Results 11 to 20 of about 125 (118)
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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Mathematics of Computation, 1958 Am 8. September 1957 ergab die schwedische Elektronenrechenmaschine BESK (siehe auch nachstehendes Referat Zbl 0082.25602) nach einer Laufzeit von 5h 30m die Zahl \(2^{3217}-1\) als Primzahl. (Nachgeprüft am 12. September.) Sie ist, mit ihren 969 Stellen vollständig mitgeteilt, nunmehr die größe bekannte Primzahl.
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Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime greater than or equal to 11. In a previous work, starting from an M-cycle in a finite field 𝔽_ρ, it has been established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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On recognition of simple group L2(r) by the number of Sylow subgroups
Acta Scientiarum: Technology, 2014 Let G be a finite group and n_{p}(G) be the number of Sylow p- subgroup of G. In this work it is proved if G is a centerless group and n_{p}(G)=n_{p}(L_{2}(r)), for every prime p in pi (G), where r is prime number, r^2 does not divide |G| and r is not ...
Alireza Khalili Asboei +1 more
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A framework for cryptographic problems from linear algebra
Journal of Mathematical Cryptology, 2020 We introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also problems coming from code-based cryptography.
Bootland Carl +3 more
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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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Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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On Triangular Secure Domination Number
InPrime, 2020 Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m)
Emily L Casinillo +3 more
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Mersenne Primes in Certain Lucas Sequences [PDF]
EPJ Web of ConferencesPrime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number.
Hadi Ahmed H., Hashim Hayder R.
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Computer Experiments with Mersenne Primes [PDF]
Computational Methods in Science and Technology, 2013 We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of the partial denominators of the continued fraction expansion of $\bar{\BB}_M$. We get values converging
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