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. 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.

Abstract. Tweakable blockciphers, first formalized by Liskov, Rivest, and Wagner [13], are blockciphers with an additional input, the tweak, which allows for variability. An open problem proposed by Liskov et al. is how to construct tweakable blockciphers without using a pre-existing blockcipher. This problem has yet to receive any significant study. There are many natural questions in this area: is it significantly more efficient to incorporate a tweak directly? How do direct constructions compare to existing techniques? Are these direct constructions optimal and for what levels of security? How large of a tweak can be securely added? In this work, we address these questions for Luby-Rackoff blockciphers. We show that tweakable blockciphers can be created directly from Feistel ciphers, and in some cases show that direct constructions of tweakable blockciphers are more efficient than previously known constructions. 1

The security of iterated hash functions relies on the properties of underlying compression functions. We study highly efficient compression functions based on block ciphers. We propose a model for highrate compression functions, and give an upper bound for the rate of any collision resistant compression function in our model. In addition, we show that natural generalizations of constructions by Preneel, Govaerts, and Vandewalle to the case of rate-2 compression functions are not collision resistant.

This report describes and analyzes the MD6 hash function and is part of our submission package for MD6 as an entry in the NIST SHA-3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desired size from 1 to 512 bits, inclusive, including

Abstract. In this paper, we study the security of permutation based hash functions, i.e. blockcipher based hash functions with fixed keys. SMASH is such a hash function proposed by Knudsen in 2005 and broken the same year by Pramstaller et al. Here we show that the two tweaked versions, proposed soon after by Knudsen to thwart the attack, can also be attacked in collision in time O(n2 n/3). This time complexity can be reduced to O(2 2 √ n) for the first tweak version, which means an attack against SMASH-256 in c ·2 32 for a small constant c. Then, we show that an efficient generalization of SMASH, using two permutations instead of one, can be proved secure against collision in the ideal-cipher model in Ω(2 n/4) queries to the permutations. In order to analyze the tightness of our proof, we devise a non-trivial attack in O(2 3n/8) queries. Finally, we also prove that our construction is preimage resistant in Ω(2 n/2) queries, which the best security level that can be reached for 2-permutation based hash functions, as proved in [12]. 1

The security notion of indifferentiability was proposed by Maurer, Renner, and Holenstein in 2004. In 2005, Coron, Dodis, Malinaud, and Puniya discussed the indifferentiability of hash functions. They showed that the Merkle-Damg˚ard construction is not secure in the sense of indifferentiability. In this paper, we analyze the security of single-block-length and rate-1 compression functions in the sense of indifferentiability. We formally show that all single-block-length and rate-1 compression functions, which include the Davies-Meyer compression function, are insecure. Furthermore, we show how to construct a secure single-block-length and rate-1 compression function in the sense of indifferentiability. This does not contradict our result above. 1

ii To my best friend and my parents. iii Table of Contents Acknowledgments vi

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