The security of some important cryptographic algorithms, notably RSA and the Blum Blum Shub pseudorandom number generator, rests in the difficulty of factorizing large integers.
32.
In particular, if there is exactly one non-linear factor, it will be the polynomial left after all linear factors have been factorized out.
33.
The TEBD algorithm is a good candidate for parallel computing because the exponential operators used to calculate the time-evolution factorize under the Suzuki-Trotter expansion.
34.
We did " not " assume this; the only assumption we made was that the distributions factorize, and the form of the distributions followed naturally.
35.
Hence, if P would succeed in factorizing uniquely into only two factors, P would have announced that prior to S being able to complete its larger task.
36.
Exact separability is extremely unphysical given that interactions between the system and its environment destroy the factorization; however, a wave function that is a support will factorize approximately.
37.
For that limit, the relevant operation was not to factorize the numerator, but rather to divide it by x-3, had it a remainder or not.
38.
The kind that protects much of the world's e-commerce, for example, is called RSA, a scheme based on the difficulty of factorizing large numbers.
39.
Dirac in the late 1920s, when he furthered the application of equation ( ) to the electron & ndash; by various manipulations he factorized the equation into the form:
40.
Thus for practical purposes, the maximally wheel factorized Sieve of Eratosthenes is faster than the Sieve of Atkin although the Sieve of Atkin is faster for lesser amounts of wheel factorization.
