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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
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 15 (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.
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 6 (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.
A new mode of operation for block ciphers and lengthpreserving MACs
 of Lecture Notes in Computer Science
, 2008
"... Abstract. We propose a new mode of operation, enciphered CBC, for domain extension of lengthpreserving functions (like block ciphers), which is a variation on the popular CBC mode of operation. Our new mode is twice slower than CBC, but has many (propertypreserving) properties not enjoyed by CBC a ..."
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Cited by 5 (2 self)
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Abstract. We propose a new mode of operation, enciphered CBC, for domain extension of lengthpreserving functions (like block ciphers), which is a variation on the popular CBC mode of operation. Our new mode is twice slower than CBC, but has many (propertypreserving) properties not enjoyed by CBC and other known modes. Most notably, it yields the first constantrate Variable Input Length (VIL) MAC from any length preserving Fixed Input Length (FIL) MAC. This answers the question of Dodis and Puniya from Eurocrypt 2007. Further, our mode is a secure domain extender for PRFs (with basically the same security as encrypted CBC). This provides a hedge against the security of the block cipher: if the block cipher is pseudorandom, one gets a VILPRF, while if it is “only ” unpredictable, one “at least ” gets a VILMAC. Additionally, our mode yields a VIL random oracle (and, hence, a collisionresistant hash function) when instantiated with lengthpreserving random functions, or even random permutations (which can be queried from both sides). This means that one does not have to rekey the block cipher during the computation, which was critically used in most previous constructions (analyzed in the ideal cipher model). 1
Cryptanalysis of Tweaked Versions of SMASH and Reparation
"... 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 soo ..."
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Cited by 4 (0 self)
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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 SMASH256 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 idealcipher model in Ω(2 n/4) queries to the permutations. In order to analyze the tightness of our proof, we devise a nontrivial 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 2permutation based hash functions, as proved in [12]. 1
Blockcipher Based Hashing Revisited
 Fast Software Encryption – FSE ’09
, 2009
"... Abstract. We revisit the rate1 blockcipher based hash functions as first studied by Preneel, Govaerts and Vandewalle (Crypto’93) and later extensively analysed by Black, Rogaway and Shrimpton (Crypto’02). We analyse a further generalization where any pre and postprocessing is considered. This lead ..."
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Cited by 3 (0 self)
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Abstract. We revisit the rate1 blockcipher based hash functions as first studied by Preneel, Govaerts and Vandewalle (Crypto’93) and later extensively analysed by Black, Rogaway and Shrimpton (Crypto’02). We analyse a further generalization where any pre and postprocessing is considered. This leads to a clearer understanding of the current classification of rate1 blockcipher based schemes as introduced by Preneel et al. and refined by Black et al. In addition, we also gain insight in chopped, overloaded and supercharged compression functions. In the latter category we propose two compression functions based on a single call to a blockcipher whose collision resistance exceeds the birthday bound on the cipher’s blocklength. 1
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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Cited by 2 (1 self)
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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
Security Analysis and Comparison of the SHA3 Finalists
"... Abstract. In 2007, the US National Institute for Standards and Technology announced a call for the design of a new cryptographic hash algorithm in response to the vulnerabilities identified in widely employed hash functions, such as MD5 and SHA1. NIST received many submissions, 51 of which got acce ..."
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Abstract. In 2007, the US National Institute for Standards and Technology announced a call for the design of a new cryptographic hash algorithm in response to the vulnerabilities identified in widely employed hash functions, such as MD5 and SHA1. NIST received many submissions, 51 of which got accepted to the first round. At present, 5 candidates are left in the third round of the competition. An important criterion in the selection process is the SHA3 hash function security and more concretely, the possible reductions of the hash function security to the security of its underlying building blocks. At NIST’s second SHA3 Candidate Conference 2010, Andreeva et al. provided a provable security classification of the second round SHA3 candidates in the ideal model. In this work, we revisit this classification for the five SHA3 finalists. We evaluate recent provable security results on the candidates, and resolve remaining open problems for Grøstl, JH, and Skein.
Efficient Hashing using the AES Instruction Set
"... Abstract. In this work, we provide a software benchmark for a large range of 256bit blockcipherbased hash functions. We instantiate the underlying blockcipher with AES, which allows us to exploit the recent AES instruction set (AESNI). Since AES itself only outputs 128 bits, we consider doublebl ..."
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Abstract. In this work, we provide a software benchmark for a large range of 256bit blockcipherbased hash functions. We instantiate the underlying blockcipher with AES, which allows us to exploit the recent AES instruction set (AESNI). Since AES itself only outputs 128 bits, we consider doubleblocklength constructions, as well as (singleblocklength) constructions based on RIJNDAEL256. Although we primarily target architectures supporting AESNI, our framework has much broader applications by estimating the performance of these hash functions on any (micro)architecture given AESbenchmark results. As far as we are aware, this is the first comprehensive performance comparison of multiblocklength hash functions in software. 1