Results 61 to 70 of about 125 (118)

NeonCROSS: Vectorized Implementation of Post-Quantum Signature CROSS on Cortex-A72 and Apple M3

Transactions on Cryptographic Hardware and Embedded Systems
The advancement of quantum computing threatens traditional public-key cryptographic systems, prompting the development of post-quantum cryptography (PQC).
Hanyu Wei, Wenqian Li, Yunlei Zhao
doaj   +1 more source

Congruence Properties of Mersenne Primes

, 2011
In this research paper, relationship between every Mersenne prime and certain Natural numbers is explored. We begin by proving that every Mersenne prime is of the form {4n + 3,for some integer 'n'} and generalize the result to all powers of 2. We also tabulate and show their relationship with other whole numbers up to 10.
Srinath, M. S., Murthy, Garimella Rama, Chandrasekharan, V.   +2 more
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On integer sequences in cryptography

Journal of Mathematical Cryptology
Integer sequences play a pivotal role in cryptography, acting as foundational elements for numerous cryptographic algorithms. This comprehensive investigation examines integer sequences that have significantly impacted the sector in domains such as key ...
Raso Mario, Venturi Daniele
doaj   +1 more source

On Even 2ⁿ-Unitary Perfect Polynomials over ${\mathbb{F}}_{\mathbf{2}}$

AppliedMath
Let k be a positive integer. A polynomial A∈F2[x] is called k-unitary perfectif the sum of the k-th powers of its distinct unitary divisors equals Ak.
Wiam Zeid, Haissam Chehade, Issam Kaddoura, Yahia Awad   +3 more
doaj   +1 more source

Proof of exponentiation: enhanced prover efficiency for algebraic statements

Cybersecurity
Recent years have seen the widespread adoption of zkSNARKs constructed over small fields, including but not limited to, the Goldilocks field, small Mersenne prime fields, and tower of binary fields.
Zhuo Wu, Shi Qi, Xinxuan Zhang, Yi Deng, Kun Lai, Hailong Wang   +5 more
doaj   +1 more source

On prime factors of Mersenne numbers

, 2016
to appear in Palestine Journal of ...
Cambraia, Ady jun., Knapp, Michael P., Lemos, Abílio, Moriya, B. K., Rodrigues, Paulo H. A.   +4 more
openaire   +3 more sources

The specifics of the Galois field GF(257) and its use for digital signal processing

Scientific Reports
An algorithm of digital logarithm calculation for the Galois field $$GF(257)$$ G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 ...
Akhat Bakirov, Dinara Matrassulova, Yelizaveta Vitulyova, Dina Shaltykova, Ibragim Suleimenov   +4 more
doaj   +1 more source

Note for the Mersenne Primes

This paper tackles a longstanding problem in number theory: the existence of odd perfect numbers. A perfect number is defined as a positive integer whose sum of all its proper divisors (excluding itself) is equal to twice the number itself. While Euclid demonstrated a method to construct even perfect numbers using Mersenne primes (primes of the form $2^
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Sieve for Mersenne prime numbers

, 2019
The algorithm generates many odd numbers, but only prime numbers of mersenne and not common prime numbers.
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On the Sum of Reciprocals of Mersenne Primes

American Journal of Computational Mathematics, 2017
The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where  is the set of perfect powers of prime numbers.
openaire   +2 more sources