Family Of Hash Functions Research Articles

Fast hash functions and convolution product

Abstract. We propose a new simple and efficient family of hash functions based on matrix-vector multiplications with a competitive software implementation. The hash design combines a hard mathematical problem based on solving a system of linear equations with special-random requirements and the fast computation of the convolution product algorithm. Such a mixing was often unrealizable. For security, the one-way and collision resistant criteria are based on the fact that inverting the compression function for random values is infeasible in reasonable time. In a subsequent result, we conjecture a general framework for producing secure matrix multiplication hash functions.

SPONGENT: The Design Space of Lightweight Cryptographic Hashing

The design of secure yet efficiently implementable cryptographic algorithms is a fundamental problem of cryptography. Lately, lightweight cryptography--optimizing the algorithms to fit the most constrained environments--has received a great deal of attention, the recent research being mainly focused on building block ciphers. As opposed to that, the design of lightweight hash functions is still far from being well investigated with only few proposals in the public domain. In this paper, we aim to address this gap by exploring the design space of lightweight hash functions based on the sponge construction instantiated with present-type permutations. The resulting family of hash functions is called spongent. We propose 13 spongent variants--or different levels of collision and (second) preimage resistance as well as for various implementation constraints. For each of them, we provide several ASIC hardware implementations--ranging from the lowest area to the highest throughput. We make efforts to address the fairness of comparison with other designs in the field by providing an exhaustive hardware evaluation on various technologies, including an open core library. We also prove essential differential properties of spongent permutations, give a security analysis in terms of collision and preimage resistance, as well as study in detail dedicated linear distinguishers.

Direct proof of security of Wegman–Carter authentication with partially known key

Information-theoretically secure (ITS) authentication is needed in Quantum Key Distribution (QKD). In this paper, we study security of an ITS authentication scheme proposed by Wegman & Carter, in the case of partially known authentication key. This scheme uses a new authentication key in each authentication attempt, to select a hash function from an Almost Strongly Universal$_2$ hash function family. The partial knowledge of the attacker is measured as the trace distance between the authentication key distribution and the uniform distribution; this is the usual measure in QKD. We provide direct proofs of security of the scheme, when using partially known key, first in the information-theoretic setting and then in terms of witness indistinguishability as used in the Universal Composability (UC) framework. We find that if the authentication procedure has a failure probability $\epsilon$ and the authentication key has an $\epsilon'$ trace distance to the uniform, then under ITS, the adversary's success probability conditioned on an authentic message-tag pair is only bounded by $\epsilon+|\mT|\epsilon'$, where $|\mT|$ is the size of the set of tags. Furthermore, the trace distance between the authentication key distribution and the uniform increases to $|\mT|\epsilon'$ after having seen an authentic message-tag pair. Despite this, we are able to prove directly that the authenticated channel is indistinguishable from an (ideal) authentic channel (the desired functionality), except with probability less than $\epsilon+\epsilon'$. This proves that the scheme is ($\epsilon+\epsilon'$)-UC-secure, without using the composability theorem.

A post‐quantum provable data possession protocol in cloud

ABSTRACTProvable data possession (PDP) is a model for efficiently checking the integrity of data in cloud storage. Most previous PDP protocols are insecure when quantum computers are considered. In this paper, we propose a homomorphic hash‐based PDP (HH‐PDP) protocol from ideal lattice assumptions. Firstly, we prove that a collision‐resistant hash function family is homomorphic. Then, we use the homomorphism to generate homomorphic verification tags and further construct a new PDP protocol. The security of the proposed protocol relies on the assumed worst‐case hardness of ideal lattice problems, which hold a great promise for post‐quantum cryptography. We prove that the proposed protocol guarantees data possession in the standard model if the shortest polynomial problem is hard. As the main operations in our construction are addition and multiplication on small integers, the proposed protocol is more efficient than previous protocols. Experimental result shows that HH‐PDP is approximately five times cheaper in preprocessing and checking proof, half cost in generating proof compared with the most efficient PDP protocol proposed by Ateniese et al. in 2011. Copyright © 2013 John Wiley & Sons, Ltd.

Chameleon Hash Functions and One-Time Signature Schemes from Inner Automorphism Groups

In this paper, we build a family of chameleon hash functions and strongly unforgeable one-time signature schemes based on the intractability assumption of the discrete logarithm problem DLP over in...

Chameleon Hash Functions and One-Time Signature Schemes from Inner Automorphism Groups

In this paper, we build a family of chameleon hash functions and strongly unforgeable one-time signature schemes based on the intractability assumption of the discrete logarithm problem DLP over inner automorphism groups. Since the DLP assumption over inner automorphism groups does not admit sub-exponential attacks, thus the sizes of the working parameters used in our constructions are shorten significantly. This leads to remarkable gains for our proposals both in running time and in storage space. In addition, as far as we know, this is the first time to build CHF and OTS based on noncommutative groups.

Quark: A Lightweight Hash

The need for lightweight (that is, compact, low-power, low-energy) cryptographic hash functions has been repeatedly expressed by professionals, notably to implement cryptographic protocols in RFID technology. At the time of writing, however, no algorithm exists that provides satisfactory security and performance. The ongoing SHA-3 Competition will not help, as it concerns general-purpose designs and focuses on software performance. This paper thus proposes a novel design philosophy for lightweight hash functions, based on the sponge construction in order to minimize memory requirements. Inspired by the stream cipher Grain and by the block cipher KATAN (amongst the lightest secure ciphers), we present the hash function family Quark, composed of three instances: u-Quark, d-Quark, and s-Quark. As a sponge construction, Quark can be used for message authentication, stream encryption, or authenticated encryption. Our hardware evaluation shows that Quark compares well to previous tentative lightweight hash functions. For example, our lightest instance u-Quark conjecturally provides at least 64-bit security against all attacks (collisions, multicollisions, distinguishers, etc.), fits in 1379 gate-equivalents, and consumes on average 2.44 μW at 100 kHz in 0.18 μm ASIC. For 112-bit security, we propose s-Quark, which can be implemented with 2296 gate-equivalents with a power consumption of 4.35 μW.

An Improved Fast and Secure Hash Algorithm

Abstract —Recently, a fast and secure hash function SFHA – 256 has been proposed and claimed as more secure and as having a better performance than the SHA – 256. In this paper an improved version of SFHA – 256 is proposed and analyzed using two parameters, namely the avalanche effect and uniform deviation. The experimental results and further analysis ensures the performance of the newly proposed and improved SFHA-256. From the analysis it can be concluded that the newly proposed algorithm is more secure, efficient, and practical. Keywords —SHA-256, SFHA-256, Improved SFHA-256 1. I NTRODUCTION The hash function H accepts the variable-sized message M as input and outputs a fixed-size representation H(M) of M, which is sometimes called a message digest [1]. I.B. Damgard et.el., discussed the construction of hash functions and presented an efficient and much more secure scheme with the combination of RSA system with the collision free hash function based on fac-toring [2]. Hash functions for message authentications are proposed in [3]. A universal one-way hash function family is discussed in [4]. SHA-1 is a cryptographic hash function published by the National Institute of Standards and Technology (NIST). The three SHA algorithms are SHA-0, SHA-1, and SHA-2. The SHA-0 algorithm was not used in many applications. On the other hand, SHA-2 differs from the SHA-1 hash function. SHA-1 is the most widely used hash function. Several widely-used security ap-plications and protocols are based on SHA-1. In 2005, security flaws were identified in SHA-1 [5]. A prime motivation for the publication of the Secure Hash Algorithm was the Digital Signa-ture Standard. The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Standard (DSS). The ElGamal signature scheme is a digital signature scheme that is based on the difficulty of com-puting discrete logarithms. It was described by Taher ElGamal in 1984 [6]. The Elliptic Curve Digital Signature Algorithm (ECDSA) is a variant of the Digital Signature Algorithm (DSA) that uses Elliptic curve cryptography [7, 8]. Recently, Hassan. M. Elkamchouchi et el., proposed a fast and secure hash function (SFHA -

Parameterized Hash Functions

In this paper we describe a family of highly parameterized hash functions. This parameterization results in great flexibility between performance and security of the algorithm. The three basic functions, HaF-256, HaF-512 and HaF-1024 constitute this hash function family. Lengths of message digests are 256, 512 and 1024 bits respectively. The paper discusses the details of functions structure. The method used to generate function S-box is also described in detail.

Cores of random r-partite hypergraphs

We show that the threshold cr,k (in terms of the average degree of the graph) for appearance of a k-core in a random r-partite r-uniform hypergraph Gr,n,m is the same as for a random r-uniform hypergraph with cn/r edges without the r-partite restriction, where r,k⩾2. In both cases, the average degree is c. The case r,k=2 was analyzed in Botelho et al. (2007) [4] but the general case r⩾3, k⩾2 is still open. Besides the proof for the general case, we have also provided a simpler proof for the case r,k=2. This problem was provided without a proof (but with strong experimental evidence) in the analysis of the algorithm presented in Botelho et al. (2007) [2]. This algorithm constructs a family of minimal perfect hash functions based on random r-partite r-uniform hypergraphs with an empty k-core subgraph, for k⩾2. For an input key set S with m keys, the family of minimal perfect hash functions generated by the algorithm can be stored in O(m) bits, where the hidden constant is within a factor of two from the information theoretical lower bound.

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).

Leftover Hashing Against Quantum Side Information

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, we prove a (strictly) more general version of the Leftover Hash Lemma that is valid even if side information is represented by the state of a quantum system. Furthermore, our result applies to arbitrary delta-almost two-universal families of hash functions. The generalized Leftover Hash Lemma has applications in cryptography, e.g., for key agreement in the presence of an adversary who is not restricted to classical information processing.

Satellite image retrieval using low memory locality sensitive hashing in Euclidean space

This paper presents the use of the Low Memory Locality Sensitive Hashing (LMLSH) technique operating in Euclidean space to build a data structure for the Defense Meteorological Satellite Program (DMSP) satellite imagery database. The LMLSH technique finds satellite image matches in sublinear search time. The texture feature vectors of the images are extracted using pyramid-structured wavelet transform coupled with Gaussian central moment technique. These feature vectors and families of hash functions, drawn randomly and independently from a Gaussian distribution, are used to build hash tables. Given a query, the hash tables are used to pull out the best matches to that query and this is done in a sublinear search time complexity. When tested, our algorithm has proven to be approximately twenty six times faster than the Linear Search (LS) algorithm. In addition, the LMLSH algorithm searches about two percent of the entire database randomly to find the possible matches to any given query without loss of accuracy compared to the absolute best matches returned by its LS counterpart.

Exponential time improvement for min-wise based algorithms

In this paper we extend the notion of min-wise independent family of hash functions by defining a k-min-wise independent family of hash functions. Informally, under this definition, all subsets of size k of any fixed set X have an equal chance to have the minimal hash values among all the elements in X, when the probability is over the random choice of hash function from the family. This property measures the randomness of the family, as choosing a truly random function, obviously, satisfies the definition for k = ∣ X∣. We define and give an efficient time and space construction of approximately k-min-wise independent family of hash functions by extending Indyk’s construction of approximately min-wise independent. The number of words needed to represent each function is O ( k log log ( 1 ϵ ) + log ( 1 ϵ ) ) , which is only suboptimal by a factor of O ( log log ( 1 ϵ ) ) , where ϵ ∈ (0, 1) is the desired error bound. This construction is the first applicable for sampling bottom- k sketches out of the universe. In addition, we introduce a general and novel technique that utilizes our construction, and can be used to improve many min-wise based algorithms. As an example we show how to apply it for similarity estimation over data streams, and reduce exponentially the run time of the current known result [5]. In addition, we also discuss improvements of known algorithms for estimating rarity and entropy of random walk over graphs.

Evolution of the StreamHash hash function family

This paper describes the evolution of StreamHash cryptographic hash function family proposed by the author. The first member of the StreamHash family was StreamHash (now called StreamHash1) function, accepted for the first round of SHA-3 competition organized by the US government standards agency NISTi¾?. The competition has been started in order to select a new SHA-3 standard as the successor of SHA-2 family of cryptographic hash functions. Function StreamHash2 mostly addresses security weaknesses identified during the SHA-3 competition, while the sketch of function StreamHash3 attempts to improve resistance to side-channel attacks and performance properties. The paper starts with an overview of basic properties of cryptographic hash functions followed by the description of the StreamHash family design principles and its basic structure. Subsequent sections illustrate the way each subsequent function uses lessons learnt while designing and testing the previous one.

On chosen target forced prefix preimage resistance

Abstract In this paper we analyze the Chosen Target Forced Prefix (CTFP) preimage resistance security notion for hash functions firstly introduced in [Kelsey, J.-Kohno, T.: Herding hash functions and the Nostradamus attack, in: Advances in Cryptology-EUROCRYPT ’06, 25th Annual Internat. Conf. on the Theory and Appl. of Cryptographic Techniques (S. Vaudenay, ed.), St. Peters- burg, Russia, 2006, Lecture Notes in Comput. Sci., Vol. 4004, Springer-Verlag, Berlin, 2006, pp. 183-200]. We give a formal definition of this property in hash function family settings and work out all the implications and separations be- tween the CTFP preimage resistance and other standard notions of hash function security (preimage resistance, collision resistance, etc.). This paper follows the work of [Rogaway, P.-Shrimpton, T.: Cryptographic hash-function basics: Def- initions, implications, and separations for preimage resistance, second-preimage resistance, and collision resistance, in: Fast Software Encryption, 11th Interna- tional Workshop-FSE ’04 (B. Roy et al., eds.), Delhi, India, 2004, Lecture Notes in Comput. Sci., Vol. 3017, Springer-Verlag, Berlin, 2004, pp. 371-388], where they define seven basic notions of hash function security and examine all the relationships among these notions. We also define a new property for security of hash function families-always CTFP preimage resistance, which guarantees CTFP security for all the hash functions in the family.

Balanced families of perfect hash functions and their applications

The construction of perfect hash functions is a well-studied topic. In this article, this concept is generalized with the following definition. We say that a family of functions from [ n ] to [ k ] is a δ-balanced ( n,k )-family of perfect hash functions if for every S ⊆ [ n ], | S |= k , the number of functions that are 1-1 on S is between T /δ and δ T for some constant T >0. The standard definition of a family of perfect hash functions requires that there will be at least one function that is 1-1 on S , for each S of size k . In the new notion of balanced families, we require the number of 1-1 functions to be almost the same (taking δ to be close to 1) for every such S . Our main result is that for any constant δ > 1, a δ-balanced ( n,k )-family of perfect hash functions of size 2 O ( k log log k ) log n can be constructed in time 2 O ( k log log k ) n log n . Using the technique of color-coding we can apply our explicit constructions to devise approximation algorithms for various counting problems in graphs. In particular, we exhibit a deterministic polynomial-time algorithm for approximating both the number of simple paths of length k and the number of simple cycles of size k for any k ≤ O (log n /log log log n ) in a graph with n vertices. The approximation is up to any fixed desirable relative error.

Cryptanalysis of the Tillich–Zémor Hash Function

At CRYPTO ’94, Tillich and Zemor proposed a family of hash functions, based on computing a suitable matrix product in groups of the form $SL_{2}(\mathbb{F}_{2^{n}})$. We show how to construct collisions between palindromic bit strings of length 2n+2 for Tillich and Zemor’s construction. The approach also yields collisions for related proposals by Petit et al. from ICECS ’08 and CT-RSA ’09. It seems fair to consider our attack as practical: for parameters of interest, the colliding bit strings have a length of a few hundred bits and can be found on a standard PC within seconds.

Securing fuzzy vault schemes through biometric hashing

The fuzzy vault scheme is a well-known technique to mitigate privacy, security, and usability related problems in biometric identification applications. The basic idea is to hide biometric data along with secret information amongst randomly selected chaff points during the enrollment process. Only the owner of the biometric data who presents correct biometrics can recover the secret and identify himself. Recent research, however, has shown that the scheme is vulnerable to certain types of attacks. The recently proposed ``correlation attack'', that allows linking two vaults of the same biometric, pose serious privacy risks that have not been sufficiently addressed. The primary aim of this work is to remedy those problems by proposing a framework based on distance preserving hash functions to render the correlation attack inapplicable. We first give definitions which capture the requirements such hash functions must posses. We then propose a specific family of hash functions that fulfills these requirements and lends itself to efficient implementation. We also provide formal proofs that the proposed family of hash functions indeed protects the fuzzy vault against correlation attacks. We implement a hashed fuzzy vault using fingerprint data and investigate the effects of the proposed method on the false accept and false reject rates (FAR and FRR, respectively) extensively. Implementation results suggest that the proposed method provides a complete protection against correlation attacks at the expense of small degradation in the FRR.

The power of primes: security of authentication based on a universal hash-function family

Message authentication codes (MACs) based on universal hash-function families are becoming increasingly popular due to their fast implementation. In this paper, we investigate a family of universal hash functions that has been appeared repeatedly in the literature and provide a detailed algebraic analysis for the security of authentication codes based on this universal hash family. In particular, the universal hash family under analysis, as appeared in the literature, uses operation in the finite field ℤ p . No previous work has studied the extension of such universal hash family when computations are performed modulo a non-prime integer n . In this work, we provide the first such analysis. We investigate the security of authentication when computations are performed over arbitrary finite integer rings ℤ n and derive an explicit relation between the prime factorization of n and the bound on the probability of successful forgery. More specifically, we show that the probability of successful forgery against authentication codes based on such a universal hash-function family is bounded by the reciprocal of the smallest prime factor of the modulus n .