Results 51 to 60 of about 986 (177)
Mersenne and Fermat numbers [PDF]
Proceedings of the American Mathematical Society, 1954 The first seventeen even perfect numbers are therefore obtained by substituting these values of n in the expression 2 n-(2n -1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 21271, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime.
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A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully +2 more
wiley +1 more source
Divisors of Mersenne numbers [PDF]
Mathematics of Computation, 1983 We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime divisors of Mersenne numbers
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International Journal of Intelligent Systems, Volume 2026, Issue 1, 2026.Federated learning (FL) is a privacy‐preserving method for short‐term load forecasting in energy networks. However, current defense mechanisms against adversarial attacks often depend on supplementary machine learning frameworks, such as anomaly detection models or Byzantine‐robust aggregators.
Habib Ullah Manzoor +5 more
wiley +1 more source
An Ultra-light PRNG Passing Strict Randomness Tests and Suitable for Low Cost Tags
Advances in Electrical and Computer Engineering, 2016 A pseudo-random number generator for low-cost RFID tags is presented. The scheme is simple, sequential and secure, yet has a high performance. Despite its lowest hardware complexity, our proposal represents a better alternative than previous proposals ...
OZCANHAN, M. H. +2 more
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Keystroke Dynamics-Based Authentication Using Unique Keypad
Sensors, 2021 Authentication methods using personal identification number (PIN) and unlock patterns are widely used in smartphone user authentication. However, these authentication methods are vulnerable to shoulder-surfing attacks, and PIN authentication, in ...
Maro Choi +3 more
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Journal of Applied Crystallography, Volume 58, Issue 6, Page 2078-2089, December 2025.We experimentally demonstrate that the scattering‐induced decrease in light intensity experienced by a crystal embedded in a high‐viscosity jet is very limited in materials such as lipidic cubic phase or hydroxyethyl cellulose, and therefore cannot justify the use of pump energies exceeding the linear excitation regime under realistic experimental ...
Stanisław Niziński +5 more
wiley +1 more source
Prime-Field Masking in Hardware and its Soundness against Low-Noise SCA Attacks
Transactions on Cryptographic Hardware and Embedded Systems, 2023 A recent study suggests that arithmetic masking in prime fields leads to stronger security guarantees against passive physical adversaries than Boolean masking.
Gaëtan Cassiers +4 more
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Engineering Reports, Volume 7, Issue 10, October 2025.StorjLedger leverages erasure‐coded sharding and Proof‐of‐Storage to deliver nearly 1000 transactions per second with sub‐second latency, 98% data redundancy, and 76% lower storage costs, resolving the blockchain trilemma by harmonizing scalability, security, and decentralization.
Saha Reno, Koushik Roy
wiley +1 more source
Contributions to Discrete Mathematics, 2023 In this paper, we define the generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further, we study their properties. Moreover, we define Gaussian Mersenne numbers and obtain some identities like Binet Formula, Cassini's identity, D'Ocagne's Identity, and generating functions.
Munesh Kumari +2 more
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