RadioGatún
RadioGatún is a cryptographic hash primitive created by Guido Bertoni, , Michaël Peeters, and . It was first publicly presented at the NIST Second Cryptographic Hash Workshop, held in , on August 24–25, 2006, as part of the NIST hash function competition.
Although RadioGatún is a derivative of Panama, a 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.
RadioGatún is actually a family of 64 different hash functions, distinguished by a single parameter, the word width in bits (w), adjustable between 1 and 64. The algorithm uses 58 words, each of size w, to store its internal state. Thus, for example, the 32-bit version needs 232 bytes to store its state and the 64-bit version 464 bytes.
RadioGatún can be used either as a hash function or a stream cipher; it can output an arbitrarily long stream of ; this kind of hash construction is now known as an “Extendable-Output Function” (XOF).
The same team that developed RadioGatún went on to make considerable revisions to this , leading to the Keccak SHA-3 algorithm.
Contents
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. In other words, they claimed that the first 608 bits of the 32-bit version and 1216 bits of the 64-bit version of RadioGatún can be used as a cryptographic hash value.
In light of the , this means that for a given word width w, RadioGatún is designed to have no attack with complexity less than 2<sup>9.5w</sup>. This corresponds to 2<sup>304</sup> for the 32-bit version and 2<sup>608</sup> for the 64-bit version.
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 (both from collision attacks and from ), and the 64-bit version offers 608 bits of security.
Cryptanalysis
In the paper “Two attacks on RadioGatún”, Dmitry Khovratovich and present two attacks that do not break the designers’ security claims, one with a complexity of 2<sup>18w</sup> and another with a complexity of 2<sup>23.1w</sup>. Khovratovich also authored a paper, entitled “Cryptanalysis of hash functions with structures”, which describes an attack with a complexity of 2<sup>18w</sup>.
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<sup>24.5</sup> 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<sup>11w</sup>, is given in the paper “Cryptanalysis of RadioGatun” by Thomas Fuhr and Thomas Peyrin. 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.
These test vectors only show the first 256 bits of the output of RadioGatún’s arbitrarily long output stream:
RadioGatun[32]("") = F30028B54AFAB6B3E55355D277711109A19BEDA7091067E9A492FB5ED9F20117 RadioGatun[32]("The quick brown fox jumps over the lazy og") = 191589005FEC1F2A248F96A16E9553BF38D0AEE1648FFA036655CE29C2E229AE RadioGatun[32]("The quick brown fox jumps over the lazy og") = EBDC1C8DCD54DEB47EEEFC33CA0809AD23CD9FFC0B5254BE0FDABB713477F2BD And hashes in 64-bit version:
RadioGatun[64]("") = 64A9A7FA139905B57BDAB35D33AA216370D5EAE13E77BFCDD85513408311A584 RadioGatun[64]("The quick brown fox jumps over the lazy og") = 6219FB8DAD92EBE5B2F7D18318F8DA13CECBF13289D79F5ABF4D253C6904C807 RadioGatun[64]("The quick brown fox jumps over the lazy og") = C06265CAC961EA74912695EBF20F1C256A338BC0E980853A3EEF188D4B06FCE5