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Salvaging MerkleDamg˚ard for Practical Applications
, 2009
"... Many cryptographic applications of hash functions are analyzed in the random oracle model. Unfortunately, most concrete hash functions, including the SHA family, use the iterative (strengthened) MerkleDamg˚ard transform applied to a corresponding compression function. Moreover, it is well known tha ..."
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Cited by 20 (2 self)
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Many cryptographic applications of hash functions are analyzed in the random oracle model. Unfortunately, most concrete hash functions, including the SHA family, use the iterative (strengthened) MerkleDamg˚ard transform applied to a corresponding compression function. Moreover, it is well known that the resulting “structured ” hash function cannot be generically used as a random oracle, even if the compression function is assumed to be ideal. This leaves a large disconnect between theory and practice: although no attack is known for many concrete applications utilizing existing (MerkleDamg˚ard based) hash functions, there is no security guarantee either, even by idealizing the compression function. Motivated by this question, we initiate a rigorous and modular study of developing new notions of (still idealized) hash functions which would be (a) natural and elegant; (b) sufficient for arguing security of important applications; and (c) provably met by the (strengthened) MerkleDamg˚ard transform, applied to a “strong enough ” compression function. In particular, we show that a fixedlength compressing random oracle, as well as the currently used DaviesMeyer compression function (the latter analyzed in the ideal cipher model) are “strong enough ” for the two specific weakenings of the random oracle that we develop. These weaker notions, described below, are quite natural and should be interesting in their own right: • Preimage Aware Functions. Roughly, if an attacker found a “later useful ” output y of the function, then it must
Constructing cryptographic hash functions from fixedkey blockciphers. Full version of this paper
, 2008
"... Abstract. We propose a family of compression functions built from fixedkey blockciphers and investigate their collision and preimage security in the idealcipher model. The constructions have security approaching and in many cases equaling the security upper bounds found in previous work of the aut ..."
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Cited by 18 (5 self)
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Abstract. We propose a family of compression functions built from fixedkey blockciphers and investigate their collision and preimage security in the idealcipher 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 2nbit to nbit compression function using three nbit permutation calls that has collision security N 0.5,whereN =2 n, and we describe 3nbit to 2nbit compression functions using five and six permutation calls and having collision security of at least N 0.55 and N 0.63. Key words: blockcipherbased hashing, collisionresistant hashing, compression functions, cryptographic hash functions, idealcipher model. 1
Careful with composition: Limitations of the indifferentiability framework
 EUROCRYPT 2011, volume 6632 of LNCS
, 2011
"... We exhibit a hashbased storage auditing scheme which is provably secure in the randomoracle model (ROM), but easily broken when one instead uses typical indifferentiable hash constructions. This contradicts the widely accepted belief that the indifferentiability composition theorem applies to any ..."
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Cited by 11 (1 self)
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We exhibit a hashbased storage auditing scheme which is provably secure in the randomoracle model (ROM), but easily broken when one instead uses typical indifferentiable hash constructions. This contradicts the widely accepted belief that the indifferentiability composition theorem applies to any cryptosystem. We characterize the uncovered limitation of the indifferentiability framework by showing that the formalizations used thus far implicitly exclude security notions captured by experiments that have multiple, disjoint adversarial stages. Examples include deterministic publickey encryption (PKE), passwordbased cryptography, hash function nonmalleability, keydependent message security, and more. We formalize a stronger notion, reset indifferentiability, that enables an indifferentiabilitystyle composition theorem covering such multistage security notions, but then show that practical hash constructions cannot be reset indifferentiable. We discuss how these limitations also affect the universal composability framework. We finish by showing the chosendistribution attack security (which requires a multistage game) of some important publickey encryption schemes built using a hash construction paradigm introduced by Dodis, Ristenpart, and Shrimpton. 1
The security of abreastdm in the ideal cipher model
"... Abstract. In this paper, we give a security proof for AbreastDM in terms of collision resistance and preimage resistance. As old as TandemDM, the compression function AbreastDM is one of the most wellknown constructions for double block length compression functions. The bounds on the number of q ..."
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Cited by 6 (3 self)
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Abstract. In this paper, we give a security proof for AbreastDM in terms of collision resistance and preimage resistance. As old as TandemDM, the compression function AbreastDM is one of the most wellknown 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 queryresponse cycles, our security proof is simpler than those for MDC2 and TandemDM. We also present a wide class of AbreastDM variants that enjoy a birthdaytype security guarantee with a simple proof. 1
Adaptive Preimage Resistance and Permutationbased Hash Functions. Available at http://eprint.iacr.org/2009/066
"... 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 ..."
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Cited by 4 (1 self)
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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 2nbit to nbit compression functions that use three calls to nbit 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 permutationbased pseudorandom oracles that outperform the Sponge construction [4] and the MD6 compression function [9] both in terms of security and efficiency.
A Modular Design for Hash Functions: Towards Making the MixCompressMix Approach Practical
, 2009
"... The design of cryptographic hash functions is a very complex and failureprone process. For this reason, this paper puts forward a completely modular and faulttolerant approach to the construction of a fullfledged hash function from an underlying simpler hash function H and a further primitive F ..."
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Cited by 2 (0 self)
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The design of cryptographic hash functions is a very complex and failureprone process. For this reason, this paper puts forward a completely modular and faulttolerant approach to the construction of a fullfledged hash function from an underlying simpler hash function H and a further primitive F (such as a block cipher), with the property that collision resistance of the construction only relies on H, whereas indifferentiability from a random oracle follows from F being ideal. In particular, the failure of one of the two components must not affect the security property implied by the other component. The MixCompressMix (MCM) approach by Ristenpart and Shrimpton (ASIACRYPT 2007) envelops the hash function H between two injective mixing steps, and can be interpreted as a first attempt at such a design. However, the proposed instantiation of the mixing steps, based on block ciphers, makes the resulting hash function impractical: First, it cannot be evaluated online, and second, it produces larger hash values than H, while only inheriting the collisionresistance guarantees for the shorter output. Additionally, it relies on a trapdoor oneway permutation, which seriously compromises the use of the resulting hash function for random oracle instantiation in certain scenarios. This paper presents the first efficient modular hash function with online evaluation and short output length. The core of our approach are novel blockcipher based designs for the mixing steps of the MCM approach which rely on significantly weaker assumptions: The first mixing step is realized without any computational assumptions (besides the underlying cipher being ideal), whereas the second mixing step only requires a oneway permutation without a trapdoor, which we prove to be the minimal assumption for the construction of injective random oracles.
S.: Some observations on indifferentiability
 In: Information Security and Privacy. Lecture Notes in Computer Science
, 2010
"... Abstract. At Crypto 2005, Coron et al. introduced a formalism to study the presence or absence of structural flaws in iterated hash functions: If one cannot differentiate a hash function using ideal primitives from a random oracle, it is considered structurally sound, while the ability to differenti ..."
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Abstract. At Crypto 2005, Coron et al. introduced a formalism to study the presence or absence of structural flaws in iterated hash functions: If one cannot differentiate a hash function using ideal primitives from a random oracle, it is considered structurally sound, while the ability to differentiate it from a random oracle indicates a structural weakness. This model was devised as atool tosee subtle real world weaknesses while in the random oracle world. In this paper we take in a practical point of view. We show, using well known examples like NMACand the MixCompressMix (MCM) construction, how we can prove a hash construction secure and insecure at the same time in the indifferentiability setting. These constructions do not differ in their implementation but only on an abstract level. Naturally, this gives rise to the question what to conclude for the implemented hash function. Ourresultscastdoubtsaboutthenotionof“indifferentiabilityfromarandomoracle ” tobeamandatory, practically relevant criterion (as e.g., proposed by Knudsen [16] for the SHA3 competition) to separate good hash structures from bad ones.
Security of Singlepermutationbased Compression Functions
"... Abstract. In this paper, we study security for a certain class of permutationbased compression functions. Denoted lp231 in [12], they are 2nbit to nbit compression functions using three calls to a single nbit random permutation. We prove that lp231 is asymptotically preimage resistant up to (2 2 ..."
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Cited by 1 (1 self)
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Abstract. In this paper, we study security for a certain class of permutationbased compression functions. Denoted lp231 in [12], they are 2nbit to nbit compression functions using three calls to a single nbit 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
MixCompressMix Revisited: Dispensing with Noninvertible Random Injection Oracles
"... Abstract. We revisit the problem of building dualmodel secure (DMS) hash functions that are simultaneously provably collision resistant (CR) in the standard model and provably pseudorandom oracle (PRO) in an idealized model. Designing a DMS hash function was first investigated by Ristenpart and Shr ..."
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Abstract. We revisit the problem of building dualmodel secure (DMS) hash functions that are simultaneously provably collision resistant (CR) in the standard model and provably pseudorandom oracle (PRO) in an idealized model. Designing a DMS hash function was first investigated by Ristenpart and Shrimpton (ASIACRYPT 2007); they put forth a generic approach, called MixCompressMix (MCM), and showed the feasibility of the MCM approach with a secure (but inefficient) construction. An improved construction was later presented by Lehmann and Tessaro (ASIACRYPT 2009). The proposed construction by Ristenpart and Shrimpton requires a noninvertible (pseudo) random injection oracle (PRIO) and the LehmannTessaro construction requires a noninvertible random permutation oracle (NIRP). Despite showing the feasibility of realizing PRIO and NIRP objects in theory–using ideal ciphers and (trapdoor) oneway permutations – these constructions suffer from several efficiency and implementation issues as pointed out by their designers and briefly reviewed in this paper. In contrast to the previous constructions, we show that constructing a DMS hash function does not require any PRIO or NIRP, and hence there is no need for additional (trapdoor) oneway permutations. In fact, Ristenpart and Shrimpton posed the question of whether MCM is secure under easytoinvert mixing steps as an open problem in their paper. We resolve this question in the affirmative in the fixedinputlength (FIL) hash setting. More precisely, we show that one can sandwich a provably CR function, which is sufficiently compressing, between two random
Cryptographic Hash Functions: Recent Design Trends and Security Notions ∗
"... Recent years have witnessed an exceptional research interest in cryptographic hash functions, especially after the popular attacks against MD5 and SHA1 in 2005. In 2007, the U.S. National Institute of Standards and Technology (NIST) has also significantly boosted this interest by announcing a publi ..."
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Recent years have witnessed an exceptional research interest in cryptographic hash functions, especially after the popular attacks against MD5 and SHA1 in 2005. In 2007, the U.S. National Institute of Standards and Technology (NIST) has also significantly boosted this interest by announcing a public competition to select the next hash function standard, to be named SHA3. Not surprisingly, the hash function literature has since been rapidly growing in an extremely fast pace. In this paper, we provide a comprehensive, uptodate discussion of the current state of the art of cryptographic hash functions security and design. We first discuss the various hash functions security properties and notions, then proceed to give an overview of how (and why) hash functions evolved over the years giving raise to the current diverse hash functions design approaches. A short version of this paper is in [1]. This version has been thoroughly extended, revised and updated. This