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.

Robust image hash functions using higher order spectra

Robust hashing is an emerging field that can be used to hash certain data types in applications unsuitable for traditional cryptographic hashing methods. Traditional hashing functions have been used extensively for data/message integrity, data/message authentication, efficient file identification and password verification. These applications are possible because the hashing process is compressive, allowing for efficient comparisons in the hash domain but non-invertible meaning hashes can be used without revealing the original data. These techniques were developed with deterministic (non-changing) inputs such as files and passwords. For such data types a 1-bit or one character change can be significant, as a result the hashing process is sensitive to any change in the input. Unfortunately, there are certain applications where input data are not perfectly deterministic and minor changes cannot be avoided. Digital images and biometric features are two types of data where such changes exist but do not alter the meaning or appearance of the input. For such data types cryptographic hash functions cannot be usefully applied. In light of this, robust hashing has been developed as an alternative to cryptographic hashing and is designed to be robust to minor changes in the input. Although similar in name, robust hashing is fundamentally different from cryptographic hashing. Current robust hashing techniques are not based on cryptographic methods, but instead on pattern recognition techniques. Modern robust hashing algorithms consist of feature extraction followed by a randomization stage that introduces non-invertibility and compression, followed by quantization and binary encoding to produce a binary hash output. In order to preserve robustness of the extracted features, most randomization methods are linear and this is detrimental to the security aspects required of hash functions. Furthermore, the quantization and encoding stages used to binarize real-valued features requires the learning of appropriate quantization thresholds. How these thresholds are learnt has an important effect on hashing accuracy and the mere presence of such thresholds are a source of information leakage that can reduce hashing security. This dissertation outlines a systematic investigation of the quantization and encoding stages of robust hash functions. While existing literature has focused on the importance of quantization scheme, this research is the first to emphasise the importance of the quantizer training on both hashing accuracy and hashing security. The quantizer training process is presented in a statistical framework which allows a theoretical analysis of the effects of quantizer training on hashing performance. This is experimentally verified using a number of baseline robust image hashing algorithms over a large database of real world images. This dissertation also proposes a new randomization method for robust image hashing based on Higher Order Spectra (HOS) and Radon projections. The method is non-linear and this is an essential requirement for non-invertibility. The method is also designed to produce features more suited for quantization and encoding. The system can operate without the need for quantizer training, is more easily encoded and displays improved hashing performance when compared to existing robust image hashing algorithms. The dissertation also shows how the HOS method can be adapted to work with biometric features obtained from 2D and 3D face images.

Higher order universal one-way hash functions from the subset sum assumption

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with ‘extension factor’ k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

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.

The suffix-free-prefix-free hash function construction and its indifferentiability security analysis

In this paper, we observe that in the seminal work on indifferentiability analysis of iterated hash functions by Coron et al. and in subsequent works, the initial value (IV) of hash functions is fixed. In addition, these indifferentiability results do not depend on the Merkle–Damgård (MD) strengthening in the padding functionality of the hash functions. We propose a generic n -bit-iterated hash function framework based on an n -bit compression function called suffix-free-prefix-free (SFPF) that works for arbitrary IV s and does not possess MD strengthening. We formally prove that SFPF is indifferentiable from a random oracle (RO) when the compression function is viewed as a fixed input-length random oracle (FIL-RO). We show that some hash function constructions proposed in the literature fit in the SFPF framework while others that do not fit in this framework are not indifferentiable from a RO. We also show that the SFPF hash function framework with the provision of MD strengthening generalizes any n -bit-iterated hash function based on an n -bit compression function and with an n -bit chaining value that is proven indifferentiable from a RO.

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.

XOR-based hash functions

Bank conflicts can severely reduce the bandwidth of an interleaved multibank memory and conflict misses increase the miss rate of a cache or a predictor. Both occurrences are manifestations of the same problem: Objects which should be mapped to different indices are accidentally mapped to the same index. Suitable chosen hash functions can avoid conflicts in each of these situations by mapping the most frequently occurring patterns conflict-free. A particularly interesting class of hash functions are the XOR-based hash functions, which compute each set index bit as the exclusive-or of a subset of the address bits. When implementing an XOR-based hash function, it is extremely important to understand what patterns are mapped conflict-free and how a hash function can be constructed to map the most frequently occurring patterns without conflicts. Hereto, this paper presents two ways to reason about hash functions: by their null space and by their column space. The null space helps to quickly determine whether a pattern is mapped conflict-free. The column space is more useful for other purposes, e. g., to reduce the fan-in of the XOR-gates without introducing conflicts or to evaluate interbank dispersion in skewed-associative caches. Examples illustrate how these ideas can be applied to construct conflict-free hash functions.

Jerim-320: A New 320-Bit Hash Function Compared To Hash Functions With Parallel Branches

This paper describes JERIM-320, a new 320-bit hash function used for ensuring message integrity and details a comparison with popular hash functions of similar design. JERIM-320 and FORK -256 operate on four parallel lines of message processing while RIPEMD-320 operates on two parallel lines. Popular hash functions like MD5 and SHA-1 use serial successive iteration for designing compression functions and hence are less secure. The parallel branches help JERIM-320 to achieve higher level of security using multiple iterations and processing on the message blocks. The focus of this work is to prove the ability of JERIM 320 in ensuring the integrity of messages to a higher degree to suit the fast growing internet applications

Biometric authentication of users through iris by using key binding and similarity preserving hash functions = Autenticación biométrica de usuarios a través del iris mediante la ocultación de claves y funciones resumen que preservan la similitud

El extraordinario auge de las nuevas tecnologías de la información, el desarrollo de la Internet de las Cosas, el comercio electrónico, las redes sociales, la telefonía móvil y la computación y almacenamiento en la nube, han proporcionado grandes beneficios en todos los ámbitos de la sociedad. Junto a éstos, se presentan nuevos retos para la protección y privacidad de la información y su contenido, como la suplantación de personalidad y la pérdida de la confidencialidad e integridad de los documentos o las comunicaciones electrónicas. Este hecho puede verse agravado por la falta de una frontera clara que delimite el mundo personal del mundo laboral en cuanto al acceso de la información. En todos estos campos de la actividad personal y laboral, la Criptografía ha jugado un papel fundamental aportando las herramientas necesarias para garantizar la confidencialidad, integridad y disponibilidad tanto de la privacidad de los datos personales como de la información. Por otro lado, la Biometría ha propuesto y ofrecido diferentes técnicas con el fin de garantizar la autentificación de individuos a través del uso de determinadas características personales como las huellas dáctilares, el iris, la geometría de la mano, la voz, la forma de caminar, etc. Cada una de estas dos ciencias, Criptografía y Biometría, aportan soluciones a campos específicos de la protección de datos y autentificación de usuarios, que se verían enormemente potenciados si determinadas características de ambas ciencias se unieran con vistas a objetivos comunes. Por ello es imperativo intensificar la investigación en estos ámbitos combinando los algoritmos y primitivas matemáticas de la Criptografía con la Biometría para dar respuesta a la demanda creciente de nuevas soluciones más técnicas, seguras y fáciles de usar que potencien de modo simultáneo la protección de datos y la identificacíón de usuarios. En esta combinación el concepto de biometría cancelable ha supuesto una piedra angular en el proceso de autentificación e identificación de usuarios al proporcionar propiedades de revocación y cancelación a los ragos biométricos. La contribución de esta tesis se basa en el principal aspecto de la Biometría, es decir, la autentificación segura y eficiente de usuarios a través de sus rasgos biométricos, utilizando tres aproximaciones distintas: 1. Diseño de un esquema criptobiométrico borroso que implemente los principios de la biometría cancelable para identificar usuarios lidiando con los problemas acaecidos de la variabilidad intra e inter-usuarios. 2. Diseño de una nueva función hash que preserva la similitud (SPHF por sus siglas en inglés). Actualmente estas funciones se usan en el campo del análisis forense digital con el objetivo de buscar similitudes en el contenido de archivos distintos pero similares de modo que se pueda precisar hasta qué punto estos archivos pudieran ser considerados iguales. La función definida en este trabajo de investigación, además de mejorar los resultados de las principales funciones desarrolladas hasta el momento, intenta extender su uso a la comparación entre patrones de iris. 3. Desarrollando un nuevo mecanismo de comparación de patrones de iris que considera tales patrones como si fueran señales para compararlos posteriormente utilizando la transformada de Walsh-Hadarmard. Los resultados obtenidos son excelentes teniendo en cuenta los requerimientos de seguridad y privacidad mencionados anteriormente. Cada uno de los tres esquemas diseñados han sido implementados para poder realizar experimentos y probar su eficacia operativa en escenarios que simulan situaciones reales: El esquema criptobiométrico borroso y la función SPHF han sido implementados en lenguaje Java mientras que el proceso basado en la transformada de Walsh-Hadamard en Matlab. En los experimentos se ha utilizado una base de datos de imágenes de iris (CASIA) para simular una población de usuarios del sistema. En el caso particular de la función de SPHF, además se han realizado experimentos para comprobar su utilidad en el campo de análisis forense comparando archivos e imágenes con contenido similar y distinto. En este sentido, para cada uno de los esquemas se han calculado los ratios de falso negativo y falso positivo. ABSTRACT The extraordinary increase of new information technologies, the development of Internet of Things, the electronic commerce, the social networks, mobile or smart telephony and cloud computing and storage, have provided great benefits in all areas of society. Besides this fact, there are new challenges for the protection and privacy of information and its content, such as the loss of confidentiality and integrity of electronic documents and communications. This is exarcebated by the lack of a clear boundary between the personal world and the business world as their differences are becoming narrower. In both worlds, i.e the personal and the business one, Cryptography has played a key role by providing the necessary tools to ensure the confidentiality, integrity and availability both of the privacy of the personal data and information. On the other hand, Biometrics has offered and proposed different techniques with the aim to assure the authentication of individuals through their biometric traits, such as fingerprints, iris, hand geometry, voice, gait, etc. Each of these sciences, Cryptography and Biometrics, provides tools to specific problems of the data protection and user authentication, which would be widely strengthen if determined characteristics of both sciences would be combined in order to achieve common objectives. Therefore, it is imperative to intensify the research in this area by combining the basics mathematical algorithms and primitives of Cryptography with Biometrics to meet the growing demand for more secure and usability techniques which would improve the data protection and the user authentication. In this combination, the use of cancelable biometrics makes a cornerstone in the user authentication and identification process since it provides revocable or cancelation properties to the biometric traits. The contributions in this thesis involve the main aspect of Biometrics, i.e. the secure and efficient authentication of users through their biometric templates, considered from three different approaches. The first one is designing a fuzzy crypto-biometric scheme using the cancelable biometric principles to take advantage of the fuzziness of the biometric templates at the same time that it deals with the intra- and inter-user variability among users without compromising the biometric templates extracted from the legitimate users. The second one is designing a new Similarity Preserving Hash Function (SPHF), currently widely used in the Digital Forensics field to find similarities among different files to calculate their similarity level. The function designed in this research work, besides the fact of improving the results of the two main functions of this field currently in place, it tries to expand its use to the iris template comparison. Finally, the last approach of this thesis is developing a new mechanism of handling the iris templates, considering them as signals, to use the Walsh-Hadamard transform (complemented with three other algorithms) to compare them. The results obtained are excellent taking into account the security and privacy requirements mentioned previously. Every one of the three schemes designed have been implemented to test their operational efficacy in situations that simulate real scenarios: The fuzzy crypto-biometric scheme and the SPHF have been implemented in Java language, while the process based on the Walsh-Hadamard transform in Matlab. The experiments have been performed using a database of iris templates (CASIA-IrisV2) to simulate a user population. The case of the new SPHF designed is special since previous to be applied i to the Biometrics field, it has been also tested to determine its applicability in the Digital Forensic field comparing similar and dissimilar files and images. The ratios of efficiency and effectiveness regarding user authentication, i.e. False Non Match and False Match Rate, for the schemes designed have been calculated with different parameters and cases to analyse their behaviour.

Security Analysis of Randomize-Hash-then-Sign Digital Signatures

At CRYPTO 2006, Halevi and Krawczyk proposed two randomized hash function modes and analyzed the security of digital signature algorithms based on these constructions. They showed that the security of signature schemes based on the two randomized hash function modes relies on properties similar to the second preimage resistance rather than on the collision resistance property of the hash functions. One of the randomized hash function modes was named the RMX hash function mode and was recommended for practical purposes. The National Institute of Standards and Technology (NIST), USA standardized a variant of the RMX hash function mode and published this standard in the Special Publication (SP) 800-106. In this article, we first discuss a generic online birthday existential forgery attack of Dang and Perlner on the RMX-hash-then-sign schemes. We show that a variant of this attack can be applied to forge the other randomize-hash-then-sign schemes. We point out practical limitations of the generic forgery attack on the RMX-hash-then-sign schemes. We then show that these limitations can be overcome for the RMX-hash-then-sign schemes if it is easy to find fixed points for the underlying compression functions, such as for the Davies-Meyer construction used in the popular hash functions such as MD5 designed by Rivest and the SHA family of hash functions designed by the National Security Agency (NSA), USA and published by NIST in the Federal Information Processing Standards (FIPS). We show an online birthday forgery attack on this class of signatures by using a variant of Dean’s method of finding fixed point expandable messages for hash functions based on the Davies-Meyer construction. This forgery attack is also applicable to signature schemes based on the variant of RMX standardized by NIST in SP 800-106. We discuss some important applications of our attacks and discuss their applicability on signature schemes based on hash functions with ‘built-in’ randomization. Finally, we compare our attacks on randomize-hash-then-sign schemes with the generic forgery attacks on the standard hash-based message authentication code (HMAC).