The aim of the invention is to propose the generation, verification and denial of an undeniable signature which has a size smaller than the currently available undeniable signatures, i.e. less than 80 bits. This aim is achieved by the method to generate an undeniable signature (y.sub.1, . . . , y.sub.t) on a set of data, this method comprising the following steps: (1) transforming the set of data (m) to a sequence of a predetermined number (t) of blocks (x.sub.1, . . . , x.sub.t), these blocks being members of an Abelian group, this transformation being a one way function, and (2) applying to each block (x.sub.i) a group homomorphism (f) to obtain a resulting value(y.sub.i), in which the number of elements of the initial group (G) is larger than the number of elements (d) of the destination group (H).