RadioGatún

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, 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 and the 64-bit version 464 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".

Claimed strength

The algorithm's designers, in the original RadioGatún paper, claimed that the first 19 × w bits 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, 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:

= R
for row = 0 to 2 do
for all i do
B = b
end for
end for
for i = 0 to 11 do
B = B ⊕ a
end for
A = Mill
b = B
for i = 0 to 2 do
A = A ⊕ b
end for

And the mill function Mill looks like this:

for all i do
A = a ⊕
end for
for all i do
a = A ≫ i/2
end for
for all i do
A = a ⊕ a ⊕ a
end for
A = A ⊕ 1

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 2^18w and another with a complexity of 2^23.1w. Khovratovich also authored a paper, entitled "Cryptanalysis of hash functions with structures", which describes an attack with a complexity of 2^18w.
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 2^24.5 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 2^11w, is given in the paper "Cryptanalysis of RadioGatun" by Thomas Fuhr and Thomas Peyrin. In the paper, they break the 2-bit 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 for are the 32-bit and 64-bit versions.

RadioGatún32

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

RadioGatún64

Here are hashes for the 64-bit version:
RadioGatun =
64A9A7FA139905B57BDAB35D33AA216370D5EAE13E77BFCDD85513408311A584
RadioGatun =
6219FB8DAD92EBE5B2F7D18318F8DA13CECBF13289D79F5ABF4D253C6904C807
RadioGatun =
C06265CAC961EA74912695EBF20F1C256A338BC0E980853A3EEF188D4B06FCE5