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Efficient and Constant Time Modular Reduction With Generalized Mersenne Primes
IEEE AccessMany cryptographic applications require a vast number of modular multiplications with a large prime modulus. Generalized Mersennes are a class of primes commonly used in cryptography because of their special forms.
Serdar S. Erdem, Sezer S. Erdem
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Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of
IEEE Access, 2020 LSB (Least Significant Bit) sequences are widely used as the initial inputs in some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPP LTE International Encryption Standard. Therefore, analyzing the statistical properties (for example,
Yuhua Sun +3 more
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Evaluating Mersenne Primes Using a Single Quadrant Expanding Square [PDF]
, 2012 By forming a table of sequential odd numbers using a single quadrant expanding square pattern it was observed that multiple Mersenne primes fall into the first column. We prove that the Mersenne primes which fall into the first column will be of the form
Sprague, Douglas +5 more
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Prime power Sylow numbers [PDF]
Journal of Mahani Mathematical ResearchIn this paper, we study finite groups with a prime-power number of Sylow \(p\)-subgroups. Motivated by the work of Yang et al.~(2022), who characterized non-solvable groups with a prime-power number of Sylow $2$-subgroups, we investigate the ...
Alireza Khalili Asboei
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, 2011 Marin Mersenne’s mathematical contributions helped paved the way for advances in mathematics. In this article, his life is not only depicted but his mathematical intellect is highlighted through his achievements.
Fryer, Joseph, Detro, Casey
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Some new results on the largest cycle consisting of quadratic residues [PDF]
Notes on Number Theory and Discrete MathematicsThe length of the largest cycle consisting of quadratic residues of a positive integer n is denoted by L(n). In this paper, we have obtained a formula for finding L(p), where p is a prime. Also, we attempt to characterize a prime number p in terms of the
Prabin Das, Pinkimani Goswami
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Secure Montgomery curves over Toeplitz matrix-vector product friendly primes for high-performance elliptic curve cryptography [PDF]
PeerJ Computer ScienceWe propose Curve5453 and Curve6071, two Montgomery curves over the Crandall prime 2545− 3 and Mersenne prime 2607− 1, providing 271 and 302 bits of classical security, respectively.
Murat Cenk +3 more
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On Generalized Mersenne and Fermat Primes [PDF]
, 2009 The classical Merseniie and Fermat primes are, respectivel3^ primes of the form 2^\u27 - 1 and 2^‘ + 1. The Mersenne primes have been studied since antiquity. It is known that if 2^ - 1 is prime then k is prime.
Putnam, Bette Catherine
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Complexity Lower Bound for Boolean Functions in the Class of Extended Operator Forms
Известия Иркутского государственного университета: Серия "Математика", 2019 Starting with the fundamental work of D.E.Muller in 1954, the polynomial representations of Boolean functions are widely investigated in connection with the theory of coding and for the synthesis of circuits of digital devices.
A.S. Baliuk
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Infinite Primes, Quadratic Polynomials, and Fermat’s Criterion
, 2023 In this study, we explore the existence of an infinite number of primes represented by the quadratic polynomial 4(Mp − 2)2 + 1 . We propose a hypothesis that considers Fermat primes as a criterion for the infinitude of such primes, where Mp represents ...
Budee U Zaman (16417167)
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