Collision Attacks against the Knudsen-Preneel Compression Functions

Knudsen and Preneel (Asiacrypt'96 and Crypto'97) introduced a hash function design in which a linear error-correcting code is used to build a wide-pipe compression function from underlying blockciphers operating in Davies-Meyer mode. Their main design goal was to deliver compression functions with collision resistance up to, and even beyond, the block size of the underlying blockciphers. In this paper, we present new collision-finding attacks against these compression functions using the ideas of an unpublished work of Watanabe and the preimage attack of Ozen, Shrimpton, and Stain (FSE'10). In brief, our best attack has a time complexity strictly smaller than the block-size for all but two of the parameter sets. Consequently, the time complexity lower bound proven by Knudsen and Preneel is incorrect and the compression functions do not achieve the security level they were designed for.

Design and Analysis of Multi-Block-Length Hash Functions

Onur Özen

Cryptographic hash functions are used in many cryptographic applications, and the design of provably secure hash functions (relative to various security notions) is an active area of research. Most of the currently existing hash functions use the Merkle-Damgård paradigm, where by appropriate iteration the hash function inherits its collision and preimage resistance from the underlying compression function. Compression functions can either be constructed from scratch or be built using well-known cryptographic primitives such as a blockcipher. One classic type of primitive-based compression functions is single-block-length : It contains designs that have an output size matching the output length n of the underlying primitive. The single-block-length setting is well-understood. Yet even for the optimally secure constructions, the (time) complexity of collision- and preimage-finding attacks is at most 2n/2, respectively 2n ; when n = 128 (e.g., Advanced Encryption Standard) the resulting bounds have been deemed unacceptable for current practice. As a remedy, multi-block-length primitive-based compression functions, which output more than n bits, have been proposed. This output expansion is typically achieved by calling the primitive multiple times and then combining the resulting primitive outputs in some clever way. In this thesis, we study the collision and preimage resistance of certain types of multi-call multi-block-length primitive-based compression (and the corresponding Merkle-Damgård iterated hash) functions : Our contribution is three-fold. First, we provide a novel framework for blockcipher-based compression functions that compress 3n bits to 2n bits and that use two calls to a 2n-bit key blockcipher with block-length n. We restrict ourselves to two parallel calls and analyze the sufficient conditions to obtain close-to-optimal collision resistance, either in the compression function or in the Merkle-Damgård iteration. Second, we present a new compression function h: {0,1}3n → {0,1}2n ; it uses two parallel calls to an ideal primitive (public random function) from 2n to n bits. This is similar to MDC-2 or the recently proposed MJH by Lee and Stam (CT-RSA'11). However, unlike these constructions, already in the compression function we achieve that an adversary limited (asymptotically in n) to O (22n(1-δ)/3) queries (for any δ > 0) has a disappearing advantage to find collisions. This is the first construction of this type offering collision resistance beyond 2n/2 queries. Our final contribution is the (re)analysis of the preimage and collision resistance of the Knudsen-Preneel compression functions in the setting of public random functions. Knudsen-Preneel compression functions utilize an [r,k,d] linear error-correcting code over 𝔽2e (for e > 1) to build a compression function from underlying blockciphers operating in the Davies-Meyer mode. Knudsen and Preneel show, in the complexity-theoretic setting, that finding collisions takes time at least 2(d-1)n2. Preimage resistance, however, is conjectured to be the square of the collision resistance. Our results show that both the collision resistance proof and the preimage resistance conjecture of Knudsen and Preneel are incorrect : With the exception of two of the proposed parameters, the Knudsen-Preneel compression functions do not achieve the security level they were designed for.

EPFL2012

Attacking the Knudsen-Preneel Compression Functions

Onur Özen, Martijn Stam

Knudsen and Preneel (Asiacrypt’96 and Crypto’97) introduced a hash function design in which a linear error-correcting code is used to build a wide-pipe compression function from underlying blockciphers operating in Davies-Meyer mode. In this paper, we (re)analyse the preimage resistance of the Knudsen-Preneel compression functions in the setting of public random functions. We give a new non-adaptive preimage attack, beating the one given by Knudsen and Preneel, that is optimal in terms of query complexity. Moreover, our new attack falsifies their (conjectured) preimage resistance security bound and shows that intuitive bounds based on the number of ‘active’ components can be treacherous. Complementing our attack is a formal analysis of the query complexity (both lower and upper bounds) of preimage-finding attacks. This analysis shows that for many concrete codes the time complexity of our attack is optimal.

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

Analysis and design of symmetric cryptographic algorithms

Jean-Philippe Aumasson

This thesis is concerned with the analysis and design of symmetric cryptographic algorithms, with a focus on real-world algorithms. The first part describes original cryptanalysis results, including: The first nontrivial preimage attacks on the (reduced) hash function MD5, and on the full HAVAL. Our results were later improved by Sasaki and Aoki, giving a preimage attack on the full MD5. The best key-recovery attacks so far on reduced versions of the stream cipher Salsa20, selected by the European Network of Excellence ECRYPT as a recommendation for software applications, and one of the two ciphers (with AES) in the NaCl cryptographic library. The academic break of the block cipher MULTI2, used in the Japanese digital-TV standard ISDB. While MULTI2 was designed in 1988, our results are the first analysis of MULTI2 to appear as an international publication. We then present a general framework for distinguishers on symmetric cryptographic algorithms, based on the cube attacks of Dinur and Shamir: our cube testers build on algebraic property-testing algorithms to mount distinguishers on algorithms that possess some efficiently testable structure. We apply cube testers to some well known algorithms: On the compression function of MD6, we distinguish 18 rounds (out of 80) from a random function. On the stream cipher Trivium, we obtain the best distinguisher known so far, reaching 885 rounds out of 1152. On the stream cipher Grain-128, using FPGA devices to run high-complexity attacks, we obtain the best distinguisher known so far, and can conjecture the existence of a shortcut attack on the full Grain-128. These results were presented at FSE 2008, SAC 2008, FSE 2009, and SHARCS 2009. The second part of this thesis presents a new hash function, called BLAKE, which we submitted to the NIST Hash Competition. Besides a complete specification, we report on our implementations of BLAKE in hardware and software, and present a preliminary security analysis. As of August 2009, BLAKE is one of the 14 submissions accepted as Second Round Candidates by NIST, and no attack on BLAKE is known.