1. A data cryptographic apparatus comprising: computational logic configured to perform an elliptic curve cryptography (ECC) point addition operation using mixed affine-Jacobian coordinates over a short Weierstrauss curve of the form y=x 3 +ax+b where a=−3; a register memory configured to store a first point in affine coordinates and a second point in Jacobian coordinates, wherein the register memory is configured for two temporary storage variables, T 1 and T 2 ; a modular multiplier electrically coupled to the register memory, wherein the modular multiplier is configured to perform at most one modular multiplication for each step in a sequence of steps in the ECC point addition operation; and a simple arithmetic processor configured to perform modular subtraction and modular multiplication by two in support of the ECC point addition operation utilizing two modular subtractors, a logical one bit left shifter to either output A−B−2C for an input of variables A, B, and C or A−B for an input of variables A and B, wherein the simple arithmetic processor is electrically coupled to the computational logic, the register memory, and the modular multiplier to output a result of the ECC point addition operation in the Jacobian coordinates.