On the Design of Provably-Secure Cryptographic Hash Functions

Naor and Yung (1989) show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by /spl epsiv/n bits, at the cost of /spl epsiv/n invocations of the one-way permutation. The show that this construction is not far from optimal, in the following sense, there exists an oracle relative to which there exists a one-way permutation with inversion probability 2/sup -p(n)/ (for any p(n)/spl isin//spl omega/(log n)), but any construction of an /spl epsiv/n-bit-compressing UOWHF. Requires /spl Omega/(/spl radic/n/p(n)) invocations of the one-way permutation, on average. (For example, there exists in this relativized world a one-way permutation with inversion probability n/sup -/spl omega/(1)/, but no UOWHF that involves it fewer than /spl Omega/(/spl radic/n/log n) times.) Thus any proof that a more efficient UOWHF can be derived from a one-way permutation is necessarily non-relativizing; in particular, no provable construction of a more efficient UOWHF can exist based solely on a black box one-way permutation. This result can be viewed as a partial justification for the practice of building efficient UOWHFs from stronger primitives (such as collision intractable hash functions), rather than from weaker primitives such as one-way permutations.

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.

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgard domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgard extender to the subset sum compression function with ‘extension factor' k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

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.

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

We present an architecture level optimization technique called divide-and-concatenate based on two observations: 1) the area of an array multiplier and its associated data path decreases quadratically and their delay decreases linearly as their operand size is reduced and 2) in universal hash functions and their associated message authentication codes, two one-way hash functions are equivalent if they have the same collision probability property. In the proposed approach, we divide a 2w-bit data path (with collision probability 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2w</sup> ) into two w-bit data paths (each with collision probability 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-w</sup> ) and concatenate their results to construct an equivalent 2w-bit data path (with a collision probability 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2w </sup> ). We applied this technique on NH universal hash, a universal hash function that uses multiplications and additions. We implemented the straightforward 32-bit pipelined NH universal hash data path and the divide-and-concatenate architecture that uses four equivalent 8-bit divide-and-concatenate NH universal hash data paths on a Xilinx Virtex II XC2VP7-7 field programmable gate array (FPGA) device. This divide-and-concatenate architecture yielded a 94% increase in throughput with only 40% hardware overhead. Finally, the implementation of universal message authentication code (UMAC) with collision probability 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-32</sup> using the divide-and-concatenate NH hash as a building block yielded a throughput of 79.2 Gb/s with only 3840 Virtex II XC2VP7-7 FPGA slices

In this paper we present a new scheme for constructing universal one-way hash functions that hash arbitrarily long messages out of universal one-way hash functions that hash fixed-length messages. The new construction is extremely simple and is also very efficient, yielding shorter keys than previously proposed composition constructions.

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

Passwords are barriers that protect unauthorized users from accessing personal information in any application. Protecting passwords is one of the challenging tasks in today's world. Currently, a combination of Username/Password used for authentication for a large number of applications. Malicious users might try to steal/misuse the user's data for unethical purposes. To prevent passwords from stealing, developers prefer to use one-way hash functions. One-way hash functions are theoretically irreversible functions that take as an input variable size text and output fixed-sized text. In reality, hash functions are not collision-resistant. Therefore it is recommended to use passwords and randomly generated text called salt to generate hash values and prevent rainbow tables and dictionary attacks. Passwords are hashed at the client-side and sent across the public channel/network. A salt is a randomly generated alphanumeric text used to concatenate with a password to generate a random hash value. This paper demonstrates how the random generation of salt is dependent on passwords and how hash values are dependent on salt. Further, analysis of the behaviour of passwords and hash values using various tools like Wireshark, Ettercap, and Hydra are presented in the paper.

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, Ishai, and Kushilevitz, SICOMP 2006]. However, this construction suffers from two limitations: (1) It can only achieve a sub-linear shrinkage of n − m = n 1 − ε; 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 = εn, 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 (ECCC 2000). Using a transformation of [Ishai, Kushilevitz, Ostrovsky and Sahai, STOC 2008], our UOWHFs give rise to a digital signature scheme with a minimal additive complexity overhead: signing n-bit messages with security parameter κ takes only O(n + κ) time instead of O(nκ) 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.KeywordsHash FunctionLinear ShrinkageRandom StringPseudorandom GeneratorInput LocalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, a new algorithm for designing one-way cryptographic hash function using chaotic Chirikov map is proposed. High sensitivity of Chirikov system makes it an ideal candidate for secure hash function design. In the proposed algorithm, the input message is split into a number of small blocks. The blocks are processed using chaotic map. The two intermediate hashes are generated using evolved control and input parameters. The two intermediate hash values are then employed to yield the final variable-length hash. The simulation and statistical analyses illustrate that the anticipated hash algorithm exhibits encouraging lineaments like high sensitivity to input messages and key, satisfactory confusion and diffusion attributes which verify the suitableness of proposed algorithm for the design of secure cryptographic variable-length hash functions.

One-way hash functions are an important tool in achieving authentication and data integrity. The aim of this paper is to propose a novel one-way hash function based on cellular automata whose cryptographic properties have been extensively studied over the past decade or so. Furthermore, security of the proposed one-way hash function is analyzed by the use of very recently published results on applications of cellular automata in cryptography. The analysis indicates that the one-way hash function is secure against all known attacks. An important feature of the proposed one-way hash function is that it is especially suitable for compact and fast implementation in hardware, which is particularly attractive to emerging security applications that employ smart cards, such as digital identification cards and electronic cash payment protocols,

Hash functions are one-way functions that map arbitrary-length input to fixed-length output. Moreover, they have many cryptographic applications, such as integrity checks, password storage, and signatures. Cryptographic hash functions have some additional properties that can be formulated as hard problems: pre-image resistance, second pre-image resistance, and collision resistance. A significant technological development in this area is unlikely. Standardized hash functions are considered secure, and open-source implementations can be used at no cost. To conclude, the security properties required from hash functions depend on the intended purpose.

This paper presents a novel keyed one-way Hash function based on a chaotic dynamic S-Box together with traditional one-way Hash function construction. The proposed approach can give a chaotic Hash value by means of the look up table of functions and chaotic dynamic S-Box. Compared with the existing chaotic Hash functions, this method improves computational performance of Hash system by using the chaotic dynamical S-Box substitution in place of iterating the original message directly in chaos system. Theoretical and experimental results show that the proposed method has strong one way property, large key space, sensitivity to initial conditions and chaotic system's parameters.

This paper presents a new group key management protocol, CKC (Code for Key Calculation). This protocol is based on logical key hierarchy. When a new member joins the group, server sends only the group key for that member. Then, current members and the new member calculate the necessary keys using node codes and one-way hash function. Node code is a code which is assigned to each node of the key tree. Again at leave, server just sends the new group key to remaining members. By this key, members calculate necessary keys using node codes and one-way hash function. The security of the keys is based on one-wayness of hash function. The results show that CKC reduces computational and communication overhead and message size at join while it keeps minimized the overhead of key update at leave.