Birthday Attack Research Articles

A provably secure non-iterative hash function resisting birthday attack

To examine the integrity and authenticity of an IP address efficiently and economically, this paper proposes a new non-iterative hash function called JUNA that is based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far. JUNA includes an initialization algorithm and a compression algorithm, and converts a short message of n bits which is regarded as only one block into a digest of m bits, where 80≤m≤232 and 80≤m≤n≤4096. The analysis and proof show that the new hash is one-way, weakly collision-free, and strongly collision-free, and its security against existent attacks such as birthday attack and meet-in-the-middle attack is to O(2m). Moreover, a detailed proof that the new hash function is resistant to the birthday attack is given. Compared with the Chaum–Heijst–Pfitzmann hash based on a discrete logarithm problem, the new hash is lightweight, and thus it opens a door to convenience for utilization of lightweight digital signing schemes.

A fast and efficient hash function based on generalized chaotic mapping with variable parameters

We present a fast and efficient hash algorithm based on a generalized chaotic mapping with variable parameters in this paper. We first define a generalized chaotic mapping by utilizing piecewise linear chaotic map and trigonometric functions. Then, we convert the arbitrary length of message into the corresponding ASCII values and perform 6-unit iterations with variable parameters and message values based on the generalized chaotic mapping. The final hash value is obtained by cascading extracted bits from iteration state values. We excessively evaluate the proposed algorithm in terms of distribution of hash value, sensitivity of hash value to the message and secret keys, statistical analysis of diffusion and confusion, analysis of birthday attacks and collision resistance, analysis of secret keys, analysis of speed, and comparison with other algorithms, and the results illustrate that the suggested algorithm is fast, efficient, and enough simple and has good confusion and diffusion capabilities, strong collision resistance, and a high level of security.

Cryptanalysis of RSA with a small parameter revisited

Let N=pq be an RSA modulus with balanced primes p and q. Suppose that the public exponent e and private exponent d satisfy ed−1=kϕ(N). We revisit the birthday attack against short exponent RSA proposed by Meng and Zheng at ACISP 2012. We show that if e>k(p+q), then N can be factored in both time and space complexity of O˜(k). This improves the former result. We also give a detail explanation on how the baby-step giant-step method works.

Quantum collision search algorithm against New FORK-256

In order to improve the attack efficiency of the New FORK-256 function, an algorithm based on Grover’s quantum search algorithm and birthday attack is proposed. In this algorithm, finding a collision for arbitrary hash function only needs O(2m/3) expected evaluations, where m is the size of hash space value. It is proved that the algorithm can obviously improve the attack efficiency for only needing O(274.7) expected evaluations, and this is more efficient than any known classical algorithm, and the consumed space of the algorithm equals the evaluation.

The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter

In this paper a parallel Hash algorithm construction based on the Chebyshev Halley methods with variable parameters is proposed and analyzed. The two core characteristics of the recommended algorithm are parallel processing mode and chaotic behaviors. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. The proposed algorithm contains variable parameters dynamically obtained from the position index of the corresponding message blocks. Theoretical analysis and computer simulation indicate that the algorithm can assure all performance requirements of hash function in an efficient and flexible style and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

Building a 256-bit hash function on a stronger MD variant

AbstractCryptographic 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.

Secured Hash2 based Message Authentication Code using GUI Controls

message that originated from an authorized user is defined as User Authentication and is provided by Message Authentication codes (MAC). The provision of assurance that the message is not been modified is defined as Message Authentication and is provided by Hash functions. Authenticated code is generated when MAC uses Hash function it is called Hash based MAC (HMAC). In this paper an algorithm is proposed for HMAC which uses SHA-2 as cryptographic hash function. The algorithm is implemented using GUI based controls in MATLAB toolbox which enables the algorithm to be friendly with the user. Theoretical analysis and experimentation show that this hash function is with high plaintext sensitivity and low collision resistance, and secure against birthday attacks or meet-in-the-middle attacks. These properties make it a suitable choice for data signature or authentication.

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.

LDPC and SHA based iris recognition for image authentication

We introduce a novel way to authenticate an image using Low Density Parity Check (LDPC) and Secure Hash Algorithm (SHA) based iris recognition method with reversible watermarking scheme, which is based on Integer Wavelet Transform (IWT) and threshold embedding technique. The parity checks and parity matrix of LDPC encoding and cancellable biometrics i.e., hash string of unique iris code from SHA-512 are embedded into an image for authentication purpose using reversible watermarking scheme based on IWT and threshold embedding technique. Simply by reversing the embedding process, the original image, parity checks, parity matrix and SHA-512 hash are extracted back from watermarked-image. For authentication, the new hash string produced by employing SHA-512 on error corrected iris code from live person is compared with hash string extracted from watermarked-image. The LDPC code reduces the hamming distance for genuine comparisons by a larger amount than for the impostor comparisons. This results in better separation between genuine and impostor users which improves the authentication performance. Security of this scheme is very high due to the security complexity of SHA-512, which is 2256 under birthday attack. Experimental results show that this approach can assure more accurate authentication with a low false rejection or false acceptance rate and outperforms the prior arts in terms of PSNR.

A Novel Biometric Cryptosystem using LDPC and SHA based Iris Recognition

We use Low Density Parity Check (LDPC) error correction code to solve fuzziness i.e., the variability and noise in iris code generated from Iris Recognition System (IRS) and Secure Hash Algorithm (SHA-512) to transform unique iris code into hash string to make them as a Cancellable Biometric. SHA-512 hash string is used as a key for 512 bits Advanced Encryption Standard (AES) encryption process. In the decryption process, Hash comparison is made between new hash generated by SHA-512 from error corrected iris code and hash stored in smart card. If authentic, 512 bits AES decryption is accomplished. Experiments indicate that, use of LDPC code results in better separation between genuine and impostor users which improves the performance of this novel cryptosystem. Security of this system is very high, which is 2 under birthday attack. AES algorithm is enhanced by using 512 bits key and increasing the number of rounds. General Terms Iris Pattern Recognition, Cryptography, Computer Security.

Challenging the increased resistance of regular hash functions against birthday attacks

At Eurocrypt 2004, Bellare and Kohno presented the concept of a regular hash function. For a hash function to be regular, every hash value must have the same number of preimages in the domain. The findings of their paper remained unchallenged for over six years, and made their way into several research papers and textbooks. In their paper, Bellare and Kohno claim that regular hash functions are more resistant against the birthday attack than random hash functions. We counter their arguments, by showing that the success probability of the birthday attack against a regular hash function can be made arbitrarily close to that of a random hash function (for the same number of trials). Our analysis uses the fact that the choices of the attacker can be limited to any subset of the domain. Furthermore, we prove that it is not possible to construct a hash function that is regular for only a small fraction of subsets of the domain. In order to avoid these problems, we propose to model hash functions as random functions. Compared to regular functions, we argue that the statistics of random functions are more similar to hash functions used in practice, regardless of how the attacker chooses the domain points.

Alternate Approach for Implementation of SHA2 Algorithm using Feed forward Neural Network

In this paper an algorithm for one-way hash function construction based on a two layer feed forward neural network along with the piece-wise linear (pwl) chaotic map is proposed. Where SHA-2 is cryptographic hash function designed by NSA(National Security Agency). Based on chaotic neural networks, a SHA-2 Hash function is constructed, which makes use of neural networks' diffusion property and chaos' confusion property. This function encodes the plaintext of arbitrary length into the hash value of fixed length (typically, 128-bit, 256-bit or 512-bit). Theoretical analysis and experimental results show that this hash function is one-way, with high key sensitivity and plaintext sensitivity, and secure against birthday attacks or meet-in-the-middle attacks. These properties make it a suitable choice for data signature or authentication.

Collision analysis of a chaos-based hash function with both modification detection and localization capability

The collision problem of a chaos-based hash function with both modification detection and localization capability is investigated [Xiao D, Shih FY, Liao XF. A chaos-based hash function with both modification detection and localization capabilities. Commun Nonlinear Sci Numer Simulat 2010;15(9):2254–61]. The simulation gives the same detection and localization hash values for distinct messages. The expense of the birthday attack on the hash function is far less than expected. The certain symmetries of message distribution may result in the same detection hash value for distinct messages.

Relation between successfulness of birthday attack on digital signature and hash function irregularity

In many network communications it is crucial to be able to authenticate both the contents and the origin of a message. Digital signatures based on public key schemas are used for such authenticatio...

Chaos-based hash function (CBHF) for cryptographic applications

As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

Cryptanalysis of a novel authentication protocol conforming to EPC-C1G2 standard

In 2006, the standard EPC Class-1 Generation-2 (EPC-C1G2) was ratified both by EPCglobal and ISO. This standard can be considered as a “universal” specification for low-cost RFID tags. Although it represents a great advance for the consolidation of RFID technology, it does not pay due attention to security and, as expected, its security level is very low. In 2007, Chien et al. published a mutual authentication protocol conforming to EPC-C1G2 which tried to correct all its security shortcomings. In this article, we point out various major security flaws in Chien et al.'s proposal. We show that none of the authentication protocol objectives are met. Unequivocal identification of tagged items is not guaranteed because of possible birthday attacks. Furthermore, an attacker can impersonate not only legitimate tags, but also the back-end database. The protocol does not provide forward security either. Location privacy is easily jeopardized by a straightforward tracking attack. Finally, we show how a successful auto-desynchronization (DoS attack) can be accomplished in the back-end database despite the security measures taken against it.

Weil sum for birthday attack in multivariate quadratic cryptosystem

We propose a new cryptanalytic application of a number theoretic tool Weil sum to birthday attack against multivariate quadratic trapdoor function. This new customization of birthday attack is developed by evaluating the explicit Weil sum of the underlying univariate polynomial and the exact number of solutions of the associated bivariate equation. We designed and implemented a new algorithm for computing Weil sum values so that we could explicitly identify some class of weak Dembowski-Ostrom polynomials and their equivalent forms in multivariate quadratic trapdoor function. Our customized attack can be also regarded as an equation solving algorithm for the system of some special quadratic equations over finite fields, and it is fundamentally different from the Gröbner basis methods. Both theoretical observation and experiment show that the required computational complexity of the attack on these weak polynomial instances can be asymptotically less than the square root complexity of the common birthday attack by factor of as large as 2n/8 in terms of the extension degree n of . We also suggest a few open problems that any MQ-based short signature scheme must explicitly take into account for the basic design principles.

Secure hash function based on neural network

A hash function is constructed based on a three-layer neural network. The three neuron-layers are used to realize data confusion, diffusion and compression, respectively, and the multi-block hash mode is presented to support the plaintext with variable length. Theoretical analysis and experimental results show that this hash function is one-way, with high key sensitivity and plaintext sensitivity, and secure against birthday attacks or meet-in-the-middle attacks. Additionally, the neural network's property makes it practical to realize in a parallel way. These properties make it a suitable choice for data signature or authentication.

Energy cost analysis of IPSec on handheld devices

We analyze the computation overhead of the IP security protocol (IPSec) on a handheld device. We design experiments to quantify the energy consumed by the individual components in IPSec. We then experiment with several measures which can potentially cut the energy consumption without compromising security. Our results show that by replacing 3DES with Advanced Encryption Standard as the encryption algorithm, the total energy consumption is reduced by up to 38%. On the other hand, MD5 and SHA-1 consume about the same amount of energy for message authentication, which makes SHA-1 more preferred because of its known higher strength against birthday attacks. We also find that the power-saving mode of the wireless LAN interface does not reduce (and may even increase) the total energy cost despite the substantial amount of network idle time. Finally, we find that the data compression option must be used carefully. When sending data from the handheld device, the lossless compression used in IPSec can actually increase the energy consumption until the network bandwidth drops down to 2 Mbps or lower. However, compression is found to save energy when the device receives compressible data under normal bandwidths. This result suggests that the compression option must be dynamically changed in IPSec between data transmission and reception.

Toward secure public-key blockwise fragile authentication watermarking

The authors describe some weaknesses of public-key blockwise fragile authentication watermarkings and the means to make them secure. Wong's original algorithm as well as a number of its variant techniques are not secure against a mere block cut-and-paste or the well known birthday attack. To make them secure, some schemes have been proposed to make the signature of each block depend on the contents of its neighbouring blocks. The authors attempt to maximise the change localisation resolution using only one dependency per block with a scheme they call hash block chaining version 1 (HBC1). They then show that HBC1, as well as any neighbour content-dependent scheme, are susceptible to another forgery technique that they have named a transplantation attack. They also show a new kind of birthday attack that can be effectively mounted against HBC1. To thwart these attacks, they propose using a nondeterministic digital signature together with a signature-dependent scheme (HBC2). Finally, they discuss the advantages of using discrete logarithm signatures instead of RSA for watermarking.