mathematics

RadioGatún

RadioGatún is a mathematics 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 RadioGatún rather than just read about it. In short: RadioGatún is a cryptographic hash primitive created by Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche. It was first publicly presented at the NIST Second Cryptographic Hash Workshop, held in Santa Barbara, California, on August 24–25, 2006, as part of the NIST hash function competition.

Key takeaways

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

Reference excerpt

RadioGatún is a cryptographic hash primitive created by Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche. It was first publicly presented at the NIST Second Cryptographic Hash Workshop, held in Santa Barbara, California, on August 24–25, 2006, as part of the NIST hash function competition. The same team that developed RadioGatún went on to make considerable revisions to this cryptographic primitive, leading to the Keccak SHA-3 algorithm. RadioGatún is a family of 64 different hash functions, distinguished by a single parameter, the word width in bits (w), adjustable between 1 and 64. The only word sizes with official test vectors are the 32-bit and 64-bit variants of RadioGatún. The algorithm uses 58 words, each using w bits, to store its internal state, so the 32-bit version needs 232 bytes to store its state (since each word needs 32 bits or four bytes, and 58 multiplied by four is 232) and the 64-bit version 464 bytes (each word using eight bytes). Although RadioGatún is a derivative of Panama, a stream cipher and hash construction from the late 1990s whose hash construction has been broken, RadioGatún does not have Panama's weaknesses when used as a hash function. As of 2022, RadioGatún is still a secure hash function; the largest version of RadioGatún that is broken is the one with a word size of two bits. RadioGatún has a claimed security strength of 304 bits for the 32-bit version and 608 bits for the 64-bit version. The best known cryptanalysis has not broken this claim: It needs 352 bits of work for the 32-bit version and 704 bits of work for the 64-bit version. RadioGatún can be used either as a hash function or a stream cipher; it can output an arbitrarily long stream of pseudo-random numbers; this kind of hash construction is now known as an "extendable-output function" (XOF).

Claimed strength The algorithm's designers, in the original RadioGatún paper, claimed that the first 19 × w bits (where w is the word width used) of RadioGatún's output is a cryptographically secure hash function. Since publishing the paper, the designers revised their security claim, and now claim that RadioGatún has the security of a cryptographic sponge function with a capacity of 19w. This means that the 32-bit version of RadioGatún can be used to make a hash with 304 bits of security (both from collision attacks and from Preimage attacks), and the 64-bit version offers 608 bits of security.

Implementation details The designers call RadioGatún an "ideal mangling function". RadioGatún uses a "belt" and "mill" to cryptographically process binary data, with the majority of mangling operations performed on the "mill" part of RadioGatún. Keccak removed the belt, increased the size of the mill from 19 words to 25 words, and made the mill function somewhat more complicated. The core belt function looks like this:

And the mill function Mill(A) looks like this:

The Wikibooks page on RadioGatún provides full implementation details, and Module:RadioGatun32 is an implementation of the 32-bit version of RadioGatún.

Cryptanalysis In the paper "Two attacks on RadioGatún", Dmitry Khovratovich presents two attacks that do not break the designers' security claims, one with a complexity of 218w and another with a complexity of 223.1w. Khovratovich also authored a paper, entitled "Cryptanalysis of hash functions with structures", which describes an attack with a complexity of 218w. In the paper "Analysis of the Collision Resistance of RadioGatún using Algebraic Techniques", Charles Bouillaguet and Pierre-Alain Fouque present a way of generating collisions with the 1-bit version of the algorithm using an attack that needs 224.5 operations. The attack can not be extended to larger versions since "all the possible trails we knew for the 1-bit version turned out to be impossible to extend to n-bit versions." This attack is less effective than the other attacks and also does not break RadioGatún's security claim. The most effective attack against the algorithm, one with a complexity of 211w, is given in the paper "Cryptanalysis of RadioGatun" by Thomas Fuhr and Thomas Peyrin. In the paper, they break the 2-bit (word size of two) version of RadioGatún. While more effective than the other attacks, this attack still does not break the security claim. The developers of RadioGatún have stated that their "own experiments did not inspire confidence in RadioGatún".

Test vectors The only RadioGatún variants that the designers supplied test vectors (published hash values for sample inputs so programmers can verify they are correctly implementing the algorithm) for are the 32-bit and 64-bit versions.

RadioGatún[32] These test vectors, generated using the 32-bit version of RadioGatún, only show the first 256 bits of RadioGatún[32]'s arbitrarily long output stream:

RadioGatun[32]("") = F30028B54AFAB6B3E55355D277711109A19BEDA7091067E9A492FB5ED9F20117

RadioGatun[32]("The quick brown fox jumps over the lazy dog") = 191589005FEC1F2A248F96A16E9553BF38D0AEE1648FFA036655CE29C2E229AE

RadioGatun[32]("The quick brown fox jumps over the lazy cog") = EBDC1C8DCD54DEB47EEEFC33CA0809AD23CD9FFC0B5254BE0FDABB713477F2BD

RadioGatún[64] Here are hashes for the 64-bit version:

RadioGatun[64]("") = 64A9A7FA139905B57BDAB35D33AA216370D5EAE13E77BFCDD85513408311A584

RadioGatun[64]("The quick brown fox jumps over the lazy dog") = 6219FB8DAD92EBE5B2F7D18318F8DA13CECBF13289D79F5ABF4D253C6904C807

RadioGatun[64]("The quick brown fox jumps over the lazy cog") = C06265CAC961EA74912695EBF20F1C256A338BC0E980853A3EEF188D4B06FCE5

References

External links

The RadioGatún Hash Function Family, RadioGatún's official web page, with the hash's official description, public domain reference code, and test vectors rg32hash, an independent public-domain implementation of the 32-bit version of RadioGatún

Illustrations

Worked examples

Example 1 — a first encounter with RadioGatún

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

In research: RadioGatún appears in mathematics 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 RadioGatún 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: RadioGatún is common in secondary-school and first-year university syllabi. It links to neighbouring topics Block ciphers, Cryptographic hash functions, Extendable-output functions, so understanding it makes those chapters shorter.
In everyday life: Look for RadioGatún 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “RadioGatún” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study RadioGatún in 20 minutes

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

Frequently asked questions

What is RadioGatún in simple terms?

Why does RadioGatún matter?

Because it connects several mathematics 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 RadioGatún?

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 RadioGatún.