Cryptographic hash functions

Cryptographic hash functions are an important tool of cryptography and play a fundamental role in efficient and secure information processing. A hash function processes an arbitrary finite length input message to a fixed length output referred to as the hash value. As a security requirement, a hash value should not serve as an image for two distinct input messages and it should be difficult to find the input message from a given hash value. Secure hash functions serve data integrity, non-repudiation and authenticity of the source in conjunction with the digital signature schemes. Keyed hash functions, also called message authentication codes (MACs) serve data integrity and data origin authentication in the secret key setting. The building blocks of hash functions can be designed using block ciphers, modular arithmetic or from scratch. The design principles of the popular Merkle–Damgård construction are followed in almost all widely used standard hash functions such as MD5 and SHA-1.

On hash functions using checksums

We analyse the security of iterated hash functions that compute an input dependent checksum which is processed as part of the hash computation. We show that a large class of such schemes, including those using non-linear or even one-way checksum functions, is not secure against the second preimage attack of Kelsey and Schneier, the herding attack of Kelsey and Kohno and the multicollision attack of Joux. Our attacks also apply to a large class of cascaded hash functions. Our second preimage attacks on the cascaded hash functions improve the results of Joux presented at Crypto’04. We also apply our attacks to the MD2 and GOST hash functions. Our second preimage attacks on the MD2 and GOST hash functions improve the previous best known short-cut second preimage attacks on these hash functions by factors of at least 226 and 254, respectively. Our herding and multicollision attacks on the hash functions based on generic checksum functions (e.g., one-way) are a special case of the attacks on the cascaded iterated hash functions previously analysed by Dunkelman and Preneel and are not better than their attacks. On hash functions with easily invertible checksums, our multicollision and herding attacks (if the hash value is short as in MD2) are more efficient than those of Dunkelman and Preneel.

On the Collision and Preimage Resistance of Certain Two-Call Hash Functions

In this paper we present concrete collision and preimage attacks on a large class of compression function constructions making two calls to the underlying ideal primitives. The complexity of the collision attack is above the theoretical lower bound for constructions of this type, but below the birthday complexity; the complexity of the preimage attack, however, is equal to the theoretical lower bound. We also present undesirable properties of some of Stam’s compression functions proposed at CRYPTO ’08. We show that when one of the n-bit to n-bit components of the proposed 2n-bit to n-bit compression function is replaced by a fixed-key cipher in the Davies-Meyer mode, the complexity of finding a preimage would be 2 n/3. We also show that the complexity of finding a collision in a variant of the 3n-bits to 2n-bits scheme with its output truncated to 3n/2 bits is 2 n/2. The complexity of our preimage attack on this hash function is about 2 n . Finally, we present a collision attack on a variant of the proposed m + s-bit to s-bit scheme, truncated to s − 1 bits, with a complexity of O(1). However, none of our results compromise Stam’s security claims.

On Randomizing Hash Functions to Strengthen the Security of Digital Signatures

Halevi and Krawczyk proposed a message randomization algorithm called RMX as a front-end tool to the hash-then-sign digital signature schemes such as DSS and RSA in order to free their reliance on the collision resistance property of the hash functions. They have shown that to forge a RMX-hash-then-sign signature scheme, one has to solve a cryptanalytical task which is related to finding second preimages for the hash function. In this article, we will show how to use Dean’s method of finding expandable messages for finding a second preimage in the Merkle-Damgård hash function to existentially forge a signature scheme based on a t-bit RMX-hash function which uses the Davies-Meyer compression functions (e.g., MD4, MD5, SHA family) in 2 t/2 chosen messages plus 2 t/2 + 1 off-line operations of the compression function and similar amount of memory. This forgery attack also works on the signature schemes that use Davies-Meyer schemes and a variant of RMX published by NIST in its Draft Special Publication (SP) 800-106. We discuss some important applications of our attack.

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.

A new twist on mode indicator functions

Mode indicator functions (MIFs) are used in modal testing and analysis as a means of identifying modes of vibration, often as a precursor to modal parameter estimation. Various methods have been developed since the MIF was introduced four decades ago. These methods are quite useful in assisting the analyst to identify genuine modes and, in the case of the complex mode indicator function, have even been developed into modal parameter estimation techniques. Although the various MIFs are able to indicate the existence of a mode, they do not provide the analyst with any descriptive information about the mode. This paper uses the simple summation type of MIF to develop five averaged and normalised MIFs that will provide the analyst with enough information to identify whether a mode is longitudinal, vertical, lateral or torsional. The first three functions, termed directional MIFs, have been noted in the literature in one form or another; however, this paper introduces a new twist on the MIF by introducing two MIFs, termed torsional MIFs, that can be used by the analyst to identify torsional modes and, moreover, can assist in determining whether the mode is of a pure torsion or sway type (i.e., having a rigid cross-section) or a distorted twisting type. The directional and torsional MIFs are tested on a finite element model based simulation of an experimental modal test using an impact hammer. Results indicate that the directional and torsional MIFs are indeed useful in assisting the analyst to identify whether a mode is longitudinal, vertical, lateral, sway, or torsion.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.

The kallikrein-related peptidase family: Dysregulation and functions during cancer progression

Cancer is the second leading cause of death with 14 million new cases and 8.2 million cancer-related deaths worldwide in 2012. Despite the progress made in cancer therapies, neoplastic diseases are still a major therapeutic challenge notably because of intra- and inter-malignant tumour heterogeneity and adaptation/escape of malignant cells to/from treatment. New targeted therapies need to be developed to improve our medical arsenal and counter-act cancer progression. Human kallikrein-related peptidases (KLKs) are secreted serine peptidases which are aberrantly expressed in many cancers and have great potential in developing targeted therapies. The potential of KLKs as cancer biomarkers is well established since the demonstration of the association between KLK3/PSA (prostate specific antigen) levels and prostate cancer progression. In addition, a constantly increasing number of in vitro and in vivo studies demonstrate the functional involvement of KLKs in cancer-related processes. These peptidases are now considered key players in the regulation of cancer cell growth, migration, invasion, chemo-resistance, and importantly, in mediating interactions between cancer cells and other cell populations found in the tumour microenvironment to facilitate cancer progression. These functional roles of KLKs in a cancer context further highlight their potential in designing new anti-cancer approaches. In this review, we comprehensively review the biochemical features of KLKs, their functional roles in carcinogenesis, followed by the latest developments and the successful utility of KLK-based therapeutics in counteracting cancer progression.

Genetic, functional, and histopathological evaluation of two C-terminal BRCA1 missense variants

Background: The vast majority of BRCA1 missense sequence variants remain uncharacterised for their possible effect on protein expression and function, and therefore are unclassified in terms of their pathogenicity. BRCA1 plays diverse cellular roles and it is unlikely that any single functional assay will accurately reflect the total cellular implications of missense mutations in this gene. Objective: To elucidate the effect of two BRCA1 variants, 5236G>C (G1706A) and 5242C>A (A1708E) on BRCA1 function, and to survey the relative usefulness of several assays to direct the characterisation of other unclassified variants in BRCA genes. Methods and Results: Data from a range of bioinformatic, genetic, and histopathological analyses, and in vitro functional assays indicated that the 1708E variant was associated with the disruption of different cellular functions of BRCA1. In transient transfection experiments in T47D and 293T cells, the 1708E product was mislocalised to the cytoplasm and induced centrosome amplification in 293T cells. The 1708E variant also failed to transactivate transcription of reporter constructs in mammalian transcriptional transactivation assays. In contrast, the 1706A variant displayed a phenotype comparable to wildtype BRCA1 in these assays. Consistent with functional data, tumours from 1708E carriers showed typical BRCA1 pathology, while tumour material from 1706A carriers displayed few histopathological features associated with BRCA1 related tumours. Conclusions: A comprehensive range of genetic, bioinformatic, and functional analyses have been combined for the characterisation of BRCA1 unclassified sequence variants. Consistent with the functional analyses, the combined odds of causality calculated for the 1706A variant after multifactorial likelihood analysis (1:142) indicates a definitive classification of this variant as "benign". In contrast, functional assays of the 1708E variant indicate that it is pathogenic, possibly through subcellular mislocalisation. However, the combined odds of 262:1 in favour of causality of this variant does not meet the minimal ratio of 1000:1 for classification as pathogenic, and A1708E remains formally designated as unclassified. Our findings highlight the importance of comprehensive genetic information, together with detailed functional analysis for the definitive categorisation of unclassified sequence variants. This combination of analyses may have direct application to the characterisation of other unclassified variants in BRCA1 and BRCA2.

Implications of gain functions in fisheries management

The appealing concept of optimal harvesting is often used in fisheries to obtain new management strategies. However, optimality depends on the objective function, which often varies, reflecting the interests of different groups of people. The aim of maximum sustainable yield is to extract the greatest amount of food from replenishable resources in a sustainable way. Maximum sustainable yield may not be desirable from an economic point of view. Maximum economic yield that maximizes the profit of fishing fleets (harvesting sector) but ignores socio-economic benefits such as employment and other positive externalities. It may be more appropriate to use the maximum economic yield that which is based on the value chain of the overall fishing sector, to reflect better society's interests. How to make more efficient use of a fishery for society rather than fishing operators depends critically on the gain function parameters including multiplier effects and inclusion or exclusion of certain costs. In particular, the optimal effort level based on the overall value chain moves closer to the optimal effort for the maximum sustainable yield because of the multiplier effect. These issues are illustrated using the Australian Northern Prawn Fishery.

Rank-based regression for analysis of repeated measures

We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation.

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "Working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.