Add to ORKGInternational audienceDeciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and we present a heuristically subexponential algorithm
Several recent cryptographic constructions - including a public key encryption scheme, a fully homom...
We present an explicit algorithmic method for computing square roots in quaternion algebras over glo...
Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) ....
Deciding whether an ideal of a number field is principal and finding a generator is a fundamental pr...
Abstract. We provide algorithms to count and enumerate representatives of the (right) ideal classes ...
An ideal is a classical object of study in the field of algebraic number theory. In maximal quadrati...
International audienceLet $\mathcal{O}$ be a maximal order in a definite quaternion algebra over $\m...
Abstract. Let O be a maximal order in a definite quaternion algebra over Q of prime discriminant p, ...
Let F be an algebraic number field of degree n over ℚ (the rationals). An algorithm is presented for...
Let O be a maximal order in a definite quaternion algebra over ℚ of prime discriminant p, and l a sm...
Let O be a maximal order in a definite quaternion algebra over ℚ of prime discriminant p, and l a sm...
Let K be a totally real number field and let B be a totally definite quaternion algebra over K. Give...
We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, compu...
AbstractWe describe in detail the implementation of an algorithm which computes the class group and ...
Abstract. We provide algorithms to count and enumerate representatives of the (right) ideal classes ...
Several recent cryptographic constructions - including a public key encryption scheme, a fully homom...
We present an explicit algorithmic method for computing square roots in quaternion algebras over glo...
Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) ....
Deciding whether an ideal of a number field is principal and finding a generator is a fundamental pr...
Abstract. We provide algorithms to count and enumerate representatives of the (right) ideal classes ...
An ideal is a classical object of study in the field of algebraic number theory. In maximal quadrati...
International audienceLet $\mathcal{O}$ be a maximal order in a definite quaternion algebra over $\m...
Abstract. Let O be a maximal order in a definite quaternion algebra over Q of prime discriminant p, ...
Let F be an algebraic number field of degree n over ℚ (the rationals). An algorithm is presented for...
Let O be a maximal order in a definite quaternion algebra over ℚ of prime discriminant p, and l a sm...
Let O be a maximal order in a definite quaternion algebra over ℚ of prime discriminant p, and l a sm...
Let K be a totally real number field and let B be a totally definite quaternion algebra over K. Give...
We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, compu...
AbstractWe describe in detail the implementation of an algorithm which computes the class group and ...
Abstract. We provide algorithms to count and enumerate representatives of the (right) ideal classes ...
Several recent cryptographic constructions - including a public key encryption scheme, a fully homom...
We present an explicit algorithmic method for computing square roots in quaternion algebras over glo...
Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) ....