An Efficient Implementation of Trace Calculation over Finite Field for a Pseudorandom Sequence

Trace function is a well known index of finite field theory and practically, it is used for some security applications. However, present trace calculation with binary method is far from the practice on an IoT device. This paper considers an efficient trace calculation without vector multiplication by focusing on the matrix representation and the linearity of trace function. By using pre-computation, a trace calculation is executed by m times multiplication and the memory consumption is 4m bytes. This paper especially uses a pseudorandom generator called NTU sequence to show the efficiency because it has paid much attention as a random generator for security applications. When considering 128-bit length of periodic sequence with NTU sequence for security applications, parameters will be p = 7 and m = 50. From the experimental results, a trace calculation with them will be executed within 5[μs], and the memory consumption is 200 bytes which is 0:625% of the storage in Arduino Uno. Therefore, this work contributes to implementing an efficient trace calculation on an IoT device with low memory consumption.