Timing analysis in software and hardware to implement NIST elliptic curves over prime fields

This paper presents an extensive study of the timing results for a software implementation of the NIST-recommended elliptic curves over prime fields. We have designed and simulated the important field operations and point operations on NIST-recommended elliptic curves over prime fields in C++ based on the MIRACL library for the purpose of optimized speed and efficiency. Specific experiments are conducted to study the data dependency relationship between input parameters (i.e., plaintext to encode) and output results (i.e., encoded message), and we found that the timing output is only contingent on the bit length of the input, regardless of the randomicity (random or fixed) of the input. We believe the work of this paper can provide more accurate and comprehensive information when we compare the performance of a software implementation of NIST prime elliptic curves with the corresponding hardware implementation under different circumstances, such as worst-case scenario or average-case scenario. We also compare the timing results of field and point operations to the critical path delay when implemented using a 90-nm cell library.