Comment on ´Cryptanalysis of public key distribution systems based on Dickson polynomials´ and reply

For the original article see ibid. vol.27, p.228-9, 1991. This comment is in response to this letter by Da-Xing Li in which it is claimed that ´public-key distribution systems based on Dickson polynomials are insecure no matter how the system parameters are chosen and no matter how the Dickson polynomials are calculated.´ The claim is based on an attack which can be executed in no more than the square of the time taken by the legal users. The attack is however flawed. The author replies that the attack and all the conclusions in his letter are only directed against the Dickson polynomial distribution system suggested by Yang Yi-xian (see ibid., vol.23, p.560-1, 1987) in which the Dickson polynomial is on integer ring Z; it is neither on residue class ring Z/(n) nor on finite field F_q. Similarly, the arguments about the choice of system parameters and the calculations of Dickson polynomial are restricted to integer ring Z. Hence, the counterexample of Burmester goes beyond the bounds of the author´s letter.