Linear Analysis of Reduced-Round CubeHash

Recent developments in the field of cryptanalysis of hash functions has inspired NIST to announce a competition for selecting a new cryptographic hash function to join the SHA family of standards. One of the 14 second-round candidates is CubeHash designed by Daniel J. Bernstein. CubeHash is a unique hash function in the sense that it does not iterate a common compression function, and offers a structure which resembles a sponge function, even though it is not exactly a sponge function. In this paper we analyze reduced-round variants of CubeHash where the adversary controls the full 1024-bit input to reduced-round CubeHash and can observe its full output. We show that linear approximations with high biases exist in reduced-round variants. For example, we present an 11-round linear approximation with bias of 2^{−235}, which allows distinguishing 11-round CubeHash using about 2^{470} queries. We also discuss the extension of this distinguisher to 12 rounds using message modification techniques. Finally, we present a linear distinguisher for 14-round CubeHash which uses about 2^{812} queries

Analysis of ARX Functions: Pseudo-linear Methods for Approximation, Differentials, and Evaluating Diffusion

This paper explores the approximation of addition mod $2^n$ by addition mod $2^w$, where $1 \le w \le n$, in ARX functions that use large words (e.g., 32-bit words or 64-bit words). Three main areas are explored. First, \emph{pseudo-linear approximations} aim to approximate the bits of a $w$-bit window of the state after some rounds. Second, the methods used in these approximations are also used to construct truncated differentials. Third, branch number metrics for diffusion are examined for ARX functions with large words, and variants of the differential and linear branch number characteristics based on pseudo-linear methods are introduced. These variants are called \emph{effective differential branch number} and \emph{effective linear branch number}, respectively. Applications of these approximation, differential, and diffusion evaluation techniques are demonstrated on Threefish-256 and Threefish-512

Multiple modular additions and crossword puzzle attack on NLSv2

NLS is a stream cipher which was submitted to the eSTREAM project. A linear distinguishing attack against NLS was presented by Cho and Pieprzyk, which was called Crossword Puzzle (CP) attack. NLSv2 is a tweak version of NLS which aims mainly at avoiding the CP attack. In this paper, a new distinguishing attack against NLSv2 is presented. The attack exploits high correlation amongst neighboring bits of the cipher. The paper first shows that the modular addition preserves pairwise correlations as demonstrated by existence of linear approximations with large biases. Next, it shows how to combine these results with the existence of high correlation between bits 29 and 30 of the S-box to obtain a distinguisher whose bias is around 2^−37. Consequently, we claim that NLSv2 is distinguishable from a random cipher after observing around 2^74 keystream words

Multiple Modular Additions and Crossword Puzzle Attack on NLSv2” , available at: www.ecrypt.eu.org/stream

Abstract. NLS is a stream cipher which was submitted to the eSTREAM project. A linear distinguishing attack against NLS was presented by Cho and Pieprzyk, which was called Crossword Puzzle (CP) attack. NLSv2 is the tweak version of NLS which aims mainly at avoiding the CP attack. In this paper, a new distinguishing attack against NLSv2 is presented. The attack exploits high correlation amongst neighboring bits of the cipher. The paper first shows that the modular addition preserves pairwise correlations as demonstrated by existence of linear approximations with large biases. Next it shows how to combine these results with the existence of high correlation between bits 29 and 30 of the S-box to obtain a distinguisher whose bias is around 2 −37. Consequently, we claim that NLSv2 is distinguishable from a random process after observing around 2 74 keystream words