Torsion-free abelian groupIn mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. While finitely generated abelian groups are completely classified, not much is known about infinitely generated abelian groups, even in the torsion-free countable case. Abelian group An abelian group is said to be torsion-free if no element other than the identity is of finite order.
Hamming spaceIn statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all binary strings of length N. It is used in the theory of coding signals and transmission. More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z2).
Malléabilité (cryptographie)La malléabilité est une propriété que peuvent posséder des protocoles cryptographiques. Un cryptosystème est dit malléable s’il est possible de transformer un chiffré d’un message m en un chiffré pour un message f(m) pour une fonction f connue sans connaître le message originel m ni obtenir d’information sur lui. Cette propriété n’est pas toujours désirable, puisqu’elle peut permettre à un attaquant de modifier le contenus de messages.
