The cryptanalysis of a public-key implementation of finite group mappings
The authors show that the public-key cryptosystem based on finite group mappings (FGM) proposed by \textit{Minghua Qu} and \textit{S. A. Vanstone} [New public-key cryptosystems based on factorizations of finite groups, Advances in Cryptology -- AUSCRYPT `92, Lect. Notes Comput. Sci. 718 (1993)]\ is not secure. This is done by presenting a generalized decryption algorithm similar to the original one, then using it to show that there are many equivalent private keys, and finally by showing that to calculate an equivalent private key one needs only knowledge of the public key. The authors conclude that not only the cryptosystem studied is not secure even as private-key cryptosystem, but that their analysis makes one to seriously reconsider the security of any cryptosystem which relies on certain generalizations of FGM, the so called transversal logarithmic signatures.
scientific article; zbMATH DE number 784595