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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
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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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.
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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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.
The collision security of TandemDM in the ideal cipher model
"... Abstract. We prove that TandemDM, one of the two “classical ” schemes for turning a blockcipher of 2nbit key into a double block length hash function, has birthdaytype collision resistance in the ideal cipher model. A collision resistance analysis for TandemDM achieving a similar birthdaytype b ..."
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Cited by 5 (1 self)
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Abstract. We prove that TandemDM, one of the two “classical ” schemes for turning a blockcipher of 2nbit key into a double block length hash function, has birthdaytype collision resistance in the ideal cipher model. A collision resistance analysis for TandemDM achieving a similar birthdaytype bound was already proposed by Fleischmann, Gorski and Lucks at FSE 2009 [3]. As we detail, however, the latter analysis is wrong, thus leaving the collision resistance of TandemDM as an open problem until now. 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.
Multipropertypreserving Domain Extension Using Polynomialbased Modes of Operation
 Advances in cryptology – EUROcrYPT’10, LNCS
"... Abstract. In this paper, we propose a new doublepiped mode of operation for multipropertypreserving domain extension of MACs (message authentication codes), PRFs (pseudorandom functions) and PROs (pseudorandom oracles). Our mode of operation performs twice as fast as the original doublepiped mode ..."
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Abstract. In this paper, we propose a new doublepiped mode of operation for multipropertypreserving domain extension of MACs (message authentication codes), PRFs (pseudorandom functions) and PROs (pseudorandom oracles). Our mode of operation performs twice as fast as the original doublepiped mode of operation of Lucks [15] while providing comparable security. Our construction, which uses a class of polynomialbased compression functions proposed by Stam [22, 23], makes a single call to a 3nbit to nbit primitive at each iteration and uses a finalization function f2 at the last iteration, producing an nbit hash function H[f1, f2] satisfying the following properties. 1. H[f1, f2] is unforgeable up to O(2 n /n) query complexity as long as f1 and f2 are unforgeable. 2. H[f1, f2] is pseudorandom up to O(2 n /n) query complexity as long as f1 is unforgeable and f2 is pseudorandom. 3. H[f1, f2] is indifferentiable from a random oracle up to O(2 2n/3) query complexity as long as f1 and f2 are public random functions. To our knowledge, our result constitutes the first time O(2 n /n) unforgeability has been achieved using only an unforgeable primitive of nbit output length. (Yasuda showed unforgeability of O(2 5n/6) for Lucks ’ construction assuming an unforgeable primitive, but the analysis is suboptimal; in the appendix, we show how Yasuda’s bound can be improved to O(2 n).) In related work, we strengthen Stam’s collision resistance analysis of polynomialbased compression functions (showing that unforgeability of the primitive suffices) and discuss how to implement our mode by replacing f1 with a 2nbit key blockcipher in DaviesMeyer mode or by replacing f1 with the cascade of two 2nbit to nbit compression functions. 1
Efficient Garbling from a FixedKey Blockcipher
, 2013
"... Abstract. We advocate schemes based on fixedkey AES as the best route to highly efficient circuitgarbling. We provide such schemes making only one AES call per garbledgate evaluation. On the theoretical side, we justify the security of these methods in the randompermutation model, where parties h ..."
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Abstract. We advocate schemes based on fixedkey AES as the best route to highly efficient circuitgarbling. We provide such schemes making only one AES call per garbledgate evaluation. On the theoretical side, we justify the security of these methods in the randompermutation model, where parties have access to a public random permutation. On the practical side, we provide the JustGarble system, which implements our schemes. JustGarble evaluates moderatesized garbledcircuits at an
Stam’s collision resistance conjecture
 In: EUROCRYPT 2010. LNCS
, 2010
"... Abstract. At CRYPTO 2008 Stam [7] made the following conjecture: if an m + sbit to sbit compression function F makes r calls to a primitive f of nbit input, then a collision for F can be obtained (with high probability) using r2 (nr−m)/(r+1) queries to f. For example, a 2nbit to nbit compressio ..."
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Abstract. At CRYPTO 2008 Stam [7] made the following conjecture: if an m + sbit to sbit compression function F makes r calls to a primitive f of nbit input, then a collision for F can be obtained (with high probability) using r2 (nr−m)/(r+1) queries to f. For example, a 2nbit to nbit compression function making two calls to a random function of nbit input cannot have collision security exceeding 2 n/3. We prove this conjecture up to a constant multiplicative factor and under the condition m ′: = (2m − n(r − 1))/(r + 1) ≥ log 2 (17). This covers nearly all cases r = 1 of the conjecture and the aforementioned example of a 2nbit to nbit compression function making two calls to a primitive of nbit input. 1
The preimage security of doubleblocklength compression functions. Cryptology ePrint Archive, Report 2011/210, 2011. http: //eprint.iacr.org
 16 Gatan Leurent, Charles Bouillaguet, and PierreAlain Fouque. SIMD Is a Message Digest
"... Abstract. We give improved bounds on the preimage security of the three “classical ” doubleblocklength, doublecall, blockcipherbased compression functions, these being AbreastDM, TandemDM and Hirose’s scheme. For Hirose’s scheme, we show that an adversary must make at least 2 2n−5 blockcipher q ..."
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Abstract. We give improved bounds on the preimage security of the three “classical ” doubleblocklength, doublecall, blockcipherbased compression functions, these being AbreastDM, TandemDM and Hirose’s scheme. For Hirose’s scheme, we show that an adversary must make at least 2 2n−5 blockcipher queries to achieve chance 0.5 of inverting a randomly chosen point in the range. For AbreastDM and TandemDM we show that at least 2 2n−10 queries are necessary. These bounds improve upon the previous best bounds of Ω(2 n) queries, and are optimal up to a constant factor since the compression functions in question have range of size 2 2n. 1