Universal One-way Hash Functions Research Articles

Simple Constructions from (Almost) Regular One-Way Functions

Two of the most useful cryptographic primitives that can be constructed from one-way functions are pseudorandom generators (PRGs) and universal one-way hash functions (UOWHFs). In order to implement them in practice, the efficiency of such constructions must be considered. The three major efficiency measures are: the seed length, the call complexity to the one-way function, and the adaptivity of these calls. Still, the optimal efficiency of these constructions is not yet fully understood: there exist gaps between the known upper bound and the known lower bound for black-box constructions. A special class of one-way functions called unknown-regular one-way functions is much better understood. Haitner, Harnik and Reingold (CRYPTO 2006) presented a PRG construction with semi-linear seed length and linear number of calls based on a method called randomized iterate. Ames, Gennaro and Venkitasubramaniam (ASIACRYPT 2012) then gave a construction of UOWHF with similar parameters and using similar ideas. On the other hand, Holenstein and Sinha (FOCS 2012) and Barhum and Holenstein (TCC 2013) showed an almost linear call-complexity lower bound for black-box constructions of PRGs and UOWHFs from one-way functions. Hence, Haitner et al. and Ames et al. reached tight constructions (in terms of seed length and the number of calls) of PRGs and UOWHFs from regular one-way functions. These constructions, however, are adaptive. In this work, we present non-adaptive constructions for both primitives which match the optimal call complexity given by Holenstein and Sinha and Barhum and Holenstein. Our constructions, besides being simple and non-adaptive, are robust also for almost-regular one-way functions.

Locally Computable UOWHF with Linear Shrinkage

We study the problem of constructing locally computable universal one-way hash functions (UOWHFs) $$\mathcal {H}:\{0,1\}^n \rightarrow \{0,1\}^m$$ . A construction with constant output locality, where every bit of the output depends only on a constant number of bits of the input, was established by Applebaum et al. (SIAM J Comput 36(4):845–888, 2006). However, this construction suffers from two limitations: (1) it can only achieve a sublinear shrinkage of $$n-m=n^{1-\epsilon }$$ and (2) it has a super-constant input locality, i.e., some inputs influence a large super-constant number of outputs. This leaves open the question of realizing UOWHFs with constant output locality and linear shrinkage of $$n-m= \epsilon n$$ , or UOWHFs with constant input locality and minimal shrinkage of $$n-m=1$$ . We settle both questions simultaneously by providing the first construction of UOWHFs with linear shrinkage, constant input locality and constant output locality. Our construction is based on the one-wayness of “random” local functions—a variant of an assumption made by Goldreich (Studies in Complexity and Cryptography, 76–87, 2011; ECCC 2010). Using a transformation of Ishai et al. (STOC, 2008), our UOWHFs give rise to a digital signature scheme with a minimal additive complexity overhead: signing n-bit messages with security parameter $$\kappa $$ takes only $$O(n+\kappa )$$ time instead of $$O(n\kappa )$$ as in typical constructions. Previously, such signatures were only known to exist under an exponential hardness assumption. As an additional contribution, we obtain new locally computable hardness amplification procedures for UOWHFs that preserve linear shrinkage.

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 -

Construction of universal one-way hash functions: Tree hashing revisited

We present a binary tree based parallel algorithm for extending the domain of a universal one-way hash function (UOWHF). For t ⩾ 2 , our algorithm extends the domain from the set of all n-bit strings to the set of all ( ( 2 t - 1 ) ( n - m ) + m ) -bit strings, where m is the length of the message digest. The associated increase in key length is 2 m bits for t = 2 ; m ( t + 1 ) bits for 3 ⩽ t ⩽ 6 and m × ( t + ⌊ log 2 ( t - 1 ) ⌋ ) bits for t ⩾ 7 .

Masking-Based Domain Extenders for UOWHFs: Bounds and Constructions

We study the class of masking-based domain extenders for universal one-way hash functions (UOWHFs). Our first contribution is to show that any correct masking-based domain extender for UOWHF which invokes the compression UOWHF s times must use at least lceillog <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> srceil masks. As a consequence, we obtain the key expansion optimality of several known algorithms among the class of all masking-based domain extending algorithms. Our second contribution is to present a new parallel domain extender for UOWHF. The new algorithm achieves asymptotically optimal speedup over the sequential algorithm and the key expansion is almost everywhere optimal, i.e., it is optimal for almost all possible number of invocations of the compression UOWHF

Bounds on the Efficiency of Generic Cryptographic Constructions

A central focus of modern cryptography is the construction of efficient, high-level cryptographic tools (e.g., encryption schemes) from weaker, low-level cryptographic primitives (e.g., one-way functions). Of interest are both the existence of such constructions and their efficiency. Here, we show essentially tight lower bounds on the best possible efficiency of any black-box construction of some fundamental cryptographic tools from the most basic and widely used cryptographic primitives. Our results hold in an extension of the model introduced by Impagliazzo and Rudich and improve and extend earlier results of Kim, Simon, and Tetali. We focus on constructions of pseudorandom generators, universal one-way hash functions, and digital signatures based on one-way permutations, as well as constructions of public- and private-key encryption schemes based on trapdoor permutations. In each case, we show that any black-box construction beating our efficiency bound would yield the unconditional existence of a one-way function and thus, in particular, prove $P \neq NP$.

Checker for data structures which sort elements

The data structure checker introduced by Blum et al. (1994) checks programs which store and retrieve data from memory according to prescribed data-structure definitions. We present a checker for data structures which sort elements — for example binary search trees or sorted lists. For these data structures the way of performing the user's operations ( First, Last, Next, Previous, Add, Delete, Find) depends on the values of the data they contain. The presented checker is on-line and invasive; if universal one-way hash functions exist, then the checker is secure.

Efficient cryptographic schemes provably as secure as subset sum

We show very efficient constructions for a pseudorandom generator and for a universal one-way hash function based on the intractability of the subset-sum problem for certain dimensions. (Pseudorandom generators can be used for private-key encryption and universal one-way hash functions for signature schemes.) The increase in efficiency in our construction is due to the fact that many bits can be generated/hashed with one application of the assumed one-way function.All of our constructions can be implemented in NC using an optimal number of processors.

Efficient Cryptographic Schemes Provably as Secure as Subset Sum

We show very efficient constructions for a pseudorandom generator and for a universal one-way hash function based on the intractability of the subset-sum problem for certain dimensions. (Pseudorand...