Really Fast Syndrome-Based Hashing

The FSB (fast syndrome-based) hash function was submitted to the SHA-3 competition by Augot, Finiasz, Gaborit, Manuel, and Sendrier in 2008, after preliminary designs proposed in 2003, 2005, and 2007. Many FSB parameter choices were broken by Coron and Joux in 2004, Saarinen in 2007, and Fouque and Leurent in 2008, but the basic FSB idea appears to be secure, and the FSB submission remains unbroken. On the other hand, the FSB submission is also quite slow, and was not selected for the second round of the competition. This paper introduces RFSB, an enhancement to FSB. In particular, this paper introduces the RFSB-509 compression function, RFSB with a particular set of parameters. RFSB-509, like the FSB-256 compression function, is designed to be used inside a 256-bit collision-resistant hash function: all known attack strategies cost more than 2 to find collisions in RFSB-509. However, RFSB-509 is an order of magnitude faster than FSB-256. On a single core of a Core 2 Quad Q9550 CPU, RFSB-509 runs at 10.67 cycles/byte: faster than SHA-256, faster than 7 of the 14 secondround SHA-3 candidates, and faster than 3 of the 5 SHA-3 finalists.