Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Fontein, Felix"'
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output
Externí odkaz:
http://arxiv.org/abs/1307.7534
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output
Externí odkaz:
http://arxiv.org/abs/1212.5100
Autor:
Fontein, Felix, Wocjan, Pawel
We study the problem of determining the probability that m vectors selected uniformly at random from the intersection of the full-rank lattice L in R^n and the window [0,B)^n generate $\Lambda$ when B is chosen to be appropriately large. This problem
Externí odkaz:
http://arxiv.org/abs/1211.6246
Secure storage of noisy data for authentication purposes usually involves the use of error correcting codes. We propose a new model scenario involving burst errors and present for that several constructions.
Comment: to be presented at MTNS 2012
Comment: to be presented at MTNS 2012
Externí odkaz:
http://arxiv.org/abs/1205.5148
Autor:
Fontein, Felix, Wocjan, Pawel
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained from global
Externí odkaz:
http://arxiv.org/abs/1111.1348
We present an algorithm that unconditionally computes a representation of the unit group of a number field of discriminant $\Delta_K$, given a full-rank subgroup as input, in asymptotically fewer bit operations than the baby-step giant-step algorithm
Externí odkaz:
http://arxiv.org/abs/1001.4187
We describe and give computational results of a procedure to compute the divisor class number and regulator of most purely cubic function fields of unit rank 2. Our implementation is an improvement to Pollard's Kangaroo method in infrastructures, usi
Externí odkaz:
http://arxiv.org/abs/1001.4095
Autor:
Fontein, Felix
We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit formulas for t
Externí odkaz:
http://arxiv.org/abs/0911.5543
Autor:
Fontein, Felix
We prove that the number of "hole elements" $H(K)$ in the infrastructure of a hyperelliptic function field $K$ of genus $g$ with finite constant field $\F_q$ with $n + 1$ places at infinity, of whom $n' + 1$ are of degree one, satisfies $|\frac{H(K)}
Externí odkaz:
http://arxiv.org/abs/0911.4346
Autor:
Fontein, Felix
Publikováno v:
Math. Comp. 80 (2011), no. 276, 2325--2357
In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant step operation and f-representations, and makes it possible to relate the i
Externí odkaz:
http://arxiv.org/abs/0809.1685