all based on existing 0.35 μm CMOS technology.

Cryptanalysis In 1999, Niels Ferguson published an impossible differential attack that breaks 6 rounds out of 16 of the 256-bit key version using 2256 steps. As of 2000, the best published cryptanalysis of the Twofish block cipher is a truncated differential cryptanalysis of the full 16-round version. The paper claims that the probability of truncated differentials is 2−57.3 per block and that it will take roughly 251 chosen plaintexts (32 petabytes worth of data) to find a good pair of truncated differentials. Bruce Schneier responded in a 2005 blog entry that this paper did not present a full cryptanalytic attack, but only some hypothesized differential characteristics: "But even from a theoretical perspective, Twofish isn't even remotely broken. There have been no extensions to these results since they were published in 2000."

See also Threefish Advanced Encryption Standard Data Encryption Standard

References

Articles Bruce Schneier; John Kelsey; Doug Whiting; David Wagner; Chris Hall; Niels Ferguson (1998-06-15). "The Twofish Encryption Algorithm" (PDF/PostScript). Cryptanalysis. Retrieved 2013-01-14. Bruce Schneier; John Kelsey; Doug Whiting; David Wagner; Chris Hall; Niels Ferguson (1999-03-22). The Twofish Encryption Algorithm: A 128-Bit Block Cipher. New York City: John Wiley & Sons. ISBN 0-471-35381-7.

External links Twofish web page, with full specifications, free source code, and other Twofish resources by Bruce Schneier 256 bit ciphers – Twofish reference implementation and derived code Products that Use Twofish by Bruce Schneier Better algorithm: Rijndael or TwoFish? by sci.crypt Standard Cryptographic Algorithm Naming: Twofish

Illustrations

Worked examples

Example 1 — a first encounter with Twofish

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

In research: Twofish appears in 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 Twofish 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: Twofish is common in secondary-school and first-year university syllabi. It links to neighbouring topics Block ciphers, Feistel ciphers, Free ciphers, so understanding it makes those chapters shorter.
In everyday life: Look for Twofish 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.

How to study Twofish in 20 minutes

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

Frequently asked questions

What is Twofish in simple terms?

In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization.

Why does Twofish matter?

Because it connects several 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 Twofish?

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 Twofish.