An application of residue number system arithmetics to secure hash functions design

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.

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-1, RIPEMD-160 and FORK-256 are built on Merkle-Damgård iterative method. Recent differential and generic attacks against these popular hash functions have shown weaknesses of both specific hash functions and their underlying Merkle-Damgård construction. In this paper we propose a hash function follows design principle of NewFORK-256 and based on HAIFA construction. Its compression function takes three inputs and generates a single output of 256-bit length. An extra input to a compression function is a 64-bit counter (number of bits hashed so far). HAIFA 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 shown that the proposed hash function has high sensitivity to an input message and is secure against different cryptanalytic attacks.

Parallel computing of hash functions along with the security requirements have great advantage in order to reduce the time consumption and overhead of the CPU. In this article, a keyed hash function based on farfalle construction and chaotic neural networks (CNNs) is proposed, which generates a hash value with arbitrary (defined by user) length (eg, 256 and 512 bits). The proposed hash function has parallelism merit because it is built over farfalle construction which avoids the dependency between the blocks of a given message. Moreover, the proposed hash function is chaos based (ie, it relies on chaotic maps and CNNs which have non‐periodic behavior). The security analysis shows that the proposed hash function is robust and satisfies the properties of hash algorithms, such as random‐like (non‐periodic) behavior, ideal sensitivity to original message and secret key, one‐way property and optimal diffusion effect. The speed performance of the hash function is also analyzed and compared with a hash function which was built based on sponge construction and CNN, and compared with secure hash algorithm (SHA) variants like SHA‐2 and SHA‐3. The results have shown that the proposed hash function has lower time complexity and higher throughput especially with large size messages. Additionally, the proposed hash function has enough resistance to multiple attacks, such as collision attack, birthday attack, exhaustive key search attack, preimage and second preimage attacks, and meet‐in‐the‐middle attack. These advantages make it ideal to be used as a good collision‐resistant hash function.

The Internet of Things is used in many application areas in our daily lives. Ensuring the security of valuable data transmitted over the Internet is a crucial challenge. Hash functions are used in cryptographic applications such as integrity, authentication and digital signatures. Existing lightweight hash functions leverage task parallelism but provide limited scalability. There is a need for lightweight algorithms that can efficiently utilize multi-core platforms or distributed computing environments with high degrees of parallelization. For this purpose, a data-parallel approach is applied to a lightweight hash function to achieve massively parallel software. A novel structure suitable for data-parallel architectures, inspired by basic tree construction, is designed. Furthermore, the proposed hash function is based on a lightweight block cipher and seamlessly integrated into the designed framework. The proposed hash function satisfies security requirements, exhibits high efficiency and achieves significant parallelism. Experimental results indicate that the proposed hash function performs comparably to the BLAKE implementation, with slightly slower execution for large message sizes but marginally better performance for smaller ones. Notably, it surpasses all other evaluated algorithms by at least 20%, maintaining a consistent 20% advantage over Grostl across all data sizes. Regarding parallelism, the proposed PLWHF achieves a speedup of approximately 40% when scaling from one to two threads and 55% when increasing to three threads. Raspberry Pi 4-based tests for IoT applications have also been conducted, demonstrating the hash function’s effectiveness in memory-constrained IoT environments. Statistical tests demonstrate a precision of ±0.004, validate the hypothesis in distribution tests and indicate a deviation of ±0.05 in collision tests, confirming the robustness of the proposed design.

In this paper, a new hash function based on RC4 stream cipher is proposed. The proposed RC4-based hash function has several advantages over many well-known hash functions. Its efficiency is much better than many widely used known hash function (e.g., MD5 and SHA-1). The application of the proposed hash function can be extended to the ultra-low devices for ubiquitous computing, which most other hash functions do not apply. The structure of the proposed hash function is absolutely different from the broken hash function class (e.g., SHA family) so that people cannot use the existing attack strategies to break the proposed hash function. The proposed hash function is very simple and rules out all possible generic attacks. We proved that this hash function is secure and efficient.

Several fast software hash functions have been proposed since the hash function MD4 was introduced by R. Rivest in 1990. At the moment, SHA-1, RIPEMD-160, and HAVAL are known as secure dedicated hash functions in MDx-family hash functions. In this paper, we propose a new hash function based on advantages of these three hash functions, which keeps the maximum security of them and is more efficient in performance. The proposed hash function processes an arbitrary finite message by 512-bit block and outputs 160 bits digest. The key feature of the proposed hash function is data-dependent rotation. This feature guarantees the strength against existing known attacks. Moreover, we propose a new keyed MAC(Message Authentication Code) constructed using the proposed hash function. The proposed MAC uses a maximum keys of 160 bits and has a bitlength less than equal to the hash result. From the viewpoint of performance, the proposed MAC is only reduced about 10% comparing to the underlying hash function.

The non-linear property of Chaos is a promising approach to information security, and many accomplishments have been made by combining Chaos with several sub-security domains, including chaos-based stream ciphers, block ciphers, image encryption, and hash functions. Most Chaos-based hash functions are insecure or inefficient due to their dependence on complex, attacked multi-dimensional maps or uncertain, weak one-dimensional maps like logistic and tent. The Collatz Conjecture is a mystery that has stumped mathematicians for decades and still has not been solved. This paper aims to introduce a novel approach to addressing current security challenges by utilizing our generalized Collatz process to create a chaos-based hash function. By leveraging the unpredictable behaviour of the Collatz sequence, the proposed hash function aims to enhance ergodicity and entropy properties, thereby making it well-suited for cryptographic applications. In the proposed method, the chaotic variables are governed by cryptographic keys, crucial in generating data sequences. These sequences are then utilized within the diffusion and confusion structures of the hashing function. The design of the chaos-hash model is carefully optimized to exhibit desirable characteristics such as randomness, collision resistance, uniformity, sensitivity to initial conditions, speed, and resistance against cryptanalysis.The primary goal of this research is to develop a robust and efficient chaos-based hash function that addresses the requirements of cryptographic systems. By incorporating the Collatz process and carefully considering key-controlled variables, the proposed model aims to offer enhanced security properties while meeting the necessary criteria for a reliable and effective hashing mechanism. The effectiveness and dependability of the proposed hash function are evaluated by comparing it with two well-known hash algorithms, namely SHA-3 and SHA-2, as well as several other Chaos-based hash algorithms. Through comprehensive evaluations conducted under various circumstances and with different datasets, the suggested hash function consistently outperforms the state-of-the-art alternatives. Experiments involving diverse input scenarios consistently demonstrate that the proposed hash function surpasses the performance of the current leading alternatives. Its superior performance is observed across various evaluation metrics, confirming its effectiveness in generating reliable and secure hash values. The results obtained from the comparative analysis highlight the superiority of the proposed hash function over existing alternatives, validating its potential as a robust solution for various cryptographic applications.

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.

In this paper, a new chaos-based hash function is proposed based on a recently proposed structure known as the deterministic chaotic finite state automata (DCFSA). Out of its various configurations, we select the forward and parameter permutation variant, $DCFSA_{FWP}$ due to its desirable chaotic properties. These properties are analogous to hash function requirements such as diffusion, confusion and collision resistance. The proposed hash function consists of six machine states and three simple chaotic maps. This particular structure of DCFSA can process larger message blocks (leading to higher hashing rates) and optimizes its randomness. The proposed hash function is analyzed in terms of various security aspects and compared with other recently proposed chaos-based hash functions to demonstrate its efficiency and reliability. Results indicate that the proposed hash function has desirable statistical characteristics, elevated randomness, optimal diffusion and confusion properties as well as flexibility.

The inherent random-like behavior and one-way property of iteration in chaotic systems provide a good basis for designing Hash function. In the era of big data, due to the increasing data capacity in applications, fast Hash functions with parallel mode are highly desirable when authenticating data integrity. We analyze the issue of how to parallelize Hash function with iterative structure. Some security requirements on parallel Hash function are presented. In addition, using chaotic map and block cipher, we construct a keyed parallel Hash function. The message blocks are firstly processed in parallel by a DM-like structure. Furthermore, a tree mode with chaotic map is utilized to combine the outputs of the hash round function in parallel. The proposed Hash function is analyzed by theory and tested by computer simulations. The test results show that the proposed scheme can resist the various common attacks against Hash functions. It satisfies the secure performance requirements of Hash function. Owing to the usage of the parallel mode to process messages, the proposed chaos-based Hash function possess high efficiency and has high potential in applications to guarantee data integrity on a parallel computing platform.

This paper presents a new structure for keyed hash function based on chaotic maps, neural network and sponge construction. The structure of proposed Keyed Sponge Chaotic Neural Network KSCNN hash function is composed of three phases: the initialization phase pads the message M and divides it into q message blocks M i of fixed size r, the absorbing phase hashes the message blocks by using CNN — Block i and produces the intermediate hash value HM i and the squeezing phase produces, starting from HM q , the final hash value h with desired length. The combining of sponge construction with the CNN — Blocki improves, on one hand, the security of proposed hash function and makes, on the other hand, the length of hash value more dynamic. Our theoretical analysis and experimental simulations show that the proposed hash function KSCNN has good statistical properties, strong collision resistance, high message sensitivity compared with SHA-3 and immune against pre-image, second pre-image and collision attacks.

Hash functions serve as the fingerprint of a message. They also serve as an authentication mechanism in many applications. Nowadays, hash functions are widely used in blockchain technology and bitcoins. Today, most of the work concentrates on the design of lightweight hash functions which needs minimal hardware and software resources. This paper proposes a lightweight hash function which makes use of Cellular Automata (CA) and sponge functions. This hash function accepts arbitrary length message and produces fixed size hash digest. An additional property of this function is that the size of the hash digest may be adjusted based on the application because of the inherent property of varying length output of sponge function. The proposed hash function can be efficiently used in resource constraint environments in a secure and efficient manner. In addition, the function is resistant to all known generic attacks against hash functions and is also preimage resistant, second preimage resistant and collision resistant.KeywordsCryptographic Hash functionsCellular automataSponge functionsOmega-flip permutation

An Introduction to Multi-trapdoor Hash Functions and It's Applications

This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal—namely, improved logistic, cosine logistic map, logistic sine system, tent sine system, and hybrid. Using DNA features and binary coding technology with complementary rules to hide information is a key challenge. This article proposes improving SHA-512 in two aspects: the modification of original hash buffer values, and the modification of additive constants Kt. This proposal is to make hash buffer values (a, b, c, d, e, f, g, and h) and Kt dependent on one-dimensional discrete chaotic maps and DNA sequences instead of constant. This modification complicates the relationship between the original message and hash value, making it unexpected. The performance of the proposed hash function is tested and analyzed the confusion, diffusion, and distributive and compared with the original SHA-512. The performance of security is analyzed by collision analysis, for which the maximum number of hits is only three, showing that the proposed hash function enhances the security and robustness of SHA-512. The statistical data and experimental analysis indicate that the proposed scheme has good properties and satisfies high-performance requirements for secure hash functions.

Hash functions are widely used in secure communication systems for message authentication and data integrity verification. For encryption of data, stream ciphers are preferred to block ciphers because it consumes less power and hardware. In this paper we propose implementation and analysis of a circuit for both Hash generation and Encryption of data, based on a single hardware block in the time shared manner. The design of stream cipher based on hardware efficient hash function was reported earlier but in a paper which appeared later, the security of this stream cipher was proved to be very low. In this paper, we investigate how to overcome this weakness and make the design more secure, without much increase in hardware complexity. Here, we implement a 128 bit message encryption circuit which facilitates data integrity check using hash function in FPGA.