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Limits on the Efficiency of OneWay PermutationBased Hash Functions
 In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science
, 1999
"... Naor and Yung ([NY89]) show that a onebit compressing universal oneway hash function (UOWHF) can be constructed based on a oneway permutation. This construction can be iterated to build a UOWHF which compresses by "n bits, at the cost of "n invocations of the oneway permutation. We show that thi ..."
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Cited by 28 (0 self)
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Naor and Yung ([NY89]) show that a onebit compressing universal oneway hash function (UOWHF) can be constructed based on a oneway permutation. This construction can be iterated to build a UOWHF which compresses by "n bits, at the cost of "n invocations of the oneway permutation. We show that this construction is not far from optimal, in the following sense: there exists an oracle relative to which there exists a oneway permutation with inversion probability 2 \Gammap(n) (for any p(n) 2 !(log n)), but any construction of an "nbitcompressing UOWHF requires \Omega\Gamma p n=p(n)) invocations of the oneway permutation, on average. (For example, there exists in this relativized world a oneway permutation with inversion probability n \Gamma!(1) , but no UOWHF that invokes it fewer than \Omega\Gamma p n= log n) times.) Thus any proof that a more efficient UOWHF can be derived from a oneway permutation is necessarily nonrelativizing; in particular, no provable construction...
Eliminating Counterevidence with Applications to Accountable Certificate Management
 Journal of Computer Security
, 2002
"... This paper presents a method to increase the accountability of certificate management by making it intractable for the certification authority (CA) to create contradictory statements about the validity of a certificate. The core of the method is a new primitive, undeniable attester, that allows s ..."
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Cited by 27 (3 self)
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This paper presents a method to increase the accountability of certificate management by making it intractable for the certification authority (CA) to create contradictory statements about the validity of a certificate. The core of the method is a new primitive, undeniable attester, that allows someone to commit to some set S of bitstrings by publishing a short digest of S and to give attestations for any x that it is or is not a member of S. Such an attestation can be verified by obtaining in authenticated way the published digest and applying a verification algorithm to the triple of the bitstring, the attestation and the digest. The most important feature of this primitive is intractability of creating two contradictory proofs for the same candidate element x and digest. We give an efficient construction for undeniable attesters based on authenticated search trees. We show that the construction also applies to sets of more structured elements. We also show that undeniable attesters exist iff collisionresistant hash functions exist.
Hash function balance and its impact on birthday attacks
 Advances in Cryptology – EUROCRYPT ’04, Lecture Notes in Computer Science
, 2004
"... Abstract. Textbooks tell us that a birthday attack on a hash function h with range size r requires r 1/2 trials (hash computations) to find a collision. But this is quite misleading, being true only if h is regular, meaning all points in the range have the same number of preimages under h; if h is ..."
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Cited by 27 (2 self)
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Abstract. Textbooks tell us that a birthday attack on a hash function h with range size r requires r 1/2 trials (hash computations) to find a collision. But this is quite misleading, being true only if h is regular, meaning all points in the range have the same number of preimages under h; if h is not regular, fewer trials may be required. But how much fewer? This paper addresses this question by introducing a measure of the “amount of regularity ” of a hash function that we call its balance, and then providing estimates of the successrate of the birthday attack, and the expected number of trials to find a collision, as a function of the balance of the hash function being attacked. In particular, we will see that the number of trials can be significantly less than r 1/2 for hash functions of low balance. This leads us to examine popular design principles, such as the MD (MerkleDamg˚ard) transform, from the point of view of balance preservation, and to mount experiments to determine the balance of popular hash functions. 1
Constructing VILMACs from FILMACs: Message authentication under weakened assumptions
, 1999
"... ..."
On the impossibility of highlyefficient blockcipherbased hash functions
 in Advances in Cryptology—EUROCRYPT 2005
, 2005
"... Abstract. Fix a small, nonempty set of blockcipher keys K. We say a blockcipherbased hash function is highlyefficient if it makes exactly one blockcipher call for each message block hashed, and all blockcipher calls use a key from K. Although a few highlyefficient constructions have been propose ..."
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Cited by 26 (3 self)
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Abstract. Fix a small, nonempty set of blockcipher keys K. We say a blockcipherbased hash function is highlyefficient if it makes exactly one blockcipher call for each message block hashed, and all blockcipher calls use a key from K. Although a few highlyefficient constructions have been proposed, no one has been able to prove their security. In this paper we prove, in the idealcipher model, that it is impossible to construct a highlyefficient iterated blockcipherbased hash function that is provably secure. Our result implies, in particular, that the Tweakable Chain Hash (TCH) construction suggested by Liskov, Rivest, and Wagner [7] is not correct under an instantiation suggested for this construction, nor can TCH be correctly instantiated by any other efficient means.
Herding hash functions and the Nostradamus attack
 of Lecture Notes in Computer Science
, 2006
"... Abstract. In this paper, we develop a new attack on Damg˚ardMerkle hash functions, called the herding attack, in which an attacker who can find many collisions on the hash function by brute force can first provide the hash of a message, and later “herd ” any given starting part of a message to that ..."
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Cited by 25 (6 self)
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Abstract. In this paper, we develop a new attack on Damg˚ardMerkle hash functions, called the herding attack, in which an attacker who can find many collisions on the hash function by brute force can first provide the hash of a message, and later “herd ” any given starting part of a message to that hash value by the choice of an appropriate suffix. We focus on a property which hash functions should have–Chosen Target Forced Prefix (CTFP) preimage resistance–and show the distinction between Damg˚ardMerkle construction hashes and random oracles with respect to this property. We describe a number of ways that violation of this property can be used in arguably practical attacks on realworld applications of hash functions. An important lesson from these results is that hash functions susceptible to collisionfinding attacks, especially bruteforce collisionfinding attacks, cannot in general be used to prove knowledge of a secret value. 1
The Classification of Hash Functions
, 1993
"... When we ask what makes a hash function `good', we usually get an answer which includes collision freedom as the main (if not sole) desideratum. However, we show here that given any collisionfree function, we can derive others which are also collisionfree, but cryptographically useless. This explai ..."
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Cited by 24 (3 self)
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When we ask what makes a hash function `good', we usually get an answer which includes collision freedom as the main (if not sole) desideratum. However, we show here that given any collisionfree function, we can derive others which are also collisionfree, but cryptographically useless. This explains why researchers have not managed to find many interesting consequences of this property. We also prove Okamoto's conjecture that correlation freedom is strictly stronger than collision freedom. We go on to show that there are actually rather many properties which hash functions may need. Hash functions for use with RSA must be multiplication free, in the sense that one cannot find X , Y and Z such that h(X)h(Y ) = h(Z); and more complex requirements hold for other signature schemes. Universal principles can be proposed from which all the freedom properties follow, but like most theoretical principles, they do not seem to give much value to a designer; at the practical level, the main imp...
Improved fast syndrome based cryptographic hash functions
 in Proceedings of ECRYPT Hash Workshop 2007 (2007). URL: http://wwwroc.inria.fr/secret/Matthieu.Finiasz
"... Abstract. Recently, some collisions have been exposed for a variety of cryptographic hash functions [19] including some of the most widely used today. Many other hash functions using similar constrcutions can however still be considered secure. Nevertheless, this has drawn attention on the need for ..."
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Cited by 24 (5 self)
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Abstract. Recently, some collisions have been exposed for a variety of cryptographic hash functions [19] including some of the most widely used today. Many other hash functions using similar constrcutions can however still be considered secure. Nevertheless, this has drawn attention on the need for new hash function designs. In this article is presented a familly of secure hash functions, whose security is directly related to the syndrome decoding problem from the theory of errorcorrecting codes. Taking into account the analysis by Coron and Joux [4] based on Wagner’s generalized birthday algorithm [18] we study the asymptotical security of our functions. We demonstrate that this attack is always exponential in terms of the length of the hash value. We also study the workfactor of this attack, along with other attacks from coding theory, for non asymptotic range, i.e. for practical values. Accordingly, we propose a few sets of parameters giving a good security and either a faster hashing or a shorter desciption for the function. Key Words: cryptographic hash functions, provable security, syndrome decoding, NPcompleteness, Wagner’s generalized birthday problem.
Formalizing human ignorance: Collisionresistant hashing without the keys
 In Proc. Vietcrypt ’06
, 2006
"... Abstract. There is a foundational problem involving collisionresistant hashfunctions: common constructions are keyless, but formal definitions are keyed. The discrepancy stems from the fact that a function H: {0, 1} ∗ → {0, 1} n always admits an efficient collisionfinding algorithm, it’s just t ..."
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Cited by 22 (0 self)
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Abstract. There is a foundational problem involving collisionresistant hashfunctions: common constructions are keyless, but formal definitions are keyed. The discrepancy stems from the fact that a function H: {0, 1} ∗ → {0, 1} n always admits an efficient collisionfinding algorithm, it’s just that us human beings might be unable to write the program down. We explain a simple way to sidestep this difficulty that avoids having to key our hash functions. The idea is to state theorems in a way that prescribes an explicitlygiven reduction, normally a blackbox one. We illustrate this approach using wellknown examples involving digital signatures, pseudorandom functions, and the MerkleDamg˚ard construction. Key words. Collisionfree hash function, Collisionintractable hash function, Collisionresistant hash function, Cryptographic hash function, Provable security. 1
The PHOTON Family of Lightweight Hash Functions
 CRYPTO, volume 6841 of LNCS
, 2011
"... Abstract. RFID security is currently one of the major challenges cryptography has to face, often solved by protocols assuming that an ontag hash function is available. In this article we present the PHOTON lightweight hashfunction family, available in many different flavors and suitable for extrem ..."
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Cited by 21 (4 self)
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Abstract. RFID security is currently one of the major challenges cryptography has to face, often solved by protocols assuming that an ontag hash function is available. In this article we present the PHOTON lightweight hashfunction family, available in many different flavors and suitable for extremely constrained devices such as passive RFID tags. Our proposal uses a spongelike construction as domain extension algorithm and an AESlike primitive as internal unkeyed permutation. This allows us to obtain the most compact hash function known so far (about 1120 GE for 64bit collision resistance security), reaching areas very close to the theoretical optimum (derived from the minimal internal state memory size). Moreover, the speed achieved by PHOTON also compares quite favorably to its competitors. This is mostly due to the fact that unlike for previously proposed schemes, our proposal is very simple to analyze and one can derive tight AESlike bounds on the number of active Sboxes. This kind of AESlike primitive is usually not well suited for ultra constrained environments, but we describe in this paper a new method for generating the column mixing layer in a serial way, lowering drastically the area required. Finally, we slightly extend the sponge framework in order to offer interesting tradeoffs between speed and preimage security for small messages, the classical usecase in hardware.