Cryptographic Hash Functions

In the modern era of information and communication technology, cryptographic hash functions play an important role in ensuring the authenticity, integrity, and nonrepudiation goals of information security as well as efficient information processing. This entry provides an overview of the role of hash functions in information security, popular hash function designs, some important analytical results, and recent advances in this field.

Biometric template security using higher order spectra

A method of improving the security of biometric templates which satisfies desirable properties such as (a) irreversibility of the template, (b) revocability and assignment of a new template to the same biometric input, (c) matching in the secure transformed domain is presented. It makes use of an iterative procedure based on the bispectrum that serves as an irreversible transformation for biometric features because signal phase is discarded each iteration. Unlike the usual hash function, this transformation preserves closeness in the transformed domain for similar biometric inputs. A number of such templates can be generated from the same input. These properties are illustrated using synthetic data and applied to images from the FRGC 3D database with Gabor features. Verification can be successfully performed using these secure templates with an EER of 5.85%

Modelling client puzzles and denial-of-service resistant protocols

Denial-of-service (DoS) attacks are a growing concern to networked services like the Internet. In recent years, major Internet e-commerce and government sites have been disabled due to various DoS attacks. A common form of DoS attack is a resource depletion attack, in which an attacker tries to overload the server's resources, such as memory or computational power, rendering the server unable to service honest clients. A promising way to deal with this problem is for a defending server to identify and segregate malicious traffic as earlier as possible. Client puzzles, also known as proofs of work, have been shown to be a promising tool to thwart DoS attacks in network protocols, particularly in authentication protocols. In this thesis, we design efficient client puzzles and propose a stronger security model to analyse client puzzles. We revisit a few key establishment protocols to analyse their DoS resilient properties and strengthen them using existing and novel techniques. Our contributions in the thesis are manifold. We propose an efficient client puzzle that enjoys its security in the standard model under new computational assumptions. Assuming the presence of powerful DoS attackers, we find a weakness in the most recent security model proposed to analyse client puzzles and this study leads us to introduce a better security model for analysing client puzzles. We demonstrate the utility of our new security definitions by including two hash based stronger client puzzles. We also show that using stronger client puzzles any protocol can be converted into a provably secure DoS resilient key exchange protocol. In other contributions, we analyse DoS resilient properties of network protocols such as Just Fast Keying (JFK) and Transport Layer Security (TLS). In the JFK protocol, we identify a new DoS attack by applying Meadows' cost based framework to analyse DoS resilient properties. We also prove that the original security claim of JFK does not hold. Then we combine an existing technique to reduce the server cost and prove that the new variant of JFK achieves perfect forward secrecy (the property not achieved by original JFK protocol) and secure under the original security assumptions of JFK. Finally, we introduce a novel cost shifting technique which reduces the computation cost of the server significantly and employ the technique in the most important network protocol, TLS, to analyse the security of the resultant protocol. We also observe that the cost shifting technique can be incorporated in any Diffine{Hellman based key exchange protocol to reduce the Diffie{Hellman exponential cost of a party by one multiplication and one addition.

Cryptanalysis of LASH

We show that the LASH-x hash function is vulnerable to attacks that trade time for memory, including collision attacks as fast as 2(4x/11) and preimage attacks as fast as 2(4x/7). Moreover, we briefly mention heuristic lattice based collision attacks that use small memory but require very long messages that are expected to find collisions much faster than 2 x/2. All of these attacks exploit the designers’ choice of an all zero IV. We then consider whether LASH can be patched simply by changing the IV. In this case, we show that LASH is vulnerable to a 2(7x/8) preimage attack. We also show that LASH is trivially not a PRF when any subset of input bytes is used as a secret key. None of our attacks depend upon the particular contents of the LASH matrix – we only assume that the distribution of elements is more or less uniform.

Known and chosen key differential distinguishers for block ciphers

In this paper we investigate the differential properties of block ciphers in hash function modes of operation. First we show the impact of differential trails for block ciphers on collision attacks for various hash function constructions based on block ciphers. Further, we prove the lower bound for finding a pair that follows some truncated differential in case of a random permutation. Then we present open-key differential distinguishers for some well known round-reduced block ciphers.

On the (in)security of IDEA in various hashing modes

In this article, we study the security of the IDEA block cipher when it is used in various simple-length or double-length hashing modes. Even though this cipher is still considered as secure, we show that one should avoid its use as internal primitive for block cipher based hashing. In particular, we are able to generate instantaneously free-start collisions for most modes, and even semi-free-start collisions, pseudo-preimages or hash collisions in practical complexity. This work shows a practical example of the gap that exists between secret-key and known or chosen-key security for block ciphers. Moreover, we also settle the 20-year-old standing open question concerning the security of the Abreast-DM and Tandem-DM double-length compression functions, originally invented to be instantiated with IDEA. Our attacks have been verified experimentally and work even for strengthened versions of IDEA with any number of rounds.

Cryptanalysis of FORK-256

In this paper we present a cryptanalysis of a new 256-bit hash function, FORK-256, proposed by Hong et al. at FSE 2006. This cryptanalysis is based on some unexpected differentials existing for the step transformation. We show their possible uses in different attack scenarios by giving a 1-bit (resp. 2-bit) near collision attack against the full compression function of FORK-256 running with complexity of 2^125 (resp. 2^120) and with negligible memory, and by exhibiting a 22-bit near pseudo-collision. We also show that we can find collisions for the full compression function with a small amount of memory with complexity not exceeding 2^126.6 hash evaluations. We further show how to reduce this complexity to 2^109.6 hash computations by using 273 memory words. Finally, we show that this attack can be extended with no additional cost to find collisions for the full hash function, i.e. with the predefined IV.

How to strengthen any weakly unforgeable signature into a strongly unforgeable signature

Standard signature schemes are usually designed only to achieve weak unforgeability – i.e. preventing forgery of signatures on new messages not previously signed. However, most signature schemes are randomised and allow many possible signatures for a single message. In this case, it may be possible to produce a new signature on a previously signed message. Some applications require that this type of forgery also be prevented – this requirement is called strong unforgeability. At PKC2006, Boneh Shen and Waters presented an efficient transform based on any randomised trapdoor hash function which converts a weakly unforgeable signature into a strongly unforgeable signature and applied it to construct a strongly unforgeable signature based on the CDH problem. However, the transform of Boneh et al only applies to a class of so-called partitioned signatures. Although many schemes fall in this class, some do not, for example the DSA signature. Hence it is natural to ask whether one can obtain a truly generic efficient transform based on any randomised trapdoor hash function which converts any weakly unforgeable signature into a strongly unforgeable one. We answer this question in the positive by presenting a simple modification of the Boneh-Shen-Waters transform. Our modified transform uses two randomised trapdoor hash functions.

Building indifferentiable compression functions from the PGV compression functions

Preneel, Govaerts and Vandewalle (PGV) analysed the security of single-block-length block cipher based compression functions assuming that the underlying block cipher has no weaknesses. They showed that 12 out of 64 possible compression functions are collision and (second) preimage resistant. Black, Rogaway and Shrimpton formally proved this result in the ideal cipher model. However, in the indifferentiability security framework introduced by Maurer, Renner and Holenstein, all these 12 schemes are easily differentiable from a fixed input-length random oracle (FIL-RO) even when their underlying block cipher is ideal. We address the problem of building indifferentiable compression functions from the PGV compression functions. We consider a general form of 64 PGV compression functions and replace the linear feed-forward operation in this generic PGV compression function with an ideal block cipher independent of the one used in the generic PGV construction. This modified construction is called a generic modified PGV (MPGV). We analyse indifferentiability of the generic MPGV construction in the ideal cipher model and show that 12 out of 64 MPGV compression functions in this framework are indifferentiable from a FIL-RO. To our knowledge, this is the first result showing that two independent block ciphers are sufficient to design indifferentiable single-block-length compression functions.

Improved Security Analysis of Fugue-256 (Poster)

We present some improved analytical results as part of the ongoing work on the analysis of Fugue-256 hash function, a second round candidate in the NIST’s SHA3 competition. First we improve Aumasson and Phans’ integral distinguisher on the 5.5 rounds of the final transformation of Fugue-256 to 16.5 rounds. Next we improve the designers’ meet-in-the-middle preimage attack on Fugue-256 from 2480 time and memory to 2416. Finally, we comment on possible methods to obtain free-start distinguishers and free-start collisions for Fugue-256.

Security Analysis of salt||password Hashes

Protection of passwords used to authenticate computer systems and networks is one of the most important application of cryptographic hash functions. Due to the application of precomputed memory look up attacks such as birthday and dictionary attacks on the hash values of passwords to find passwords, it is usually recommended to apply hash function to the combination of both the salt and password, denoted salt||password, to prevent these attacks. In this paper, we present the first security analysis of salt||password hashing application. We show that when hash functions based on the compression functions with easily found fixed points are used to compute the salt||password hashes, these hashes are susceptible to precomputed offline birthday attacks. For example, this attack is applicable to the salt||password hashes computed using the standard hash functions such as MD5, SHA-1, SHA-256 and SHA-512 that are based on the popular Davies-Meyer compression function. This attack exposes a subtle property of this application that although the provision of salt prevents an attacker from finding passwords, salts prefixed to the passwords do not prevent an attacker from doing a precomputed birthday attack to forge an unknown password. In this forgery attack, we demonstrate the possibility of building multiple passwords for an unknown password for the same hash value and salt. Interestingly, password||salt (i.e. salts suffixed to the passwords) hashes computed using Davies-Meyer hash functions are not susceptible to this attack, showing the first security gap between the prefix-salt and suffix-salt methods of hashing passwords.

Grøstl – a SHA-3 candidate

Grøstl is a SHA-3 candidate proposal. Grøstl is an iterated hash function with a compression function built from two fixed, large, distinct permutations. The design of Grøstl is transparent and based on principles very different from those used in the SHA-family. The two permutations are constructed using the wide trail design strategy, which makes it possible to give strong statements about the resistance of Grøstl against large classes of cryptanalytic attacks. Moreover, if these permutations are assumed to be ideal, there is a proof for the security of the hash function. Grøstl is a byte-oriented SP-network which borrows components from the AES. The S-box used is identical to the one used in the block cipher AES and the diffusion layers are constructed in a similar manner to those of the AES. As a consequence there is a very strong confusion and diffusion in Grøstl. Grøstl is a so-called wide-pipe construction where the size of the internal state is significantly larger than the size of the output. This has the effect that all known, generic attacks on the hash function are made much more difficult. Grøstl has good performance on a wide range of platforms and counter-measures against side-channel attacks are well-understood from similar work on the AES.

Grøstl

The Grøstl Hash Function Grøstl is FAST Grøstl is PROVABLY SECURE Grøstl is SIDE-CHANNEL RESISTANT Grøstl is SIMPLE

Grøstl - a SHA-3 candidate

Grøstl is a SHA-3 candidate proposal. Grøstl is an iterated hash function with a compression function built from two �fixed, large, distinct permutations. The design of Grøstl is transparent and based on principles very different from those used in the SHA-family. The two permutations are constructed using the wide trail design strategy, which makes it possible to give strong statements about the resistance of Grøstl against large classes of cryptanalytic attacks. Moreover, if these permutations are assumed to be ideal, there is a proof for the security of the hash function. Grøstl is a byte-oriented SP-network which borrows components from the AES. The S-box used is identical to the one used in the block cipher AES and the diffusion layers are constructed in a similar manner to those of the AES. As a consequence there is a very strong confusion and diffusion in Grøstl

SHA-3 Design and Cryptanalysis Report

The competition to select a new secure hash function standard SHA-3 was initiated in response to surprising progress in the cryptanalysis of existing hash function constructions that started in 2004. In this report we survey design and cryptanalytic results of those 14 candidates that remain in the competition, about 1.5 years after the competition started with the initial submission of the candidates in October 2008. Implementation considerations are not in the scope of this report. The diversity of designs is also reflected in the great variety of cryptanalytic techniques and results that were applied and found during this time. This report gives an account of those techniques and results.