Till now geometric structures don't play a major role in cryptography. Gilbert, MacWilliams and Sloane introduced in 1974 an authentication scheme in the projective plane and showed its perfectness in the sense of the definition of Shannon. In this paper we will show that this authentication scheme also fulfills the requirement of completeness according to Kam and Davida and we will extend the application of geometric structures in cryptography by introducing an encryption scheme in the M\"obius plane. We will further examine its properties, showing that it also fulfills the requirement of completeness and Shannon's requirement of perfectness in first approximation. The results of this paper can be used to define similar encryption schemes in the circle geometries of Laguerre and Minkowski.
翻译:到目前为止,几何结构在加密方面没有发挥主要作用。 Gilbert, MacWilliams 和 Sloane 于1974年在投影平面上引入了认证计划,并展示了香农定义的完美性。在本文中,我们将表明,这一认证计划还符合Kam和Davida对完整性的要求,我们将通过在M\“Obius”平面上引入加密计划,在加密中扩大几何结构的应用。我们将进一步检查其特性,表明它也满足了完整性的要求和香农在第一近似时要求完美性的要求。这份文件的结果可以用来界定Laguerre和Minkowski圆圈的类似加密计划。