## LiDIA -- A Library for Computational Number Theory -- Reference Manual (2001)

Citations: | 16 - 1 self |

### BibTeX

@MISC{(ed.)01lidia--,

author = {S. Hamdy (ed.)},

title = {LiDIA -- A Library for Computational Number Theory -- Reference Manual},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

212 | Lattice basis reduction: Improved practical algorithms and solving subset sum problems
- Schnorr, Euchner
- 1994
(Show Context)
Citation Context ... . . , xk−1 ∈ Z satisfying ∑ k−1 i=0 xiai = 0. • The Buchmann-Kessler algorithm [13] which computes a reduced basis for a lattice represented by a generating system A. • The Schnorr-Euchner algorithm =-=[55]-=- (modified for generating systems) as well as variations [64] which compute an LLL reduced basis of the lattice L represented by the generating system A. 2. Lattice bases: • The original Schnorr-Euchn... |

99 | Fast key exchange with elliptic curve systems - Schroeppel, Orman, et al. - 1995 |

63 | A new polynomial factorization algorithm and its implementation
- Shoup
- 1995
(Show Context)
Citation Context ...low. Description The pre-computations for variables of type Fp_poly_modulus as well as for variables of type Fp_poly_multiplier consist of evaluating FFT-representations. For further description, see =-=[59]-=-. However, if the degree of the polynomials involved is small, pre-computations are not necessary. In this case, arithmetic with Fp_poly_modulus or Fp_poly_multiplier is not faster than modular arithm... |

28 | Computing Frobenius maps and factoring polynomials
- Gathen, Shoup, et al.
- 1992
(Show Context)
Citation Context ...nic polynomial whose irreducible factors all have degree d (otherwise, the behaviour of this function is undefined); returns the complete factorization of f using an algorithm of von zur Gathen/Shoup =-=[62]-=-. factorization< Fp_polynomial > a.edf (lidia_size_t d) const returns edf(a.base(), d).single factor< Fp polynomial > 317 factorization< Fp_polynomial > factor (const Fp_polynomial & f) returns the c... |

24 |
a theory of factorization and genera
- Shanks, number
- 1971
(Show Context)
Citation Context ...n. The parameter v is the size of the initial step-width. This parameter is ignored if the corresponding quadratic order is real. bigint A.order_h () const computes the order of A using the method of =-=[57]-=- where the class number is known. The class number of the current quadratic order is computed if it has not been already. bigint A.order_mult (bigint & h, rational_factorization & hfact) const compute... |

13 |
Quadratic fields and factorization, Computational methods in number theory
- Schoof
- 1982
(Show Context)
Citation Context ...as already been computed, the function simply returns this value. base_vector< bigint > O.class_group_shanks () computes the structure of the ideal class group of O using variations of the methods of =-=[56]-=- which have complexity O(|∆| ( 1/4)). The correctness and complexity of both algorithms are conditional on the truth of the ERH. If the class group has already been computed, the function simply retur... |

7 |
New Results on Lattice Basis Reduction in Practice
- Backes, Wetzel
- 2000
(Show Context)
Citation Context ...-Kessler algorithm [13] which computes a reduced basis for a lattice represented by a generating system A. • The Schnorr-Euchner algorithm [55] (modified for generating systems) as well as variations =-=[64]-=- which compute an LLL reduced basis of the lattice L represented by the generating system A. 2. Lattice bases: • The original Schnorr-Euchner lattice reduction algorithm [55] as well as variations [64... |

6 |
Systematic examination of Littlewood’s bounds on L(1,χ)”inAnalytic Number Theory
- SHANKS
- 1972
(Show Context)
Citation Context ... be the Kronecker symbol, is intimately related to computations in class groups of quadratic orders, especially at s = 1, due to the analytic class number formula of Dirichlet. The Littlewood indices =-=[43, 58]-=- are values which test the accuracy of Littlewood’s bounds on L(1, χ) and a related function L∆(1) = (2 − ( ) ∆ 2 )/2 L(1, χ) defined by Shanks [58]. Under the ERH, we expect the lower Littlewood indi... |

1 |
Faktorisieren mit dem Quadratischen Sieb auf dem Hypercube
- Sosnowski
- 1994
(Show Context)
Citation Context ...ssarily a prime factorization. The version of QS used in LiDIA is called self initializing multiple polynomial large prime quadratic sieve. A description of the algorithm can be found in [1], [22] or =-=[60]-=-. The linear equation step uses an implementation of the Block Lanczos algorithm for Z/2Z. Note that the running time of QS depends on the size of the number to be factored, not on the size of the fac... |

1 |
Ein Algorithmus zur Zerlegung von Primzahlen
- Weber
- 1993
(Show Context)
Citation Context ...tion has been succesfully computed, the remaining computations can be done in (probabilistic) polynomial time as described e.g. in [17], chapter 4.8.2 (for numbers not dividing the index) and [14] or =-=[63]-=- (for index divisors). For fractional ideals, one needs to factor the denominator in addition, however, this can be handled separately. Therefore the generic factorization functions are factorization<... |

1 |
Ein Framework zur Berechnung der Hermite-Normalform von groSSen, dünnbesetzten, ganzzahligen Matrizen
- Theobald
- 2000
(Show Context)
Citation Context ...hen (const bigint& d) Algorithm from [17]. void A.hnfmod_mueller (bigint_matrix& T ) Algorithm by Müller [48]. A description of these algorithms and references to the original papers are contained in =-=[63]-=-. Smith Normal Form The following functions tranform the given matrix into Smith Normal Form (SNF). A matrix in SNF is a diagonal matrix A = (ai,j) (0 ≤ i ≤ n, 0 ≤ j ≤ n) such that for all 0 ≤ i < n: ... |