Constructions Of Authentication Codes Based On Geometric Spaces And Combinational Designs Over Finite Fields

This article mainly research the constructions of splitting authentication codes and Non-Cartesian codes using the relevant knowledge of combinational designs and rational normal curves.Working is as follows:Firstly,in affine space,firstly,by constructing a restricted partially balance t-design,using the restricted partially balance t-design,getting a perfect splitting authentication code,and calculate the probability of spoofing attack of order r of the splitting authentication code.When ts(28),it is a perfect authentication code of type I.Then getting second scheme by specialized processing the above construction,calculating the spoofing attack of order r and confirming it is a perfect authentication code of type II.Secondly,in projective space,a splitting authentication code is constructed using the relevant knowledge of the rational normal curve,then the parameters and the attack probability of this splitting authentication code are calculated and comparison.Meanwhile,its performance is analyzed: when q(28)31,the change trend of impersonation attack probability and substitution attack probability is analyzed as the change of variables t.Observing when impersonation attack probability and substitution attack probability is small,that is,the constructed splitting authentication codes is safely.Finally,by constructing a t-design based on the rational normal curve firstly,then using the t-design to get a authentication code.