Results 31 to 40 of about 100 (72)
Improvements to Lucas-sequence modular square roots and primality testing [PDF]
Lucas sequences are a helpful tool in mathematical and cryptographic calculations, providing in particular an efficient way to exponentiate in a quotient ring $R[x]/(x^2 - Px + Q)$. As with exponentiation in other finite rings and fields, we can use the
Mike Hamburg
core
Average case error estimates of the strong Lucas test [PDF]
Reliable probabilistic primality tests are fundamental in public-key cryptography. In adversarial scenarios, a composite with a high probability of passing a specific primality test could be chosen.
Paterson, Kenneth, Einsele, Semira
core +1 more source
, 2015 Primzahltests (d.s. Tests, die untersuchen, ob eine für gewöhnlich große Zahl eine Primzahl ist oder nicht) sind in der heutigen Zeit zu einer wichtigen Grundlage für die Kryptographie und damit für unseren Alltag (z.B. E-Mails) geworden.
Koller, Gernot
core
Pseudopowers and primality proving
, 2007 It has been known since the 1930s that so-called pseudosquares yield a very powerful machinery for the primality testing of large integers N. In fact, assuming reasonable heuristics (which have been confirmed for numbers to 2^80) this gives a ...
Mueller, Siguna +2 more
core +1 more source
Some Primality Tests Constructed from a Cubic Extension of the Lucas Functions
, 2020 The properties of a pair of integer valued sequences, similar to those of Lucas, are used to produce a sufficiency test for the primality of numbers $N$ such that $N^2 + N + 1$ is divisible by a large power of a prime p.Non UBCUnreviewedAuthor ...
Roettger, Eric
core
The 25th and 26th Mersenne primes
, 1980 The 25th and 26th Mersenne primes are 2 21701 − 1 {2^{21701}} - 1 and 2 23209
Laura Nickel, Curt Noll
core +1 more source
Mersenne primes and the proof of the Lucas-Lehmer test
V magistrskem delu so obravnavana Mersennova praštevila in Lucas-Lehmerjev test. Mersennova praštevila, ki so oblike 2^p-1, kjer je p praštevilo, so tudi največja znana praštevila. Njihovo praštevilskost preverjamo z Lucas-Lehmerjevim testom, ki je podan
Zupančič, Andrej
core
A polynomial time primality algorithm
, 2018 Bir n pozitif tamsayısının 1 ve kendisinden başka pozitif böleni yoksa bu sayıya asal sayı denir. Asal sayıların sonsuz çoklukta olduğu ve her pozitif tam sayının asal sayıların çarpımı şeklinde tek türlü yazıldığı Euclid tarafından ispatlanmıştır ...
Özçim, Süleyman Serkan
core
, 1986 One can associate with an arbitrary algebroid formal group law F, defined over Fp, a sequence [n]F(x̄) (= [n − 1]F(x̄) ⊕Fx̄). These sequences for various F (multiplicative group, reduced elliptic curves and Abelian varieties) provide a variety of new ...
Chudnovsky, D.V, Chudnovsky, G.V
core +1 more source
Probable prime tests for generalized mersenne numbers
, 2008 The classical Lucas-Lehmer test gives necessary and sufficient conditions for the primality of 2 p -1, p an odd prime. Such primes are called Mersenne primes.
Melham, RS
core