Merkle-Damgard Research Articles

Radial kernelized regressive merkle–damgård cryptographic hash blockchain for secure data transmission with IoT sensor node

The concept of the Internet of Things (IoT) has drawn noteworthy attention to use the collected data anywhere in the world. Wireless Sensor Node (WSN) is integrated into the IoT for data collection. The IoT is very intense towards the security investigation. Patient data is medical information about an individual patient. Patient data contains their past and current health, treatment history, lifestyle options and genetic data. The patient data security is a most important issue in IoT. When a collected data get transmitted from the sensor node to the server it theft or altered by various intruders and it may cause a lack of security. In order to address these issues, in this research work, a novel technique called Radial Kernelized Regressive Merkle–Damgard Cryptographic Hash Blockchain (RKRMDCHB) technique is introduced to improve secure data transmission. The wireless sensor nodes are deployed to sense and monitor the data. At first, the sensing data are collected for secure transmission to the server. The RKRMDCHB technique uses the Radial Basis Kernelized Regression Function to perform the data classification. The regression function analyzes the input data and is categorized into various types of classes based on the radial basis kernel function. The classified data is given to the data block of the blockchain for secure transmission. The RKRMDCHB technique uses the Merkle–Damgard Cryptographic technique to generate the hash for each input data with the help of the one-way compression function. The data in the form of a hash is transmitted to the server through the internet. As a result, the RKRMDCHB technique ensures security and confidentiality to preserve the data and provide better communication. Experimental assessment is carried out on certain factors such as data confidentiality rate, data integrity, and processing time, with respect to a number of data sensed from the sensor device. The results demonstrate that the proposed RKRMDCHB technique provides an efficient solution for secure data transmission while preserving sensitive information against potential threats.

Evolutionary double-pipe prefix-free hash function

Recent works have presented collision attacks based on differentiability of classical hash functions. In this article a new hash function is proposed with enhanced Merkle-Damgard construction. It has a single length compression function which is based on Miyaguchi-Preneel block cipher and benefit of Genetic Algorithm for diffusion. Fitness function of GA provides maximum cryptographic diffusion and resist against well-known weaknesses like differentiability and collision attacks.

A chaos-based keyed hash function based on fixed point representation

Chaotic maps are used in the design of hash functions due to their characteristics that are analogous to cryptographic requirements. However, these maps are commonly implemented using floating point representation which has high computational complexity. They also suffer from interoperability problems and are not easy to analyse from the binary point of view. These drawbacks lead to a lack of acceptance of chaos-based cryptography for practical use. This paper overcomes these problems by introducing a chaos-based hash function implemented using fixed point representation which computes digital chaotic maps using integers. Its design is based on the Merkle–Damgard construction and the generalised Feistel structure for strong security justifications. Security evaluation indicates that the proposed hash function has near-perfect statistical properties which include diffusion, confusion, collision resistance and distribution. The proposed hash function also surpasses existing chaos-based hash functions in terms of performance, making it a viable hash function for practical implementation.

Simple hash function using discrete-time quantum walks

Hash functions play an essential role in many cryptographic applications such as digital signature, integrity authentication, and key derivation. Most of them are iteratively built based on the Merkle–Damgard (MD) structure. Unfortunately the traditional MD structure is suffering from various attacks, and thus the design of new hash functions is emerging. In this paper, inspired by quantum computation, we present a new hash function by introducing alternate single-qubit coin operators into discrete-time quantum walk. The present hash function is classical with classical input and output. The compressive function can be implemented by performing alternate single-qubit coin operators on the coin state controlled by a classical input binary message and then applying the global conditional shift operator on the position state and the coin state. The classical output hash value is generated by making amplification, truncation, and modular operation on the final probability distribution. Numerical simulation and performance comparison show that the present hash function has an excellent property of collision resistance and easier implementation than existing quantum-walk-based hash functions. It promotes more applications of quantum computation in the design of hash functions.

Enhanced Message Digest Version 5 Architecture for Secure Hashing

The message digest algorithm is a widely used cryptographic hash function. It produces a 128-bit hash value. It has been used in a variety of security applications and is also commonly used to check data integrity. However MD5 has been found not to be collision resistant. It is possible to find a pseudo-collision, that is, two different initialization vectors which produce an identical digest. Other attacks that have been found to be working on MD5 are rainbow, dictionary and brute-forcing attacks. The ability to find collisions has been greatly aided by the graphics processing unit (GPU). The solution to these collisions is a robust MD5 compression function. This research paper focused on enhancing the Merkle Damgard model construction, which is the core component of the hashing process. It involved adding an extra iteration so that instead of the current two -cycle looping, we have a three-cycle looping per message block. The aim is to make it computationally infeasible to reverse the hash function. In this way, make the whole MD5 algorithm would be made stronger. This algorithm could then be used for password hashing in an effort to make them robust. The new password hashing mechanism find applications in areas such as digital signatures and digital certificates.

Enhancing the Security Level of SHA-1 by Replacing the MD Paradigm

Cryptographic hash functions are important cryptographic techniques and are used widely in many cryptographic applications and protocols. All the MD4 design based hash functions such as MD5, SHA-0, SHA-1 and RIPEMD-160 are built on Merkle-Damgard iterative method. Recent differential and generic attacks against these popular hash functions have shown weaknesses of both specific hash functions and their underlying Merkle-Damgard construction. In this paper we propose a hash function which follows design principle of SHA-1 and is based on dither construction. Its compression function takes three inputs and generates a single output of 160-bit length. An extra input to a compression function is generated through a fast pseudo-random function. Dither construction shows strong resistance against major generic and other cryptanalytic attacks. The security of proposed hash function against generic attacks, differential attack, birthday attack and statistical attack was analyzed in detail. It is exhaustedly compared with SHA-1 because hash functions from SHA-2 and SHA-3 are of higher bit length and known to be more secure than SHA-1. It is shown that the proposed hash function has high sensitivity to an input message and is secure against different cryptanalytic attacks.

R-Hash: Hash Function Using Random Quadratic Polynomials Over GF(2)

In this paper we describe an improved version of HF -hash [7] viz. R-hash: Hash Function Using Random Quadratic Polynomials Over GF(2). The compression function of HF -hash consists of 32 polynomials with 64 variables over GF(2), which were taken from the first 32 polynomials of HFE challenge -1 by forcing last 16 variables as 0. The mode operation used in computing HF -hash was Merkle-Damgard. We have randomly selected 32 quadratic non-homogeneous polynomialshaving 64 variables over GF(2)in case of R-hash to improve the security of the compression function used in HF -hash. In designing R-hash, we have also changed the mode operation used in HF-hash, because of the theoretical weakness found in the Merkle-Damgard construction. In this paper we will prove that R-hash is more secure than HF-hash and SHA-256 as well as we will show that it is also faster than HF-hash.

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.

Security Analysis of Zipper Hash Against Multicollisions Attacks

In this paper, the existence of multicollisions in Zipper Hash structure, a new Hash structure which was introduced to strengthen the iterated Hash structures, is presented. This study shows that finding multicollisions, i.e. 2k-way collision, in this Hash structure is not much harder than finding such multicollisions in ordinary Merkle - Damgard (MD) structure. In fact, the complexity of the attacks is approximately n/2 times harder than what has been found for MD structures. Then, these large multicollisions are used as a tool to find D-way preimage for this structure. The complexity of finding 2K-way multicollisions and 2k-way preimages are (eq) and (eq) respectively. Similar to what has been proved by Joux for MD, it is shown in this paper that this structure could not be used to create a Hash function with 2n-bit length by concatenating this structure with any other Hash structure by Hash’s output length of n-bite. It is also shown that time complexity of finding a collision for this concatenated structure is (eq) which is much smaller than what was expected from generic-birthday attack which would be (eq) . In addition, it is shown that increasing the number of rounds of this Hash function can not improve its security against this attack significantly and the attacker can find multicollisions on this Hash function which means that this Hash function has a structural flaw.

Higher order eTCR hash functions

We study higher order eTCR (enhanced target collision resistance) hash functions, where rth-order eTCR is denoted by eTCR(r). We prove that a few rounds of the MD (Merkle–Damgård) scheme and a few levels of the TR (tree) scheme can be eTCR under the compression function is eTCR(r) for some positive integer r. Additionally, we prove that the TH (tree hash) scheme also preserves eTCR.

TTradeoff tables for compression functions: how to invert hash values radeoff Tables for Compression Functions: How to Invert Hash Values

Hash functions are one of the ubiquitous cryptographic functions used widely for various applications such as digital signatures, data integrity, authentication protocols, MAC algorithms, RNGs, etc. Hash functions are supposed to be one-way, i.e., preimage resistant. One interesting property of hash functions is that they process arbitrary-length messages into fixed-length outputs. In general, this can be achieved mostly by applying compression functions onto the message blocks of fixed length, recursively. The length of the message is incorporated as padding in the last block prior to the hash, a procedure called the Merkle-Damgard strengthening. In this paper, we introduce a new way to find preimages on a hash function by using a rainbow table of its compression function even if the hash function utilizes the Merkle-Damgard (MD) strengthening as a padding procedure. To overcome the MD strengthening, we identify the column functions as representatives of certain set of preimages, unlike conventional usage of rainbow tables or Hellman tables to invert one-way functions. As a different approach, we use the position of the given value in the table to invert it. The workload of finding a preimage of a given arbitrary digest value is 2^{2n/3} steps by using 2^{2n/3} memory, where n is both the digest size and the length of the chaining value. We give some extensions of the preimage attack on certain improved variants of MD constructions such as using output functions, incorporating the length of message blocks or using random salt values. Moreover, we introduce the notion of ``near-preimage'' and mount an attack to find near-preimages. We generalize the attack when the digest size is not equal to the length of chaining value. We have verified the results experimentally, in which we could find a preimage in one minute for the 40-bit hash function, whereas the exhaustive search took roughly one week on a standard PC.

Meet-in-the-Middle Preimage Attacks on Hash Modes of Generalized Feistel and Misty Schemes with SP Round Function

We assume that the domain extender is the Merkle-Damgård (MD) scheme and he message is padded by a ‘1’, and minimum number of ‘0’s, followed by a fixed size length information so that the length of padded message is multiple of block length. Under this assumption, we analyze securities of the hash mode when the compression function follows the Davies-Meyer (DM) scheme and the underlying block cipher is one of the plain Feistel or Misty scheme or the generalized Feistel or Misty schemes with Substitution-Permutation (SP) round function. We do this work based on Meet-in-the-Middle (MitM) preimage attack techniques, and develop several useful initial structures.

On the Full MAC Security of a Double-Piped Mode of Operation

We revisit the double-pipe construction introduced by Lucks at Asiacrypt 2005. Lucks originally studied the construction for iterated hash functions and showed that the approach is effective in improving security against various types of collision and (second-)preimage attacks. Instead, in this paper we apply the construction to the secret-key setting, where the underlying FIL (fixed-input-length) compression function is equipped with a dedicated key input. We make some adjustments to Lucks' original design so that now the new mode works with a single key and operates as a domain extension of MACs (message authentication codes). Though more than twice as slow as the Merkle-Damgard construction, the double-piped mode enjoys security strengthened beyond the birthday bound. More specifically, when iterating an FIL-MAC whose output size is n-bit, the new double-piped mode yields an AIL-(arbitrary-input-length-)MAC with security up to O(2n) query complexity. This bound contrasts sharply with the birthday bound of O(2n/2), which was the best MAC security accomplished by earlier constructions.

A Simple Variant of the Merkle–Damgård Scheme with a Permutation

We propose a new composition scheme for hash functions. It is a variant of the Merkle–Damgard construction with a permutation applied right before the processing of the last message block. We analyze the security of this scheme using the indifferentiability formalism, which was first adopted by Coron et al. to the analysis of hash functions. We also study the security of simple MAC constructions out of this scheme. Finally, we discuss the random oracle indifferentiability of this scheme with a double-block-length compression function or the Davies–Meyer compression function composed of a block cipher.

Merkle-Damgard Hash Functions with Split Padding

We introduce the “split padding” into a current Merkle-Damgard hash function H. The patched hash function $\\bar{H}$ satisfies the following properties: (i) $\\bar{H}$ is second-preimage-resistant (SPR) if the underlying compression function h satisfies an “SPR-like” property, and (ii) $\\bar{H}$ is one-way (OW) if h satisfies an “OW-like” property. The assumptions we make about h are provided with simple definitions and clear relations to other security notions. In particular, they belong to the class whose existence is ensured by that of OW functions, revealing an evident separation from the strong collision-resistance (CR) requirement. Furthermore, we get the full benefit from the patch at almost no expense: The new scheme requires no change in the internals of a hash function, runs as efficiently as the original, and as usual inherits CR from h.

Omega Network Hash Construction

Problem statement: Cryptographic hash functions are important cryptographic primitives. They are commonly used for data integrity checking and data authentication. Most of the cryptographic hash functions are based on the Merkle-Damgard construction. The basic Merkle-Damgard construction runs over the input sequentially, which can lead to problems when the input size is large since the computation time increases linearly. Approach: Therefore, an alternative architecture which can reduce the computation time is needed, especially in today’s world where multi-core processors and multithreaded programming are common. An Omega Network Hash Construction (ONHC) run parallel in multi-core machine has been proposed as an alternative to the existing hash constructions. Result: The ONHC performed better than the Merkle-Damgard construction. ONHC permutation architecture also showed improved security strength in term of digest value randomness when compared to Merkle-Damgard construction. Conclusion: Therefore, it is believed that the proposed ONHC is a valuable structure that can improve the performance of any hash function that can run on top of it.

Cryptanalysis of an Iterated Halving-based hash function: CRUSH

Iterated Halving has been suggested as a replacement to the Merkle–Damgård (MD) construction in 2004 anticipating the attacks on the MDx family of hash functions. The CRUSH hash function provides a specific instantiation of the block cipher for Iterated Halving. The authors identify structural problems with the scheme and show that they can trivially identify collisions and second preimages on many equal-length messages of length ten blocks or more. The cost is ten decryptions of the block cipher, this being less than the generation of a single digest. In addition, these attacks can be used to differentiate CRUSH from a random oracle in O(1). The authors show that the complexity of finding a preimage in the unpadded CRUSH with the length encoding is negligible and extend this attack on CRUSH with the length encoding in cost O(232). This attack is a multi-preimage attack, since the attacker can produce a large number of messages for a given message digest for the cost of O(232). Hence, this attack can be used as a multi-collision and a multi-second-preimage as well. They show that if the attacker knows the last 64-bits of the message digest in advance, he can do the time-consuming part of the attack off-line. The authors show that even if Iterated Halving is repaired, the construction has practical issues that means it is not suitable for general deployment.

Secure and Fast Hashing Algorithm with Multiple Security Levels

We propose a new secure and fast hashing algorithm with multiple security levels (SFHA-MSL). It is based on the generic 3C (3 compressions) construction and the 3C-X (3C XOR) hash function which is the simplest and efficient variant of the generic 3C hash function and it is the simplest modification to the Merkle-Damgard (M-D) iterated construction that one can achieve. The design principle of the proposed algorithm is to have variable output length of 128, 192 and 256 bits, variable number of compression functions, variable number of iterations in each compression function and variable compression function structure. The compression function used in this algorithm is more dynamic in the sense that the input controls what happen in the algorithm. This enable us to achieve a novel design principle: when message is changed, different shift rotations are done which causes more complexity for someone trying to create a collision. Instead of mixing a single word of a message block, four words are mixed per iteration which achieve faster data diffusion and hence better avalanching effect. There is no message expansion in the proposed scheme and it doesn't use Boolean functions but uses only addition, XOR and rotations to achieve its security. This in addition to increasing the algorithm efficiency, it distributes non-linearity among all blocks in a round.

Indifferentiability of Single-Block-Length and Rate-1 Compression Functions

The security notion of indifferentiability was proposed by Maurer, Renner, and Holenstein in 2004. In 2005, Coron, Dodis, Malinaud, and Puniya discussed the indifferentiability of hash functions. They have shown that the Merkle-Damgard construction is not secure in the sense of indifferentiability. In this paper, we analyze the security of single-block-length and rate-1 compression functions in the sense of indifferentiability. We formally show that all single-block-length and rate-1 compression functions, which include the Davies-Meyer compression function, are insecure. Furthermore, we show how to construct a secure single-block-length and rate-1 compression function in the sense of indifferentiability. This does not contradict our result above.