Affiliation:
1. CISUC, Dept. of Informatics Engineering, University of Coimbra , Coimbra Portugal
Abstract
Abstract
At ProvSec 2013, Minematsu presented the circulant hash, an almost-xor universal hash using only the xor and rotation operations. The circulant hash is a variant of Carter and Wegman’s H
3 hash as well as Krawczyk’s Toeplitz hash, both of which are hashes based on matrix-vector multiplication over 𝔽2. In this paper we revisit the circulant hash and reinterpret it as a multiplication in the polynomial ring 𝔽2[x]/(xn
+ 1). This leads to simpler proofs, faster implementations in modern computer chips, and newer variants with practical implementation advantages.
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications