Prime field elliptic curve cryptography processors are provided, having corresponding methods and computer-readable media. The processors comprise a prime field circuit comprising a first memory configured to store data, and an arithmetic logic unit (ALU) circuit configured to perform prime field operations upon the data; and a curve operation processor comprising a second memory configured to store instructions, and a controller configured to execute the instructions; wherein the instructions include instructions for performing curve operations upon the data, wherein the curve operations require performing the prime field operations upon the data; and wherein the instructions for performing the curve operations cause the ALU circuit to perform the prime field operations.