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The gap-ETH assumption (Dinur 2016; Manurangsi and Raghavendra 2016) asserts that it is exponentially-hard to distinguish between a satisfiable 3-CNF formula and a 3-CNF formula which is at most 0.99-satisfiable. We show that this assumption follows from the exponential hardness of finding a satisfying assignment for smooth 3-CNFs. Here smoothness means that the number of satisfying assignments is...
Pseudorandom number generators are required to generate pseudorandom numbers which have not only good statistical properties but also unpredictability in cryptography. A geometric sequence is a sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol, and...
Gao [6] conjectured that if a general finite field has qn elements, and m is the smallest power of q greater or equal to n, then there exists a polynomial g (x) ∊ Fq [x] of degree at most 2 ⌈log2 n⌉ such that xm − g (x) has an irreducible factor f (x) of degree n. If the conjecture holds, this guarantees existence of high order elements that are used in the known cryptographic primitives. The conjecture...
In this brief paper we present a low-complexity digital architecture for the probabilistic characterization of ergodic TRBGs. Differently from other methods based on the direct estimation of the generation probabilities of finite sets of binary words, in this study we investigate some theoretical relationships between the autocorrelation function of the binary source and the dynamical symbol generation...
The presented work of this paper is to propose the implementation of chaotic crypto-system with the new key generator using chaos in digital filter for data encryption and decryption. The chaos in digital filter of the second order system is produced by the coefficients which are initialed in the key generator to produce other new coefficients. Private key system using the initial coefficients value...
True random numbers have a fair role in modern digital transactions. In order to achieve secured authentication, true random numbers are generated as security keys which are highly unpredictable and non-repetitive. True random number generators are used mainly in the field of cryptography to generate random cryptographic keys for secure data transmission. The proposed work aims at the generation of...
Lattice-based cryptography has recently produced several time-efficient cryptosystems that are provably secure under assumptions that are not known to be more easily solvable by quantum computers. An interesting research direction is improving their storage complexity, as current solutions are far from practical with respect to this metric. In this paper we show that program obfuscators for point...
In this study a numerical cryptanalysis of a random number generator (RNG) which is built on a continuous-time chaotic oscillator is introduced. In order to scrutinize the security weaknesses of the RNG, a master-slave synchronization approach is presented as the basis of an attack scheme. By proposing this attack scheme, it is aimed to verify whether there exist any possibility to divulge the hidden...
The class of information set decoding algorithms is the best known way of decoding general codes, i.e. codes that admit no special structure, in the Hamming metric. Stern's algorithm is the origin of the most efficient algorithms in this class. In this paper we consider the same decoding problem but for a channel with soft information. We give a version of Stern's algorithm for a channel with soft...
Random number generators (RNG) are a fundamental hardware component in modern cryptographic systems [1]. The generation of random numbers can be subdivided into two classes, pseudo-RNGs and hardware RNGs. In pseudo-RNGs software algorithms are implemented on deterministic hardware but are dependent on a set of initial values or “seed”, which reduces the security. In contrast, hardware RNGs generate...
The authors in this paper have proposed a multi-value sequence generated by a primitive polynomial, trace function, k-th power residue symbol, and a certain mapping function over the proper sub extension field. Here, the trace function actually maps an element of the extension field to an element of the proper sub extension field, which is actually a vector space. The distribution of numbers within...
Wireless sensor communication is managing critical applications that require serious security and privacy concerns to decrease hacking attacks. As a solution, most cryptographic algorithms include secure encoding and decoding which are based on random number generator (RNG), This paper suggests an efficient solution for the generation of low cost and low power random number for Internet of Things’...
We present a parallel algorithm to compute promising candidate states for modifying the state space of a pseudo-random number generator in order to increase its cycle length. This is important for generators in low-power devices where increase of state space is not an alternative. The runtime of the parallel algorithm is improved by an analogy to ant colony behavior: if two paths meet, the resulting...
Cryptographic primitives such as hash chains or pseudo-random number generators (PRNGs) work for some time without input. State space in embedded applications is often moderate because of resource restrictions, so that state repetitions might occur too soon and may compromise security. We investigate the question whether it is possible to change the transition function of such a primitive only for...
In this work, numerical cryptanalysis of a random number generator (RNG) designed using a continuous time chaotic oscillator is presented. For the purpose of examining the vulnerabilities of the RNG, a master-slave synchronization approach was presented as a basis for an attack scheme. By suggesting this attack scheme, we intend to verify whether there is the possibility of revealing the secret information...
True random number generators (TRNGs) are important hardware primitives required for many applications including cryptography, communication, and statistical simulation. This paper presents a TRNG with failure detection capability targeting cryptographic applications with a limited power budget. The proposed TRNG extracts entropy from latch comparators, whose metastable states are detected and encoded...
Random numbers find their usefulness and utility in domains which have a significant role, sometimes even critical or obtaining some unpredictable results: Simulations based on Monte Carlo methods, simulations from mathematical modeling simulations, statistics, prime numbers generation, cryptography, spreaded spectrum communication, games, etc. In cryptography, the property of being random is fundamental...
In this paper, a new scheme for a random key generator as a method to implement Steganography has been introduced. The main idea is based on principle of LFSR stream cipher. The simplicity of the design the LFSRs based on user demand that will give the user some experience about the best generator which will fulfill not only the requirement of the cryptography but also Steganography. Here, the factor...
We have developed a one-time pad cryptographic method using a star network of N Lorenz subsystems, referred to as augmented Lorenz equations, which generates chaotic time series as pseudorandom numbers to be used for masking a plaintext. Our cryptographic method uses an N-dimensional vector as a secret key, which is assumed to be delivered from Alice to Bob using a quantum key distribution. Here,...
In this paper, we propose a new generic construction of signatures from trapdoor commitments with strong openings in the random oracle model. Our construction is very efficient; signatures consist of just a single decommitment of the underlying commitment scheme. Furthermore, assuming the commitment scheme provides sufficiently strong statistical hiding and trapdoor opening properties, the reduction...
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