Automatic Test Case Generation for Prime Field Elliptic Curve Cryptographic Circuits

Abstract

Elliptic curve is a major area of research due to its application in elliptic curve cryptography. Due to their small key sizes, they offer the twofold advantage of reduced storage and transmission requirements. This also results in faster execution times. The authors propose an architecture to automatically generate test cases, for verification of elliptic curve operational circuits, based on user-defined prime field and the parameters used in the circuit to be tested. The ECC test case generations are based on the Galois field arithmetic operations which were the subject of previous work by the authors. One of the strengths of elliptic curve mathematics is its simplicity, which involves just three points (P, Q, and R), which pass through a line on the curve. The test cases generate points for a user-defined prime field which sequentially selects the input vector points (P and/or Q), to calculate the resultant output vector (R) easily. The testbench proposed here targets field programmable gate array (FPGAs) platforms and experimental results for ECC test case generation on different prime fields are presented, while ModelSim is used to validate the correctness of the ECC operations.