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Cryptanalysis of the Rédei-scheme. (English) Zbl 0602.94012

Contributions to general algebra 3, Proc. Conf., Vienna 1984, 255-264 (1985).
R. Lidl and W. B. Müller [Advances in cryptology, Proc. Crypto 83, 293-301 (1984)] have introduced a new public-key cryptosystem, and in ,,Rédei-Funktionen und ihre Anwendungen in der Kryptographie” [Acta Sci. Math. (to appear)], the author has proposed a generalized version of their scheme. Similar to the well-known RSA-scheme, in this cryptosystem the plaintext alphabet is given by Z/(m), the ring of residue classes of the integers Z modulo an odd natural number m. The encryption polynomials \(x^ k\) of the RSA-scheme, however, are replaced by certain rational functions. Since these functions firstly have been studied by L. Rédei [Acta Sci. Math., Szeged 11, 85–92 (1946; Zbl 0061.01607)], we call them Rédei functions, and we call the cryptosystem Rédei-scheme.
So far only very little is known about the security of the Rédei-scheme. The goal of this paper is to perform a cryptanalysis of the Rédei-scheme. Having outlined the algebraic background and having given a short description of the scheme, we discuss several possibilities for a cryptanalytic attack, and we formulate requirements to the key parameters, which guarantee the system to be secure from the described attacks.
For the entire collection see [Zbl 0559.00002].
Reviewer: Rupert Nöbauer

MSC:

94A60 Cryptography