We propose a hash function based on arithmetic coding and public-key cryptography. The resistance of the hash function to second preimage attack, collision and differential cryptanalysis is based on the properties of arithmetic coding as a non-linear dynamical system. The resistance of the hash function to first preimage attack is based on the public-key cryptography. The new hash function uses the strength of HMAC with the difference that it didn't need a secret key for calculating the hash (in this step, it uses one, two or three public -keys) and in the classical attack, an adversary need to break the public key algorithm or to have all the secret keys to perform his attack.
Due to hostile environment and wireless communication channel, security mechanisms are essential for wireless sensor networks (WSNs). Existence of a pair of shared key is a prerequisite for many of these security mechanisms; a task that key management system addresses. Recently, an energy efficient method based on public key cryptography (PKC) was proposed. We analyze this protocol and show that it is vulnerable to denial of service (DOS) attacks and adversary can exhaust memory and battery of nodes. Then, we analyze this protocol and show that using a more knowledgeable BS this vulnerability …
NSUCRYPTO is the unique cryptographic Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. From the very beginning, the concept of the Olympiad was not to focus on solving olympic tasks but on including unsolved research problems at the intersection of mathematics and cryptography. The Olympiad history starts in 2014. In 2019, it was held for the sixth time. In this paper, problems and their solutions of the Sixth I…
Mathematical problems and their solutions of the Fourth International Students' Olympiad in cryptography NSUCRYPTO'2017 are presented. We consider problems related to attacks on ciphers and hash functions, cryptographic Boolean functions, the linear branch number, addition chains, error correction codes, etc. We discuss several open problems on algebraic structure of cryptographic functions, useful proof-of-work algorithms, the Boolean hidden shift problem and quantum computings.
Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most of the other subclasses of TFNP, no complete problem is known for PPP. Our work identifies the first PPP-complete problem without any circuit or Turing Machine given explicitly in the input, and thus we answer a longstanding open question from [Papadimitriou1994]. Specifically, we show that constrained-SIS (cSIS), a generalized version of the well-known Sho…
Problems and their solutions of the Fifth International Students' Olympiad in cryptography NSUCRYPTO'2018 are presented. We consider problems related to attacks on ciphers and hash functions, Boolean functions, quantum circuits, Enigma, etc. We discuss several open problems on orthogonal arrays, Sylvester matrices and disjunct matrices. The problem of existing an invertible Sylvester matrix whose inverse is again a Sylvester matrix was completely solved during the Olympiad.
Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function $h:\{0,1\}^n\to \mathbb{Z}_n$ is a $(d,δ)$ {\em locality-preserving hash function for shifts} (LPHS) if: (1) $h$ can be computed by (adaptively) querying $d$ bits of its input, and (2) $\Pr [ h(x) \neq h(x \ll 1) + 1 ] \leq δ$, where $x$ is random and $\ll 1$ denote…
National Institute of Technology Silchar（西尔查尔国家理工学院）
Malicious URL detection is an emerging research area due to continuous modernization of various systems, for instance, Edge Computing. In this article, we present a novel malicious URL detection technique, called deepBF (deep learning and Bloom Filter). deepBF is presented in two-fold. Firstly, we propose a learned Bloom Filter using 2-dimensional Bloom Filter. We experimentally decide the best non-cryptography string hash function. Then, we derive a modified non-cryptography string hash function from the selected hash function for deepBF by introducing biases in the hashing method and compare…
The extensive networking of devices and the large amount of data generated from the Internet of Things (IoT) has brought security issues to the attention of the researcher. Java is the most common platform for embedded applications such as IoT, Wireless Sensors Networks (WSN), Near Field Communications (NFC) and Radio Frequency Identification (RFID). The object programming languages such as Java, SWIFT, PHP and C++ use garbage collection after any object run which creates security loophole for attacks such as Next Memory Address Occupation (NMAO), memory replay, Learning Tasks Behaviors (LTB).…
Hash functions map data of arbitrary length to data of predetermined length. Good hash functions are hard to predict, making them useful in cryptography. We are interested in the elliptic curve CGL hash function, which maps a bitstring to an elliptic curve by traversing an input-determined path through an isogeny graph. The nodes of an isogeny graph are elliptic curves, and the edges are special maps betwixt elliptic curves called isogenies. Knowing which hash values are most likely informs us of potential security weaknesses in the hash function. We use stochastic matrices to compute the expe…
This paper investigates the use of dynamical chaotic systems to encrypt and exchange images between different devices. Two devices were used to simulate the Cubic Map, having the same set of initial conditions, to generate an encryption key. Although both devices are floating-point compliant, the simulations, and consequently the encryption key, turned out to differ from one another. This indicates that many existing chaos-based encryption schemes are just special cases of computational arithmetic properties, in which some characteristics in the construction of the devices coincided. A method …
An ideal signature material and method, which can be used to prove the authenticity of a physical item and against forgery, should be immune to the fast developments in digital and engineering technologies. Herein, the design of signature material combining cryptographic hash function and DNA steganography is proposed. The encrypting materials are used to construct a series of time-stamped records (blockchain) associated with published hash values, while each DNA-encrypted block is associated with a set of DNA keys. The decrypted DNA information, as digital keys, can be validated through a has…
Post-Quantum Cryptography PQC attempts to find cryptographic protocols resistant to attacks using Shors polynomial time algorithm for numerical field problems or Grovers algorithm to find the unique input to a black-box function that produces a particular output value. The use of non-standard algebraic structures like non-commutative or non-associative structures, combined with one-way trapdoor functions derived from combinatorial group theory, are mainly unexplored choices for these new kinds of protocols and overlooked in current PQC solutions. In this paper, we develop an algebraic extensio…
Spinel: A Post-Quantum Signature Scheme Based on $\mathrm{SL}_n(\mathbb{F}_p)$ Hashing
Hassan II University（哈桑二世大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Queens College, City University of New York（纽约市立大学皇后学院）；Graduate Center, City University of New York（纽约市立大学研究生院）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）；University of York（约克大学）
Last year Takashima proposed a version of Charles, Goren and Lauter's hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field Fp2. In a very recent paper Flynn and Ti point out that Takashima's hash function is insecure due to the existence of small isogeny cycles. We revisit the construction and show that it can be repaired by imposing a simple restriction, which moreover clarifies the security analysis. The runtime of the resulting hash function is dominated by the extraction of 3 square roo…
Property-preserving hash functions allow for compressing long inputs $x_0$ and $x_1$ into short hashes $h(x_0)$ and $h(x_1)$ in a manner that allows for computing a predicate $P(x_0, x_1)$ given only the two hash values without having access to the original data. Such hash functions are said to be adversarially robust if an adversary that gets to pick $x_0$ and $x_1$ after the hash function has been sampled, cannot find inputs for which the predicate evaluated on the hash values outputs the incorrect result. In this work we construct robust property-preserving hash functions for the hamming-di…
Privacy amplification (PA) is an essential part in a quantum key distribution (QKD) system, distilling a highly secure key from a partially secure string by public negotiation between two parties. The optimization objectives of privacy amplification for QKD are large block size, high throughput and low cost. For the global optimization of these objectives, a novel privacy amplification algorithm is proposed in this paper by combining multilinear-modular-hashing and modular arithmetic hashing. This paper proves the security of this hybrid hashing PA algorithm within the framework of both inform…
As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum spe…
Public key cryptography protocols, such as RSA and elliptic curve cryptography, will be rendered insecure by Shor's algorithm when large-scale quantum computers are built. Cryptographers are working on quantum-resistant algorithms, and lattice-based cryptography has emerged as a prime candidate. However, high computational complexity of these algorithms makes it challenging to implement lattice-based protocols on low-power embedded devices. To address this challenge, we present Sapphire - a lattice cryptography processor with configurable parameters. Efficient sampling, with a SHA-3-based PRNG…
Non-Archimedean analysis, T-functions, and cryptography
These are lecture notes of a 20-hour course at the International Summer School \emph{Mathematical Methods and Technologies in Computer Security} at Lomonosov Moscow State University, July 9--23, 2006. Loosely speaking, a $T$ -function is a map of $n$ -bit words into $n$ -bit words such that each $i$ -th bit of image depends only on low-order bits $0,..., i$ of the pre-image. For example, all arithmetic operations (addition, multiplication) are $T$ -functions, all bitwise logical operations ( $\XOR$ , $\AND$ , etc.) are $T$ -functions. Any composition of $T$ -functions is a $T$ -function as wel…
Privacy amplification (PA) is the art of distilling a highly secret key from a partially secure string by public discussion. It is a vital procedure in quantum key distribution (QKD) to produce a theoretically unconditional secure key. The throughput of PA has become a bottleneck of the high-speed discrete variable QKD (DV-QKD) system. In this paper, a high-speed modular arithmetic hash PA scheme with GNU multiple precision (GMP) arithmetic library is presented. This scheme is implemented on two different central processing unit (CPU) platforms. The experimental results demon-strate that the t…
