Collision Resistance Research Articles

Elliptic Curve Multiset Hash

A homomorphic, or incremental, multiset hash function, associates a hash value to arbitrary collections of objects (with possible repetitions) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves: it is simply their sum under a suitable group operation. In particular, hash values of large collections can be computed incrementally and/or in parallel. Homomorphic hashing is thus a very useful primitive with applications ranging from database integrity verification to streaming set/multiset comparison and network coding. Unfortunately, constructions of homomorphic hash functions in the literature are hampered by two main drawbacks: they tend to be much longer than usual hash functions at the same security level (e.g. to achieve a collision resistance of 2^128, they are several thousand bits long, as opposed to 256 bits for usual hash functions), and they are also quite slow. In this paper, we introduce the Elliptic Curve Multiset Hash (ECMH), which combines a usual bit string-valued hash function like BLAKE2 with an efficient encoding into binary elliptic curves to overcome both difficulties. On the one hand, the size of ECMH digests is essentially optimal: 2m-bit hash values provide O(2^m) collision resistance. On the other hand, we demonstrate a highly-efficient software implementation of ECMH, which our thorough empirical evaluation shows to be capable of processing over 3 million set elements per second on a 4 GHz Intel Haswell machine at the 128-bit security level---many times faster than previous practical methods.

Binary quantum hashing

We propose a binary quantum hashing technique that allows to present binary inputs by quantum states. We prove the cryptographic properties of the quantum hashing, including its collision resistance and preimage resistance. We also give an efficient quantum algorithm that performs quantum hashing, and altogether this means that this function is quantum one-way. The proposed construction is asymptotically optimal in the number of qubits used.

Optimal collision security in double block length hashing with single length key

The idea of double block length hashing is to construct a compression function on 2n bits using a block cipher with an n-bit block size. All optimally secure double block length hash functions known in the literature employ a cipher with a key space of double block size, 2n-bit. On the other hand, no optimally secure compression functions built from a cipher with an n-bit key space are known. Our work deals with this problem. Firstly, we prove that for a wide class of compression functions with two calls to its underlying n-bit keyed block cipher collisions can be found in about $$2^{n/2}$$2n/2 queries. This attack applies, among others, to functions where the output is derived from the block cipher outputs in a linear way. This observation demonstrates that all security results of designs using a cipher with 2n-bit key space crucially rely on the presence of these extra n key bits. The main contribution of this work is a proof that this issue can be resolved by allowing the compression function to make one extra call to the cipher. We propose a family of compression functions making three block cipher calls that asymptotically achieves optimal collision resistance up to $$2^{n(1-\varepsilon )}$$2n(1-ź) queries and preimage resistance up to $$2^{3n(1-\varepsilon )/2}$$23n(1-ź)/2 queries, for any $$\varepsilon >0$$ź>0. To our knowledge, this is the first optimally collision secure double block length construction using a block cipher with single length key space. We additionally prove this class of functions indifferentiable from random functions in about $$2^{n/2}$$2n/2 queries, and demonstrate that no other function in this direction achieves a bound of similar kind.

Occurrences of large-magnitude earthquakes in the Kachchh region, Gujarat, western India: Tectonic implications

Moderate-to-large damaging earthquakes in the peninsular part of the Indian plate do not support the long-standing belief of the seismic stability of this region. The historical record shows that about 15 damaging earthquakes with magnitudes from 5.5 to ~8.0 occurred in the Indian peninsula. Most of these events were associated with the old rift systems. Our analysis of the 2001 Bhuj earthquake and its 12-year aftershock sequence indicates a seismic zone bound by two linear trends (NNW and NNE) that intersect an E–W-trending graben. The Bouguer gravity values near the epicentre of the Bhuj earthquake are relatively low (~2mgal). The gravity anomaly maps, the distribution of earthquake epicentres, and the crustal strain-rate patterns indicate that the 2001 Bhuj earthquake occurred along a fault within strain-hardened mid-crustal rocks. The collision resistance between the Indian plate and the Eurasian plate along the Himalayas and anticlockwise rotation of the Indian plate provide the far-field stresses that concentrate within a fault-bounded block close to the western margin of the Indian plate and is periodically released during earthquakes, such as the 2001MW 7.7 Bhuj earthquake. We propose that the moderate-to-large magnitude earthquakes in the deeper crust in this area occur along faults associated with old rift systems that are reactivated in a strain-hardened environment.

The Security of Tandem-DM in the Ideal Cipher Model

We prove that Tandem-DM, one of the two "classical" schemes for turning an n-bit blockcipher of 2n-bit key into a double-block-length hash function, has birthday-type collision resistance in the ideal cipher model. For $$n=128$$n=128, an adversary must make at least $$2^{120.87}$$2120.87 blockcipher queries to achieve chance 0.5 of finding a collision. A collision resistance analysis for Tandem-DM achieving a similar birthday-type bound was already proposed by Fleischmann, Gorski and Lucks at FSE 2009. As we detail, however, the latter analysis is wrong, thus leaving the collision resistance of Tandem-DM as an open problem until now. Our analysis exhibits a novel feature in that we introduce a trick never used before in ideal cipher proofs. We also give an improved bound on the preimage security of Tandem-DM. For $$n=128$$n=128, we show that an adversary must make at least $$2^{245.99}$$2245.99 blockcipher queries to achieve chance 0.5 of inverting a randomly chosen point in the range. Asymptotically, Tandem-DM is proved to be preimage resistant up to $$2^{2n}/n$$22n/n blockcipher queries. This bound improves upon the previous best bound of $${{\varOmega }}(2^n)$$Ω(2n) queries and is optimal (ignoring log factors) since Tandem-DM has range of size $$2^{2n}$$22n.

Dynamics of ion temperature gradient turbulence and transport with a static magnetic island

Understanding the interaction mechanisms between large-scale magnetohydrodynamic instabilities and small-scale drift-wave microturbulence is essential for predicting and optimizing the performance of magnetic confinement based fusion energy experiments. We report progress on understanding these interactions using both analytic theory and numerical simulations performed with the BOUT++ [Dudson et al., Comput. Phys. Commun. 180, 1467 (2009)] framework. This work focuses upon the dynamics of the ion temperature gradient instability in the presence of a background static magnetic island, using a weakly electromagnetic two-dimensional five-field fluid model. It is found that the island width must exceed a threshold size (comparable with the turbulent correlation length in the no-island limit) to significantly impact the turbulence dynamics, with the primary impact being an increase in turbulent fluctuation and heat flux amplitudes. The turbulent radial ion energy flux is shown to localize near the X-point, but does so asymmetrically in the poloidal dimension. An effective turbulent resistivity which acts upon the island outer layer is also calculated and shown to always be significantly (10×–100×) greater than the collisional resistivity used in the simulations.

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.

On the balanced quantum hashing

In the paper we define a notion of a resistant quantum hash function which combines a notion of pre-image (one-way) resistance and the notion of collision resistance. In the quantum setting one-way resistance property and collision resistance property are correlated: the “more” a quantum function is one-way resistant the “less” it is collision resistant and vice versa. We present an explicit quantum hash function which is “balanced” one-way resistant and collision resistant and demonstrate how to build a large family of balanced quantum hash functions.

TDHA: A Timestamp Defined Hash Algorithm for Secure Data Dissemination in VANET

The safety application in vehicular ad hoc network provides active road safety to avoid road accidents by disseminating life critical information among drivers securely. Such information must be protected from the access of intruder or attacker. A timestamp defined hash algorithm is proposed in the present work for secure data dissemination among vehicles. The sender vehicle sends a deformed version of the original message along with the incomplete message digest to its neighbors. The receiver vehicle generates message digest from the deformed version of the original message and also from the incomplete message digest. It accepts the message if both the digests are equal. The proposed algorithm fulfils all the basic properties such as preimage resistance, collision resistance of a one-way unkeyed hash function. Finally the comparative usability of the hash algorithm in the said application domain is worked out and that shows the dominance of the scheme over the existing schemes.

A Robust Hash Function Using Cross-Coupled Chaotic Maps with Absolute-Valued Sinusoidal Nonlinearity

This paper presents a compact and effective chaos-based keyed hash function implemented by a cross-coupled topology of chaotic maps, which employs absolute-value of sinusoidal nonlinearity, and offers robust chaotic regions over broad parameter spaces with high degree of randomness through chaoticity measurements using the Lyapunov exponent. Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. The results of hashing performances show that the mean changed probabilities are very close to 50%, and the mean number of bit changes is also close to a half of hash value lengths. The collision tests reveal the mean absolute difference of each character values for the hash values of 128, 160 and 256 bits are close to the ideal value of 85.43. The proposed keyed hash function enhances the collision resistance, comparing to MD5 and SHA1, and the other complicated chaos-based approaches. An implementation of hash function Android application is demonstrated.

Robust Hashing Algorithm for Data Verification

This paper presents a method for data authentication. Data authentication is the process of being able to verify the source of data. With data authentication, one can distinguish messages originating from the intended sender and an attacker. Data authenticity verification procedure uses cryptographic hash functions as the core algorithm. This algorithm based on linear combination of matrices to find non-invertible matrix, DILH takes advantage about of the compact representation of a set of numbers in a matrix, we design a robust method by employing strong collision resistance and reduces the hashing time.

Cryptographic Hardness of Random Local Functions

Constant parallel-time cryptography allows to perform complex cryptographic tasks at an ultimate level of parallelism, namely by local functions that each of their output bits depend on a constant number of input bits. A natural way to obtain local cryptographic constructions is to use random local functions in which each output bit is computed by applying some fixed d-ary predicate P to a randomly chosen d-size subset of the input bits. In this work, we will study the cryptographic hardness of random local functions. In particular, we will survey known attacks and hardness results, discuss different flavors of hardness (one-wayness, pseudorandomness, collision resistance, public-key encryption), and mention applications to other problems in cryptography and computational complexity. We also present some open questions with the hope to develop a systematic study of the cryptographic hardness of local functions.

THERMAL FRONTS IN SOLAR FLARES

We studied the formation of a thermal front during the expansion of hot plasma into colder plasma. We used a three-dimensional electromagnetic particle-in-cell model that includes inductive effects. In early phases, in the area of the expanding hot plasma, we found several thermal fronts, which are defined as a sudden decrease of the local electron kinetic energy. The fronts formed a cascade. Thermal fronts with higher temperature contrast were located near plasma density depressions, generated during the hot plasma expansion. The formation of the main thermal front was associated with the return-current process induced by hot electron expansion and electrons backscattered at the front. A part of the hot plasma was trapped by the thermal front while another part, mainly with the most energetic electrons, escaped and generated Langmuir and electromagnetic waves in front of the thermal front, as shown by the dispersion diagrams. Considering all of these processes and those described in the literature, we show that anomalous electric resistivity is produced at the location of the thermal front. Thus, the thermal front can contribute to energy dissipation in the current-carrying loops of solar flares. We estimated the values of such anomalous resistivity in the solar atmosphere together with collisional resistivity and electric fields. We propose that the slowly drifting reverse drift bursts, observed at the beginning of some solar flares, could be signatures of the thermal front.

On the concept of cryptographic quantum hashing

In the letter we define the notion of a quantum resistant (-resistant) hash function which consists of a combination of pre-image (one-way) resistance (ε-resistance) and collision resistance (δ-resistance) properties.We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.

건강정보를 이용한 OTP 생성 방식 설계

Abstract User Authentication in Online service is essential for accurate and safe service. For this user authentication, One Time Password(OTP) is frequently used. To satisfy one-time-use characteristic of OTP, Offset information to generate OTP or final OTP value get generated through OTP generator or security card which could be lost. In this study, OTP generation method that bypasses OTP generator or security card by using health information collected from u-Health care system is proposed. Suggestion is that health information collected through wearable devices get utilized to offset information that are applied in OTP generations. OTP generated using suggested methods showed similar results than current OTP generation methods in the collision resistance test which tests how often it generate same authentication numbers, this implies that new proposed method can be applied to various on-line services. Key Words : OTP, Convergence User Authentication, Health Information, Collision resistance, u-Health

TURBULENT GENERAL MAGNETIC RECONNECTION

Plasma flows with an MHD-like turbulent inertial range, such as the solar wind, require a generalization of General Magnetic Reconnection (GMR) theory. We introduce the slip-velocity source vector, which gives the rate of development of slip velocity per unit arc length of field line. The slip source vector is the ratio of the curl of the non ideal electric field in the Generalized Ohm's Law and the magnetic field strength. It diverges at magnetic nulls, unifying GMR with magnetic null-point reconnection. Only under restrictive assumptions is the slip velocity related to the gradient of the quasi potential (integral of parallel electric field along field lines). In a turbulent inertial range the curl becomes extremely large while the parallel component is tiny, so that line slippage occurs even while ideal MHD becomes accurate. The resolution of this paradox is that ideal MHD is valid for a turbulent inertial-range only in a weak sense which does not imply magnetic line freezing. The notion of weak solution is explained in terms of spatial coarse-graining and renormalization group (RG) theory. We give an argument for the weak validity of the ideal Ohm's law in the inertial range, via rigorous estimates of the terms in the Generalized Ohm's Law for an electron-ion plasma. All of the nonideal terms (from collisional resistivity, Hall field, electron pressure anisotropy, and electron inertia) are shown to be irrelevant in the RG sense and large-scale reconnection is thus governed solely by ideal dynamics. We briefly discuss some implications for heliospheric reconnection, in particular for deviations from the Parker spiral model of interplanetary magnetic field. Solar wind observations show that reconnection in a turbulence broadened heliospheric current sheet, consistent with the Lazarian-Vishniac theory, leads to slip velocities that cause field lines to lag relative to the spiral model.

One-Way Hash Function based on Cascade Chaos

This paper proposes a novel hash function construction based on cascade chaos. Firstly, the L-length original message is divided into a number of blocks according to every character, which are transformed into corresponding ASCII values. Then the ASCII values are normalized into the interval of (0, 1), which compose a big array with the L-length. Regarding the first normalized ASCII value with the algorithm parameter H as the initial input of the cascade chaos, a series of sequences are obtained, where the CBC mode is adopted. The 128-bit hash value is generated by transforming the sequences into binary sequence according to a rule. Simulation results and performance analysis show that the proposed hash function has high sensitivity to the original message and system parameters, strong confusion and diffusion, excellent statistical properties, strong collision resistance and flexible to generated 160, 256, 512-bit hash value after modifying the algorithm slightly.

Parallel chaotic hash function based on the shuffle-exchange network

In recent years, cryptologists have been delving into chaos theory to design more secure cryptographic primitives. However, many existing chaos-based algorithms are slow due to floating point operations. They are mostly sequential in nature and therefore cannot take advantage of multicore processors for faster speed. In this paper, a new chaos-based hash function is proposed that utilizes multiple instances of chaotic maps that run in parallel to improve hashing speed. Parallelization is realized using the baseline network that also strengthens the security of the hash function due to its shuffling mechanism. The combination of linear and nonlinear chaotic maps is used to provide a high level of sensitivity to initial conditions, confusion and diffusion characteristics as well as strong collision resistance. Results show that the proposed design has strong security strength with near-perfect statistical qualities and fast hashing speed that surpasses both chaotic hash functions and the MD5 hash function.

A structure-based chaotic hashing scheme

We propose a new chaotic keyed hashing scheme based on the structure of the input message. The structure of the message is identified with maps of the appearances of each character throughout the input message. We use a $$2$$ -dimensional generalized cat map whose chaotic orbits are used to introduce randomness to the computation of the hash value and hence facilitate uniform sensitivity of the hash value to the input message and the secret key. Our proposed hashing scheme is fast, efficient, and flexible. Empirical results verify the high sensitivity of the proposed hash function to the input message and the secret key. Further simulations presented demonstrate the strong capability of the proposed scheme for confusion, diffusion, and collision resistance. Compared with existing schemes, especially those based on chaotic maps, the proposed scheme is shown to have superior performance.

The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η1∕7 scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.