The most common way of constructing a hash function (e.g., SHA-1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a block-cipher. In this paper, we introduce a new security notion for hash-functions, stronger than collision-resistance. Under this notion, the arbitrary length hash function H must behave as a random oracle when the fixed-length building block is viewed as a random oracle or an ideal block-cipher. The key property is that if a particular construction meets this definition, then any cryptosystem proven secure assuming H is a random oracle remains secure if one plugs in this construction (still assuming that the underlying fixed-length primitive is ideal). In this paper, we show that the current design principle behind hash functions such as SHA-1 and MD5 — the (strengthened) Merkle–Damgård transformation — does not satisfy this security notion. We provide several constructions that provably satisfy this notion; those new constructions introduce minimal changes to the plain Merkle–Damgård construction and are easily implementable in practice.

Abstract We point out that the seemingly strong pseudorandom oracle preserving (PRO-Pr) propertyof hash function domain-extension transforms defined and implemented by Coron et. al. [12] can actually weaken our guarantees on the hash function, in particular producing a hash functionthat fails to be even collision-resistant (CR) even though the compression function to which the transform is applied is CR. Not only is this true in general, but we show that all the transformspresented in [12] have this weakness. We suggest that the appropriate goal of a domain extension transform for the next generation of hash functions is to be multi-property preserving, namelythat one should have a single transform that is simultaneously at least collision-resistance preserving, pseudorandom function preserving and PRO-Pr. We present an efficient new transformthat is proven to be multi-property preserving in this sense.

Recent collision-finding attacks against hash functions such as MD5 and SHA-1 motivate the use of provably collision-resistant (CR) functions in their place. Finding a collision in a provably CR function implies the ability to solve some hard problem (e.g., factoring). Unfortunately, existing provably CR functions make poor replacements for hash functions as they fail to deliver behaviors demanded by practical use. In particular, they are easily distinguished from a random oracle. We initiate an investigation into building hash functions from provably CR functions. As a method for achieving this, we present the Mix-Compress-Mix (MCM) construction; it envelopes any provably CR function H (with suitable regularity properties) between two injective “mixing” stages. The MCM construction simultaneously enjoys (1) provable collision-resistance in the standard model, and (2) indifferentiability from a monolithic random oracle when the mixing stages themselves are indifferentiable from a random oracle that observes injectivity. We instantiate our new design approach by specifying a blockcipher-based construction that

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) Merkle-Damg˚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 (Merkle-Damg˚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) Merkle-Damg˚ard transform, applied to a “strong enough ” compression function. In particular, we show that a fixed-length compressing random oracle, as well as the currently used Davies-Meyer 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

It is well understood that passwords must be very long and complex to have sufficient entropy for security purposes. Unfortunately, these passwords tend to be hard to memorize, and so alternatives are sought. Smart Cards, Biometrics, and Reverse Turing Tests (human-only solvable puzzles) are options, but another option is to use pass-phrases. This paper explores

Skein [13] is a fast, versatile, and secure hash function that has been submitted as an AHS candidate. One of Skein’s features is that it is backed by security proofs. This paper presents, explains, and justifies the various provable security claims underlying Skein.

We introduce the notion of “non-malleable codes ” which relaxes the notion of error-correction and errordetection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error-correction and error-detection, nonmalleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that effect each bit of the codeword arbitrarily (i.e. leave it untouched, flip it or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every “small enough ” family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions — e.g. functions where every bit in the tampered codeword can depend arbitrarily on any 99 % of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g. signature cards) against “tampering attacks”. In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem, was previously studied in the work of Gennaro et al. in 2004 under the name “algorithmic tamper proof security ” (ATP). We show that non-malleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret-state with a non-malleable code while it is stored in memory. 1

Shabal is based on a new provably secure mode of operation. Some related-key distinguishers for the underlying keyed permutation have been exhibited recently by Aumasson et al. and Knudsen et al., but with no visible impact on the security of Shabal. This paper then aims at extensively studying such distinguishers for the keyed permutation used in Shabal, and at clarifying the impact that they exert on the security of the full hash function. Most interestingly, a new security proof for Shabal’s mode of operation is provided where the keyed permutation is not assumed to be an ideal cipher anymore, but observes a distinguishing property i.e., an explicit relation verified by all its inputs and outputs. As a consequence of this extended proof, all known distinguishers for the keyed permutation are proven not to weaken the security of Shabal. In our study, we provide the foundation of a generalization of the indifferentiability framework to biased random primitives, this part being of independent interest. 1

Abstract. RSA-FDH and many other schemes secure in the Random-Oracle Model (ROM) require a hash function with output size larger than standard sizes. We show that the random-oracle instantiations proposed in the literature for such cases are weaker than a random oracle, including the proposals by Bellare and Rogaway from 1993 and 1996, and the ones implicit in IEEE P1363 and PKCS standards: for instance, we obtain a practical preimage attack on BR93 for 1024-bit digests (with complexity less than 2 30). Next, we study the security impact of hash function defects for ROM signatures. As an extreme case, we note that any hash collision would suffice to disclose the master key in the ID-based cryptosystem by Boneh et al. from FOCS ’07, and the secret key in the Rabin-Williams signature for which Bernstein proved tight security at EUROCRYPT ’08. We also remark that collisions can be found as a precomputation for any instantiation of the ROM, and this violates the security definition of the scheme in the standard model. Hence, this gives an example of a natural scheme that is proven secure in the ROM but that in insecure for any instantiation by a single function. Interestingly, for both of these schemes, a slight modification can prevent these attacks, while preserving the ROM security result. We give evidence that in the case of RSA and Rabin/Rabin-Williams, an appropriate PSS padding is more robust than all other paddings known. 1

Abstract not found