Abstract. We propose a family of compression functions built from fixed-key blockciphers and investigate their collision and preimage security in the ideal-cipher model. The constructions have security approaching and in many cases equaling the security upper bounds found in previous work of the authors [24]. In particular, we describe a 2n-bit to n-bit compression function using three n-bit permutation calls that has collision security N 0.5,whereN =2 n, and we describe 3n-bit to 2n-bit compression functions using five and six permutation calls and having collision security of at least N 0.55 and N 0.63. Key words: blockcipher-based hashing, collision-resistant hashing, compression functions, cryptographic hash functions, ideal-cipher model. 1

Abstract. Due to recent breakthroughs in hash functions cryptanalysis, some new hash schemes have been proposed. GRINDAHL is a novel hash function, designed by Knudsen, Rechberger and Thomsen and published at FSE 2007. It has the particularity that it follows the RIJNDAEL design strategy, with an efficiency comparable to SHA-256. This paper provides the first cryptanalytic work on this new scheme. We show that the 256-bit version of GRINDAHL is not collision resistant. With a work effort of approximatively 2 112 hash computations, one can generate a collision. Key words: GRINDAHL, hash functions, RIJNDAEL. 1

At ASIACRYPT’06, Chang et al. analyzed the indifferentiability of some popular hash functions based on block ciphers, namely, the twenty collision resistant PGV, the MDC2 and the PBGV hash functions, etc. In particular, two indifferentiable attacks were presented on the four of the twenty collision resistant PGV and the PBGV hash functions with the prefix-free padding. In this article, a synthetic indifferentiability analysis of some block-cipher-based hash functions is considered. First, a more precise definition is proposed on the indifferentiability adversary in block-cipher-based hash functions. Next, the advantage of indifferentiability is extended by considering whether the hash function is keyed or not. Finally, a limitation is observed in Chang et al.’s indifferentiable attacks on the four PGV and the PBGV hash functions. The formal proofs show the fact that those hash functions are indifferentiable from a random oracle in the ideal cipher model with the prefix-free padding, the NMAC/HMAC and the chop construction. 1

Abstract. The security challenges posed by RFID-tag deployments are wellknown. In response there is a rich literature on new cryptographic protocols and an on-tag hash function is often assumed by protocol designers. Yet cheap tags pose severe implementation challenges and it is far from clear that a suitable hash function even exists. In this paper we consider the options available, including constructions based around compact block ciphers. While we describe the most compact hash functions available today, our work serves to highlight the difficulties in designing lightweight hash functions and (echoing [17]) we urge caution when routinely appealing to a hash function in an RFID-tag protocol. 1

Abstract. We analyse the Double-Mix Merkle-Damg˚ard construction (DMMD) used in the AU-RORA family of hash functions. We show that DMMD falls short of providing the expected level of security. Specifically, we are able to find 2nd pre-images for AURORA-512 in time 2 291, and collisions in time 2 234.4. A limited-memory variant finds collisions in time 2 249. 1

Abstract. In this paper, we introduce a new notion of security, called adaptive preimage resistance. We prove that a compression function that is collision resistant and adaptive preimage resistant can be combined with a public random function to yield a hash function that is indifferentiable from a random oracle. Specifically, we analyze adaptive preimage resistance of 2n-bit to n-bit compression functions that use three calls to n-bit public random permutations. This analysis also provides a simpler proof of their collision resistance and preimage resistance than the one provided by Rogaway and Steinberger [19]. By using such compression functions as building blocks, we obtain permutation-based pseudorandom oracles that outperform the Sponge construction [4] and the MD6 compression function [9] both in terms of security and efficiency.

most basic ways to construct a hash function from a block cipher, and regarded 12 of those 64 schemes as secure. Black, Pogaway and Shrimpton[3](BRS) provided a formal and quantitative treatment of those 64 constructions and proved that, in black-box model, the 12 schemes ( group − 1) that PGV singled out as secure really are secure. By stepping outside of the Merkle-Damg˚ard[4] approach to analysis, an additional 8 (group − 2) of the 64 schemes are just as collision resistant as the first group of schemes. Tight upper and lower bounds on collision resistance of those 20 schemes were given. In this paper, those collision resistance and preimage resistance bounds are improved, which shows that, in black box model, collision bounds of those 20 schemes are same. In Group − 1 schemes, 8 out of 12 can find fixed point easily. Bounds on second preimage, multicollisions of Joux[6], fixed-point multicollisons[8] and combine of the two kinds multicollisions are also given. From those bound, Group − 1 schemes can also be deviled into two group. Key Words: Hash Function, Block Cipher, M-D Construction 1

(on the leave to Bauhaus-University Weimar, Germany) Abstract. This paper proposes a construction for collision resistant 2n-bit hash functions, based on n-bit block ciphers with 2n-bit keys. The construction is analysed in the ideal cipher model; for n = 128 an adversary would need roughly 2 122 units of time to find a collision. The construction employs “combinatorial ” hashing as an underlying building block (like Universal Hashing for cryptographic message authentication by Wegman and Carter). The construction runs at rate 1, thus improving on a similar rate 1/2 approach by Hirose (FSE 2006). 1

Abstract. In this paper, we give a security proof for Abreast-DM in terms of collision resistance and preimage resistance. As old as Tandem-DM, the compression function Abreast-DM is one of the most well-known constructions for double block length compression functions. The bounds on the number of queries for collision resistance and preimage resistance are given by O (2 n). Based on a novel technique using query-response cycles, our security proof is simpler than those for MDC-2 and Tandem-DM. We also present a wide class of Abreast-DM variants that enjoy a birthday-type security guarantee with a simple proof. 1

Abstract. In this paper, we study security for a certain class of permutation-based compression functions. Denoted lp231 in [12], they are 2n-bit to n-bit compression functions using three calls to a single n-bit random permutation. We prove that lp231 is asymptotically preimage resistant up to (2 2n 3 /n) queries, adaptive preimage resistant up to (2 n 2 /n) queries/commitments, and collision resistant up to (2 n 2 /n 1+ɛ) queries for ɛ> 0. 1