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Some Plausible Constructions of DoubleBlockLength Hash Functions
 FSE 2006, volume 4047 of LNCS
, 2006
"... Abstract. In this article, it is discussed how to construct a compression function with 2nbit output using a component function with nbit output. The component function is either a smaller compression function or a block cipher. Some constructions are presented which compose collisionresistant ..."
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Abstract. In this article, it is discussed how to construct a compression function with 2nbit output using a component function with nbit output. The component function is either a smaller compression function or a block cipher. Some constructions are presented which compose collisionresistant hash functions: Any collisionfinding attack on them is at most as efficient as the birthday attack in the random oracle model or in the ideal cipher model. A new security notion is also introduced, which we call indistinguishability in the iteration, with a construction satisfying the notion. 1
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 27 (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
Building a collisionresistant compression function from noncompressing primitives
 In ICALP 2008, Part II
, 2008
"... Abstract. We consider how to build an efficient compression function from a small number of random, noncompressing primitives. Our main goal is to achieve a level of collision resistance as close as possible to the optimal birthday bound. We present a 2nton bit compression function based on three ..."
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Cited by 17 (3 self)
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Abstract. We consider how to build an efficient compression function from a small number of random, noncompressing primitives. Our main goal is to achieve a level of collision resistance as close as possible to the optimal birthday bound. We present a 2nton bit compression function based on three independent nton bit random functions, each called only once. We show that if the three random functions are treated as black boxes then finding collisions requires Θ(2 n/2 /n c) queries for c ≈ 1. This result remains valid if two of the three random functions are replaced by a fixedkey ideal cipher in DaviesMeyer mode (i.e., EK(x) ⊕ x for permutation EK). We also give a heuristic, backed by experimental results, suggesting that the security loss is at most four bits for block sizes up to 256 bits. We believe this is the best result to date on the matter of building a collisionresistant compression function from noncompressing functions. It also relates to an open question from Black et al. (Eurocrypt’05), who showed that compression functions that invoke a single noncompressing random function cannot suffice. We also explore the relationship of our problem with that of doubling the output of a hash function and we show how our compression function can be used to double the output length of ideal hashes.
M.: Indifferentiable security analysis of popular hash functions with prefixfree padding
 ASIACRYPT 2006. LNCS
, 2006
"... Abstract. Understanding what construction strategy has a chance to be a good hash function is extremely important nowadays. In TCC’04, Maurer et al. [13] introduced the notion of indifferentiability as a generalization of the concept of the indistinguishability of two systems. In Crypto’2005, Coron ..."
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Cited by 15 (2 self)
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Abstract. Understanding what construction strategy has a chance to be a good hash function is extremely important nowadays. In TCC’04, Maurer et al. [13] introduced the notion of indifferentiability as a generalization of the concept of the indistinguishability of two systems. In Crypto’2005, Coron et al. [5] suggested to employ indifferentiability in generic analysis of hash functions and started by suggesting four constructions which enable eliminating all possible generic attacks against iterative hash functions. In this paper we continue this initial suggestion and we give a formal proof of indifferentiability and indifferentiable attack for prefixfree MD hash functions (for single block length (SBL) hash and also some double block length (DBL) constructions) in the random oracle model and in the ideal cipher model. In particular, we observe that there are sixteen PGV hash functions (with prefixfree padding) which are indifferentiable from random oracle model in the ideal cipher model. 1
Security of Cyclic Double Block Length Hash Functions including AbreastDM
"... Abstract. We provide the first proof of security for AbreastDM, one of the oldest and most wellknown constructions for turning a block cipher with nbit block length and 2nbit key length into a 2nbit cryptographic hash function. In particular, we prove that when AbreastDM is instantiated with AE ..."
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Abstract. We provide the first proof of security for AbreastDM, one of the oldest and most wellknown constructions for turning a block cipher with nbit block length and 2nbit key length into a 2nbit cryptographic hash function. In particular, we prove that when AbreastDM is instantiated with AES256, i.e. a block cipher with 128bit block length and 256bit key length, any adversary that asks less than 2 124.42 queries cannot find a collision with success probability greater than 1/2. Surprisingly, this about 15 years old construction is one of the few constructions that have the desirable feature of a nearoptimal collision resistance guarantee. We generalize our techniques used in the proof of AbreastDM to a huge class of double block length (DBL) hash functions that we will call cyclic. Using this generalized theorem we are able to derive several DBL constructions that lead to compression functions that even have a higher security guarantee and are more efficient than AbreastDM. Furthermore we give DBL constructions that have the highest security guarantee of all DBL compression functions currently known in literature. We also provide an analysis of preimage resistance for cyclic compression functions. Note that this work has been already presented at Dagstuhl ’09.
Hash functions and RFID tags: Mind the gap
 of Lecture Notes in Computer Science
, 2008
"... Abstract. The security challenges posed by RFIDtag deployments are wellknown. In response there is a rich literature on new cryptographic protocols and an ontag hash function is often assumed by protocol designers. Yet cheap tags pose severe implementation challenges and it is far from clear that ..."
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Abstract. The security challenges posed by RFIDtag deployments are wellknown. In response there is a rich literature on new cryptographic protocols and an ontag 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 RFIDtag protocol. 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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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
On the Security of TandemDM
"... Abstract. We provide the first proof of security for TandemDM, one of the oldest and most wellknown constructions for turning a blockcipher with nbit blocklength and 2nbit keylength into a 2nbit cryptographic hash function. We prove, that when TandemDM is instantiated with AES256, i.e. blockle ..."
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Cited by 8 (2 self)
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Abstract. We provide the first proof of security for TandemDM, one of the oldest and most wellknown constructions for turning a blockcipher with nbit blocklength and 2nbit keylength into a 2nbit cryptographic hash function. We prove, that when TandemDM is instantiated with AES256, i.e. blocklength 128 bits and keylength 256 bits, any adversary that asks less than 2 120.4 queries cannot find a collision with success probability greater than 1/2. We also prove a bound for preimage resistance of TandemDM. Interestingly, as there is only one practical construction known (FSE’06, Hirose) turning such an (n,2n)bit blockcipher into a 2nbit compression function that has provably birthdaytype collision resistance, TandemDM is one out of two structures that possess this desirable feature.
MJH: A Faster Alternative to MDC2
 CTRSA 2011, LNCS 6558
, 2011
"... Abstract. In this paper, we introduce a new class of doubleblocklength hash functions. Using the ideal cipher model, we prove that these hash functions, dubbed MJH, are asymptotically collision resistant up to O(2n(1−)) query complexity for any > 0 in the iteration, where n is the block size of ..."
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Cited by 7 (1 self)
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Abstract. In this paper, we introduce a new class of doubleblocklength hash functions. Using the ideal cipher model, we prove that these hash functions, dubbed MJH, are asymptotically collision resistant up to O(2n(1−)) query complexity for any > 0 in the iteration, where n is the block size of the underlying blockcipher. When based on nbit key blockciphers, our construction, being of rate 1/2, provides better provable security than MDC2, the only known construction of a rate1/2 doublelength hash function based on an nbit key blockcipher with nontrivial provable security. Moreover, since key scheduling is performed only once per message block for MJH, our proposal significantly outperforms MDC2 in efficiency. When based on a 2nbit key blockcipher, we can use the extra n bits of key to increase the amount of payload accordingly. Thus we get a rate1 hash function that is much faster than existing proposals, such as TandemDM with comparable provable security. This is the full version of [19]. 1
Multicollision Attacks on a Class of Hash Functions
 IACR PREPRINT ARCHIVE
, 2005
"... In a recent paper, A. Joux [7] showed multicollision attacks on the classical iterated hash function. (A multicollision is a set of inputs whose hash values are same.) He also showed how the multicollision attacks can be used to get a collision attack on the concatenated hash function. In this paper ..."
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Cited by 6 (0 self)
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In a recent paper, A. Joux [7] showed multicollision attacks on the classical iterated hash function. (A multicollision is a set of inputs whose hash values are same.) He also showed how the multicollision attacks can be used to get a collision attack on the concatenated hash function. In this paper, we first try to fix the attack by introducing a natural and wide class hash functions. However, we show that the multicollision attacks also exist in this general class. Thus, we rule out a natural and a wide class of hash functions as candidates for multicollision secure hash functions.