V O R T E X
A family of one way hash functions
based on Rijndael rounds and multiplication
“Security Enhancement of the Vortex Family of Hash Functions”, by Michael Kounavis and Shay Gueron, May 2009. This paper addresses some recently published attacks on the Vortex family.
Vortex is a new family of one way hash functions that can produce message digests of 224, 256, 384 and 512 bits. The main idea behind the design of these hash functions is to use well known algorithms that can support very fast diffusion in a small number of steps. Vortex also balances the cryptographic strength that comes from iterating block cipher rounds with SBox substitution and diffusion (like Whirlpool) against the need to have a lightweight implementation with as small number of rounds as possible. Vortex uses a variable number of Rijndael rounds with a stronger key schedule. Rijndael rounds are followed by a variant of Galois Field (or integer) multiplication. This achieves cross-mixing between 128-bit or 256-bit sets. Vortex uses the Enveloped Merkle-Damgård construction to support properties such as collision resistance, first and second pre-image resistance, pseudorandom oracle preservation and pseudorandom function preservation. The Vortex SHA-3 submission document provides analytical results that demonstrate that the number of queries required for finding a collision with probability greater or equal to 0.5 in an ideal block cipher approximation of Vortex 256 is at least 1.18•2122.55 if the attacker uses randomly selected message words. The main strength of the Vortex design is that this hash function can demonstrate high performance in future processors with instruction set support for AES rounds and carry-less multiplication.
Shay Gueron and Michael Kounavis: “Vortex: A New Family of One Way Hash Functions based on AES rounds and Carry-less Multiplication”, Proceedings, ISC 2008. This paper describes the first design of the Vortex family called “Vortex 0”.
Shay Gueron and Michael Kounavis: “Vortex: A New Family of One Way Hash Functions based on Rijndael rounds and Carry-less Multiplication”, Submission to NIST, 2008. This paper describes Vortex as submitted to the SHA-3 competition.
Michael Kounavis and Shay Gueron: “Security Enhancement of the Vortex Family of Hash Functions”, May 2009. This paper addresses some recently published attacks on the Vortex family.
Shay Gueron and Michael Kounavis: “The Vortex Software Submission Package”, Submission to NIST, 2008. This zip file contains Vortex implementations and test vectors.
An implementation with our latest amendments will be posted soon.
Shay Gueron is an Associate Professor at the
Department of Mathematics in the Faculty of Science at the
Michael E Kounavis is a Senior Research Scientist working with the Corporate Technology Group at Intel Corporation.
Last updated 05/28/2009